title: Polaris Sales Agreement

abstract: The Polaris Sales Agreement was a treaty between the United States and the United Kingdom which began the UK Polaris programme. The agreement was signed on 6 April 1963. It formally arranged the terms and conditions under which the Polaris missile system was provided to the United Kingdom. The United Kingdom had been planning to buy the air-launched Skybolt missile to extend the operational life of the British V bombers, but the United States decided to cancel the Skybolt program in 1962 as it no longer needed the missile. The crisis created by the cancellation prompted an emergency meeting between the President of the United States, John F. Kennedy, and the Prime Minister of the United Kingdom, Harold Macmillan, which resulted in the Nassau Agreement, under which the United States agreed to provide Polaris missiles to the United Kingdom instead. The Polaris Sales Agreement provided for the implementation of the Nassau Agreement. The United States would supply the United Kingdom with Polaris missiles, launch tubes, and the fire control system. The United Kingdom would manufacture the warheads and submarines. In return, the US was given certain assurances by the United Kingdom regarding the use of the missile, but not a veto on the use of British nuclear weapons. The British Resolution-class Polaris ballistic missile submarines were built on time and under budget, and came to be seen as a credible deterrent. Along with the 1958 US–UK Mutual Defence Agreement, the Polaris Sales Agreement became a pillar of the nuclear Special Relationship between Britain and the United States. The agreement was amended in 1982 to provide for the sale of the Trident missile system.

text:
# Polaris Sales Agreement

The **Polaris Sales Agreement** was a treaty between the United States and the United Kingdom which began the UK Polaris programme. The agreement was signed on 6 April 1963. It formally arranged the terms and conditions under which the Polaris missile system was provided to the United Kingdom.

The United Kingdom had been planning to buy the air-launched Skybolt missile to extend the operational life of the British V bombers, but the United States decided to cancel the Skybolt program in 1962 as it no longer needed the missile. The crisis created by the cancellation prompted an emergency meeting between the President of the United States, John F. Kennedy, and the Prime Minister of the United Kingdom, Harold Macmillan, which resulted in the Nassau Agreement, under which the United States agreed to provide Polaris missiles to the United Kingdom instead.

The Polaris Sales Agreement provided for the implementation of the Nassau Agreement. The United States would supply the United Kingdom with Polaris missiles, launch tubes, and the fire control system. The United Kingdom would manufacture the warheads and submarines. In return, the US was given certain assurances by the United Kingdom regarding the use of the missile, but not a veto on the use of British nuclear weapons. The British *Resolution*-class Polaris ballistic missile submarines were built on time and under budget, and came to be seen as a credible deterrent.

Along with the 1958 US–UK Mutual Defence Agreement, the Polaris Sales Agreement became a pillar of the nuclear Special Relationship between Britain and the United States. The agreement was amended in 1982 to provide for the sale of the Trident missile system.

## Background

During the early part of the Second World War, Britain had a nuclear weapons project, codenamed Tube Alloys. In August 1943, the Prime Minister of the United Kingdom, Winston Churchill and the President of the United States, Franklin Roosevelt, signed the Quebec Agreement, which merged Tube Alloys with the American Manhattan Project. The British government trusted that the United States would continue to share nuclear technology, which it regarded as a joint discovery, but the 1946 McMahon Act ended cooperation. Fearing a resurgence of United States isolationism, and Britain losing its great power status, the British government restarted its own development effort, now codenamed High Explosive Research. The first British atomic bomb was tested in Operation Hurricane on 3 October 1952. The subsequent British development of the hydrogen bomb, and a favourable international relations climate created by the Sputnik crisis, led to the McMahon Act being amended in 1958, and the restoration of the nuclear Special Relationship in the form of the 1958 US–UK Mutual Defence Agreement (MDA), which allowed Britain to acquire nuclear weapons systems from the United States.

Britain's nuclear weapons armament was initially based on free-fall bombs delivered by the V bombers of the Royal Air Force (RAF), but the possibility of the crewed bomber becoming obsolete by the late 1960s due to improvements in anti-aircraft defences was foreseen. In 1953, work began on a medium-range ballistic missile (MRBM) called Blue Streak, but by 1958, there were concerns about the vulnerability of this liquid-propellant-missile to a pre-emptive nuclear strike. To extend the effectiveness and operational life of the V bombers, an air-launched, rocket-propelled standoff missile called Blue Steel was developed, but it was anticipated that the air defences of the Soviet Union would improve to the extent that V bombers might still find it difficult to attack their targets. A solution appeared to be the American Skybolt missile, which combined the range of Blue Streak with the mobile basing of the Blue Steel, and was small enough that two could be carried on an Avro Vulcan bomber.

An institutional challenge to Skybolt came from the United States Navy, which was developing a submarine-launched ballistic missile (SLBM), the UGM-27 Polaris. The US Chief of Naval Operations, Admiral Arleigh Burke, kept the First Sea Lord, Lord Mountbatten, apprised of its development. By moving the deterrent out to sea, Polaris offered the prospect of a deterrent that was invulnerable to a first strike, and reduced the risk of a nuclear strike on the British Isles. The British Nuclear Deterrent Study Group (BNDSG) produced a study that argued that SLBM technology was as yet unproven, that Polaris would be expensive, and that given the time it would take to build the boats, it could not be deployed before the early 1970s. The Cabinet Defence Committee therefore approved the acquisition of Skybolt in February 1960. The Prime Minister, Harold Macmillan, met with the President, Dwight D. Eisenhower, in March 1960, and secured permission to buy Skybolt. In return, the Americans could base the US Navy's Polaris ballistic missile submarines in the Holy Loch in Scotland. The financial arrangement was particularly favourable to Britain, as the US was charging only the unit cost of Skybolt, absorbing all the research and development costs. With this agreement in hand, the cancellation of Blue Streak was announced in the House of Commons on 13 April 1960.

The subsequent American decision to cancel Skybolt created a political crisis in the UK, and an emergency meeting between Macmillan and President John F. Kennedy was called in Nassau, Bahamas. Macmillan rejected the US offers of paying half the cost of developing Skybolt, and of supplying the AGM-28 Hound Dog missile instead. This brought options down to Polaris, but the Americans would only supply it on condition that it be used as part of a proposed Multilateral Force (MLF). Kennedy ultimately relented, and agreed to supply Britain with Polaris missiles, while "the Prime Minister made it clear that except where Her Majesty's Government may decide that supreme national interests are at stake, these British forces will be used for the purposes of international defence of the Western Alliance in all circumstances." A joint statement to this effect, the Nassau Agreement, was issued on 21 December 1962.

## Negotiations

With the Nassau Agreement in hand, it remained to work out the details. Vice Admiral Michael Le Fanu had a meeting with the United States Secretary of Defense, Robert S. McNamara, on 21 December 1962, the final day of the Nassau conference. He found McNamara eager to help, and enthusiastic about the idea of Polaris costing as little as possible. The first issue identified was how many Polaris boats should be built. While the Vulcans to carry Skybolt were already in service, the submarines to carry Polaris were not, and there was no provision in the defence budget for them. Some naval officers feared that their construction would adversely impact the hunter-killer submarine programme. The First Sea Lord, Admiral of the Fleet Sir Caspar John, denounced the "millstone of Polaris hung around our necks" as "potential wreckers of the real navy".

The number of missiles required was based on substituting for Skybolt. To achieve the same capability, the BNDSG calculated that this would require eight Polaris submarines, each of which would have 16 missiles, for a total of 128 missiles, with 128 one-megaton warheads. It was subsequently decided to halve this, based on the decision that the ability to destroy twenty Soviet cities would have nearly as great a deterrent effect as the ability to destroy forty. The Admiralty considered the possibility of hybrid submarines that could operate as hunter-killers while carrying eight Polaris missiles, but McNamara noted that this would be inefficient, as twice as many submarines would need to be on station to maintain the deterrent, and cautioned that the effect of tinkering with the US Navy's 16-missile layout was unpredictable. The Treasury costed a four-boat Polaris fleet at £314 million by 1972/73. A Cabinet Defence Committee meeting on 23 January 1963 approved the plan for four boats, with Thorneycroft noting that four boats would be cheaper and faster to build.

A mission led by Sir Solly Zuckerman, the Chief Scientific Adviser to the Ministry of Defence, left for the United States to discuss Polaris on 8 January 1963. It included the Vice Chief of the Naval Staff, Vice Admiral Sir Varyl Begg; the Deputy Secretary of the Admiralty, James Mackay; Rear Admiral Hugh Mackenzie; and physicist Sir Robert Cockburn and F. J. Doggett from the Ministry of Aviation. That the involvement of the Ministry of Aviation might be a complicating factor was foreseen, but it had experience with nuclear weapons development. Mackenzie had been the Flag Officer Submarines until 31 December 1962, when Le Fanu had appointed him the Chief Polaris Executive (CPE). As such, he was directly answerable to Le Fanu as Controller of the Navy. His CPE staff was divided between London and Foxhill, near Bath, Somerset, where Royal Navy had its ship design, logistics and weapons groups. It was intended as a counterpart to the United States Navy Special Projects Office (SPO), with whom it would have to deal.

The principal finding of the Zuckerman mission was that the Americans had developed a new version of the Polaris missile, the A3. With a range extended of 2,500 nautical miles (4,600 km), it had a new weapons bay housing three re-entry vehicles (REBs or Re-Entry Bodies in US Navy parlance) and a new 200-kilotonne-of-TNT (840 TJ) W58 warhead to penetrate improved Soviet anti-missile defences expected to become available around 1970. A decision was therefore required on whether to purchase the old A2 missile or the new A3. The Zuckerman mission came out in favour of the new A3 missile, although it was still under development and not expected to enter service until August 1964, as the deterrent would remain credible for much longer. The decision was endorsed by the First Lord of the Admiralty, Lord Carrington, in May 1963, and was officially made by Thorneycroft on 10 June 1963.

The choice of the A3 created a problem for the Atomic Weapons Research Establishment (AWRE) at Aldermaston, for the Skybolt warhead that had recently been tested in the Tendrac nuclear test at the Nevada Test Site in the United States would require a redesigned Re-Entry System (RES) in order to be fitted to a Polaris missile, at an estimated cost of between £30 million and £40 million. The alternative was to make a British copy of the W58. While the AWRE was familiar with the W47 warhead used in the A2, it knew nothing of the W58. A presidential determination was required to release information on the W58 under the MDA, but with this in hand, a mission led by John Challens, the Chief of Warhead Development at the AWRE, visited the Lawrence Livermore Laboratory from 22 to 24 January 1963, and was shown details of the W58.

The Zuckerman mission found the SPO helpful and forthcoming, but there was one major shock. The British were expected to contribute to the research and development costs of the A3, backdated to 1 January 1963. These were expected to top $700 million by 1968. Skybolt had been offered to the UK at unit cost, with the US absorbing the research and development costs, but no such agreement had been reached at Nassau for Polaris. Thorneycroft baulked at the prospect of paying research and development costs, but McNamara pointed out that the United States Congress would not stand for an agreement that placed all the burden on the United States. Macmillan instructed the British Ambassador to the United States, Sir David Ormsby-Gore, to inform Kennedy that Britain was not willing to commit to an open-ended sharing of research and development costs, but, as a compromise, would pay an additional five per cent for each missile. He asked that Kennedy be informed that a breakdown of the Nassau Agreement would likely cause the fall of his government. Ormsby-Gore met with Kennedy that very day, and while Kennedy noted that the five per cent offer "was not the most generous offer he had ever heard of", he accepted it. McNamara, certain that the United States was being ripped off, calculated the five per cent on top of not just the missiles, but their fire control and navigation systems as well, adding around £2 million to the bill. On Ormsby-Gore's advice, this formulation was accepted.

An American mission now visited the United Kingdom. This was led by Paul H. Nitze, the Assistant Secretary of Defense for International Security Affairs, and included Walt W. Rostow, the Director of Policy Planning at the State Department, and Admiral Ignatius J. Galantin, the head of the SPO. The Americans had ideas about how the programme should be organised. They foresaw the UK Polaris programme having project officers from both countries, with a Joint Steering Task Group that met regularly to provide advice. This was accepted, and would become part of the final agreement. However, a follow-up British mission under Leslie Williams, the Director General Atomic Weapons at the Ministry of Aviation, whose members included Challens and Rear Admiral Frederick Dossor, was given a letter by the SPO with a list of subjects that were off limits. These included penetration aids, which were held to be outside the scope of the Nassau Agreement.

One remaining obstacle in the path of the programme was how it would be integrated with the MLF. The British response to the MLF concept "ranged from unenthusiastic to hostile throughout the military establishment and in the two principal political parties". Apart from anything else, it was estimated to cost as much as £100 million over ten years. Nonetheless, the Foreign Office argued that Britain must support the MLF. The Nassau Agreement had invigorated the MLF effort in the United States. Kennedy appointed Livingston T. Merchant to negotiate the MLF with the European governments, which he did in February and March 1963. While reaffirming support for those parts of the Nassau Agreement concerning the MLF, the British were successful in getting them omitted from the Polaris Sales Agreement.

The British team completed drafting the agreement in March 1963, and copies were circulated for discussion. The contracts for their construction were announced that month. The Polaris boats would be the largest submarines built in Britain up to that time, and would be built by Vickers Armstrong Shipbuilders in Barrow-in-Furness and Cammell Laird in Birkenhead. For similar reasons to the US Navy, the Royal Navy decided to base the boats at Faslane, on the Gareloch, not far from the US Navy's base on the Holy Loch. The drawback of the site was that it isolated the Polaris boats from the rest of the navy. The Polaris Sales Agreement was signed in Washington, D.C., on 6 April 1963 by Ormsby-Gore and Dean Rusk, the United States Secretary of State.

## Outcome

The two liaison officers were appointed in April; Captain Peter la Niece became the Royal Navy project officer in Washington, D.C., while Captain Phil Rollings became the US Navy project officer in London. The Joint Steering Task Group held its first meeting in Washington on 26 June 1963. The shipbuilding programme would prove to be a remarkable achievement, with the four *Resolution*-class submarines built on time and within the budget. The first boat, HMS *Resolution* was launched in September 1966, and commenced its first deterrent patrol in June 1968. The annual running costs of the Polaris boats came to around two per cent of the defence budget, and they came to be seen as a credible deterrent that enhanced Britain's international status. Along with the more celebrated 1958 US–UK Mutual Defence Agreement, the Polaris Sales Agreement became a pillar of the nuclear Special Relationship between Britain and the United States.

## Trident

The Polaris Sales Agreement provided an established framework for negotiations over missiles and re-entry systems. The legal agreement took the form of amending the Polaris Sales Agreement through an exchange of notes between the two governments so that "Polaris" in the original now also covered the purchase of Trident. There were also some amendments to the classified annexes of the Polaris Sales Agreement to delete the exclusion of penetrating aids. Under the Polaris Sales Agreement, the United Kingdom paid a five per cent levy on the cost of equipment supplied in recognition of US research and development costs already incurred. For Trident, a payment of $116 million was substituted. The United Kingdom procured the Trident system from America and fitted them to their own submarines, which had only 16 missile tubes like Polaris rather than the 24 in the American *Ohio* class. The first *Vanguard*-class submarine, HMS *Vanguard*, entered operational service in December 1994, by which time the Cold War had ended.

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## InfoBox

Polaris Sales Agreement
| Polaris Sales Agreement between the Government of the United Kingdom of Great Britain and Northern Ireland and the Government of the United States of America | |
| --- | --- |
| British Polaris missile on display at the Imperial War Museum in London | |
| Signed | 6 April 1963 (1963-04-06) |
| Location | Washington, D.C. |
| Effective | 6 April 1963 (1963-04-06) |
| Signatories | Dean Rusk (US)<br>David Ormsby-Gore (UK) |


title: Political Warfare Bureau

abstract: The Political Warfare Bureau is the affiliated authority of the Ministry of National Defense (MND) of the Republic of China (Taiwan) that is responsible for all the political warfare affairs of the Republic of China Armed Forces.

text:
# Political Warfare Bureau

The **Political Warfare Bureau** (**GPWB**; traditional Chinese: 國防部政治作戰局; simplified Chinese: 国防部政治作战局; pinyin: *Guófángbù Zhèngzhì Zuòzhànjú*) is the affiliated authority of the Ministry of National Defense (MND) of the Republic of China (Taiwan) that is responsible for all the political warfare affairs of the Republic of China Armed Forces.

## History

Since its establishment in 1924, the Whampoa Military Academy has run a set political work system. In April 1950, the academy reformed the political work system by changing the **Political Staff Bureau** to **Political Department**. In May 1951, it was renamed **General Political Department** and in August 1963 as **General Political Warfare Department** with some modifications to its structural agencies. The department was led by deputy director Yi Kuo-juei. On 1 March 2002, the Organizational Ordinance of the **General Political Warfare Bureau** was put into performance.

In response to increasing Chinese Communist Party (CCP) political warfare campaigns on social media in the late 2010s the Political Warfare Bureau set up a team dedicated to the expeditious handling of false information. The Bureau uses big data system analysis in its efforts to understand and counter CCP disinformation campaigns in real time.

## Organizational structure

* General Administration Division (主計室)
* Office of Military Spokesperson (軍事新聞處)
* Military Dependents Service Division (軍眷服務處)
* Military Discipline & Ethics Division (政戰綜合處)
* Counter Intelligence & Security Division (保防安全處)
* Cultural & Political Division (文宣心戰處)

## InfoBox

Political Warfare Bureau
| 政治作戰局
Zhèngzhì Zuòzhàn Jú | |
| --- | --- |
|  | |
| Agency overview | |
| Formed | 1 March 2002 |
| Jurisdiction | Republic of China |
| Headquarters | Zhongshan, Taipei
25°04′48″N 121°32′34″E / 25.0799°N 121.5427°E / 25.0799; 121.5427 |
| Parent agency | Ministry of National Defense |
| Website | gpwd.mnd.gov.tw |


title: Political Theory Project

abstract: The Political Theory Project (PTP) was an interdisciplinary research center at Brown University in Providence, Rhode Island. The center has since transitioned into the university's Center for Philosophy, Politics and Economics. The center's stated mission was to "investigate the ideas and institutions that make societies free, prosperous, and fair." From its establishment in 2003 until 2021, the Project was directed by founder John Tomasi. According to Tomasi, the PTP focuses "on the interplay of democratic and market-based ideals, with a commitment to examining issues from a variety of ideological perspectives." The Project is officially nonpartisan and maintains that it is not committed "to any particular ideological orientation."

text:
# Political Theory Project

The **Political Theory Project** (**PTP**) was an interdisciplinary research center at Brown University in Providence, Rhode Island. The center has since transitioned into the university's **Center for Philosophy, Politics and Economics**.

The center's stated mission was to "investigate the ideas and institutions that make societies free, prosperous, and fair." From its establishment in 2003 until 2021, the Project was directed by founder John Tomasi. According to Tomasi, the PTP focuses "on the interplay of democratic and market-based ideals, with a commitment to examining issues from a variety of ideological perspectives." The Project is officially nonpartisan and maintains that it is not committed "to any particular ideological orientation."

## History

At inception, the Political Theory Project originally focused on offering post-doctoral researchers to pursue scholarship regarding political theory. The center grew to encompass a wider range of programing, including seminars and lecture series. Among these is the Janus Forum Lecture Series which featured speakers of contrasting viewpoints. Established in 2007, the lecture series hosted Noam Chomsky, Steven Pinker, Paul Krugman, Jeffrey Sachs, and Glenn Greenwald, among others.

Two student publications, the *Brown Political Review* and *Brown Journal of Philosophy, Politics and Economics* were sponsored by the Political Theory Project.

## Funding

The Project gained attention and faced criticism for its acceptance of gifts from free-market organizations and foundations. Among the groups that donated to the Project are Atlas Network, Searle Freedom Trust, and the Charles Koch Foundation. The PTP maintained that it followed a "Programming First" policy wherein donors are not given input regarding the center's activities.

## People

### Faculty associates

## InfoBox

Political Theory Project
| Established | 2003 (2003) |
| --- | --- |
| Director | John Tomasi |
| Address | 25 George Street |
| Location | Brown University |
| Publications | *Brown Political Review* |


title: Dyschirius baenningeri

abstract: Dyschirius baenningeri is a species of ground beetle in the subfamily Scaritinae. It was described by Fedorenko in 2004.

text:
# Dyschirius baenningeri

***Dyschirius baenningeri*** is a species of ground beetle in the subfamily Scaritinae. It was described by Fedorenko in 2004.

## InfoBox

| *Dyschirius baenningeri* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Carabidae |
| Genus: | *Dyschirius* |
| Species: | ***D. baenningeri*** |
| Binomial name | |
| ***Dyschirius baenningeri***<br>(Fedorenko, 2004) | |
|


title: Dyschirius baicalensis

abstract: Dyschirius baicalensis is a species of ground beetle in the subfamily Scaritinae. It was described by Victor Motschulsky in 1844.

text:
# Dyschirius baicalensis

***Dyschirius baicalensis*** is a species of ground beetle in the subfamily Scaritinae. It was described by Victor Motschulsky in 1844.

## InfoBox

| *Dyschirius baicalensis* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Coleoptera |
| Family: | Carabidae |
| Genus: | *Dyschirius* |
| Species: | ***D. baicalensis*** |
| Binomial name | |
| ***Dyschirius baicalensis***<br>Motschulsky, 1844 | |
|


title: Polcevera

abstract: The Polcevera is a 19-kilometre (12 mi) river in Liguria (Italy).

text:
# Polcevera

The **Polcevera** (in Ligurian *Pûçéivia* or *Ponçéivia*) is a 19-kilometre (12 mi) river in Liguria (Italy).

## Geography

The river is named the Polcevera from Pontedecimo, at the confluence of the Torrente Riccò (left-hand) and torrente Verde (right-hand). Between Pontedecimo and the Ligurian Sea, the Polcevera is 11 kilometres (6.8 mi) long, but its total length including the Torrente Verde is 19 kilometres (12 mi).

From Pontedecimo the Polcevera heads south, and at Bolzaneto it receives the waters of the Torrente Secca, another important left-hand tributary. After being crossed by the *Ponte Morandi*, a motorway bridge that partially collapsed in August 2018, it ends its course in the Ligurian Sea between Sampierdarena and Cornigliano, two *quartieri* of Genoa.

The 140-square-kilometre (54 sq mi) drainage basin of the Polcevera is totally included in the Province of Genova. Its highest point is Monte Taccone (1,113 m).

### Main tributaries

* Left hand:
    + torrente Riccò,
    + torrente Secca,
    + torrente Geminiano (or *Goresina*),
    + torrente Torbella.
* Right hand:
    + torrente Verde,
    + torrente Burba,
    + torrente Trasta,
    + torrente Fegino (or *Pianego*).

## History

The *Département du Polcevera* or *Dipartimento della Polcevera* of Ligurian Republic took its name at the end of the 18th century from the stream.

Media related to Polcevera at Wikimedia Commons

## InfoBox

| Polcevera | |
| --- | --- |
| The Polcevera at its confluence with the Secca | |
|  | |
| Location | |
| Country | Italy |
| Physical characteristics | |
|  | |
| Source |  |
| location | Monte Leco (torr. Verde) |
|  | |
| Mouth | Ligurian Sea |
| location | Genoa |
| coordinates | 44°24′27″N 8°52′30″E / 44.40750°N 8.87500°E / 44.40750; 8.87500 (Mediterranean Sea-Polcevera) |
| elevation | 0 m (0 ft) |
| Length | 19 km (12 mi) |
| Basin size | 140 km2 (54 sq mi) |


title: Polch

abstract: Polch is a town in the district Mayen-Koblenz, Rhineland-Palatinate, Germany. It is part of the Verbandsgemeinde of Maifeld. It is situated east of Mayen. Polch is twinned with the commune of Vineuil, located near Blois, Centre-Val de Loire, France

text:
# Polch

**Polch** (German pronunciation: \[pɔlç\] ) is a town in the district Mayen-Koblenz, Rhineland-Palatinate, Germany. It is part of the *Verbandsgemeinde* ("collective municipality") of Maifeld. It is situated east of Mayen.

Polch is twinned with the commune of Vineuil, located near Blois, Centre-Val de Loire, France

## Local council (Stadtrat)

Elections were held in May 2014:

| Election | SPD | CDU | The Left | FWG Free voters | Total |
| --- | --- | --- | --- | --- | --- |
| 2014 | 7 | 11 | 1 | 3 | 22 seats |
| 2009 | 9 | 10 |  | 3 | 22 seats |
| 2004 | 6 | 14 |  | 2 | 22 seats |

* FWG = Freie Wählergruppe Polch e.V.

## InfoBox

| Polch | |
| --- | --- |
| Town | |
|  | |
| Location of Polch within Mayen-Koblenz district | |
| Polch Polch | |
| Coordinates: 50°18′04″N 7°19′00″E / 50.30111°N 7.31667°E / 50.30111; 7.31667 | |
| Country | Germany |
| State | Rhineland-Palatinate |
| District | Mayen-Koblenz |
| Municipal assoc. | Maifeld |
| Government | |
| Mayor (201924) | Gerd Klasen |
| Area | |
| Total | 28.70 km2 (11.08 sq mi) |
| Elevation | 219 m (719 ft) |
| Population (2022-12-31) | |
| Total | 6,976 |
| Density | 240/km2 (630/sq mi) |
| Time zone | UTC+01:00 (CET) |
| Summer (DST) | UTC+02:00 (CEST) |
| Postal codes | 56751 |
| Dialling codes | 02654 |
| Vehicle registration | MYK, MY |
| Website | www.polch.de |


title: Dysgonia

abstract: Dysgonia is a genus of moths in the family Erebidae. The genus was erected by Jacob Hübner in 1823.

text:
# Dysgonia

***Dysgonia*** is a genus of moths in the family Erebidae. The genus was erected by Jacob Hübner in 1823.

## Taxonomy

Many species formerly in the genus were moved to other genera, such as *Bastilla*, *Buzara*, *Pindara* and *Macaldenia* by Jeremy Daniel Holloway and Scott E. Miller in 2003. Other former members of *Dysgonia* were moved to the genus *Parallelia*.

## Species

### Species of which placement in *Dysgonia* is uncertain

### Former species

* Media related to *Dysgonia* at Wikimedia Commons

## InfoBox

| *Dysgonia* | |
| --- | --- |
|  | |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Arthropoda |
| Class: | Insecta |
| Order: | Lepidoptera |
| Superfamily: | Noctuoidea |
| Family: | Erebidae |
| Tribe: | Ophiusini |
| Genus: | *Dysgonia*<br>Hübner, \[1823\] |
|


title: Symphony No. 1 (Milhaud)

abstract:
The Symphony No. 1, Op. 210, by Darius Milhaud is a work for orchestra composed in France in 1939, during a period of illness and anxiety following the outbreak of World War II. Nearly fifty years old at the time and already a very prolific and mature composer, Milhaud had never attempted a symphony before. In spite of his expressed antipathy toward the "German music" typified by the symphony, he accepted a commission for this work from the Chicago Symphony Orchestra, then approaching its 50th anniversary. Milhaud went on to write twelve more numbered symphonies by 1963. In spite of the trying circumstances in which it was written, Milhaud's First Symphony is a bright, optimistic work in its composer's unique neo-classical style. With a total running time of some 24 minutes, the piece's four movements are:
  - Pastoral. Modérément animé
  - Très vif
  - Très modéré
  - Final. Animé This symphony, which is not to be confused with Milhaud's Little Symphony No.1 "Le printemps", Op.43 (1917), is published by Heugel & Cie.

text:
# Symphony No. 1 (Milhaud)

The **Symphony No. 1**, Op. 210, by Darius Milhaud is a work for orchestra composed in France in 1939, during a period of illness and anxiety following the outbreak of World War II. Nearly fifty years old at the time and already a very prolific and mature composer, Milhaud had never attempted a symphony before. In spite of his expressed antipathy toward the "German music" typified by the symphony, he accepted a commission for this work from the Chicago Symphony Orchestra, then approaching its 50th anniversary. Milhaud went on to write twelve more numbered symphonies by 1963.

In spite of the trying circumstances in which it was written, Milhaud's First Symphony is a bright, optimistic work in its composer's unique neo-classical style. With a total running time of some 24 minutes, the piece's four movements are:

1. Pastoral. Modérément animé (approx. 7')
2. Très vif (approx. 4'30")
3. Très modéré (approx. 6'30")
4. Final. Animé (approx. 6'20")

This symphony, which is not to be confused with Milhaud's Little Symphony No.1 "Le printemps", Op.43 (1917), is published by Heugel & Cie.

## Recordings


title: Polytechnics Central Admissions System

abstract: The Polytechnics Central Admissions System was an administrative body handling admissions in England and Wales to most courses at polytechnics and some other higher education institutions for the entry years 1986 to 1992. It ran in parallel to the university admissions system, UCCA, as well as the Central Register and Clearing House, which dealt with teacher-training applications to both polytechnics and specialist teacher training colleges, and ADAR which originally handled art and design course admissions to both polytechnics and specialist art and design colleges. All these admissions systems are now united within the UCAS admissions system.

text:
# Polytechnics Central Admissions System

The **Polytechnics Central Admissions System** (**PCAS** /ˈpkɑːs/) was an administrative body handling admissions in England and Wales to most courses at polytechnics and some other higher education institutions for the entry years 1986 to 1992. It ran in parallel to the university admissions system, UCCA, as well as the Central Register and Clearing House, which dealt with teacher-training applications to both polytechnics and specialist teacher training colleges, and ADAR which originally handled art and design course admissions to both polytechnics and specialist art and design colleges. All these admissions systems are now united within the UCAS admissions system.

## History

### Earlier organisations

The establishment of the teacher training admission system, the Central Register and Clearing House, in 1933, and the central admissions system for British universities, called UCCA, in 1961 had shown the benefits of a single admission system for higher education applicants. Although the polytechnics were degree-teaching institutions, through the CNAA awards system, they were not eligible for admission to UCCA as it was reserved only for universities with degree awarding powers. Despite this the Polytechnics (see Polytechnic (United Kingdom)) were involved as early as 1972 in discussions with UCCA and the Central Register and Clearing House about the possible future shape of one or more admissions systems. At this stage applicants dealt directly with each polytechnic and the polytechnics themselves were strongly regional or local in their appeal. A study in 1977 found that between sixty and seventy per cent of those admitted to a polytechnic had applied to that institution only, and that forty per cent of admissions to polytechnics resulted from applications made in August or September of the year of entry.

### Formation

In 1983 the Committee of Directors of Polytechnics began negotiations with UCCA to share its computing, technical and office facilities in Cheltenham to establish a course entrance system, based on the existing model used by UCCA. A grant of £210,000, from the British Department for Education and Science, was awarded to set up a new unified admissions system, provisionally called PUCCA. However, instead of a unified system for both the universities and polytechnics a separate system for polytechnics emerged from the negotiations, modelled on UCCA, but known as PCAS. The first chairman was Harry Law of Portsmouth Polytechnic; his deputy was Keith Thompson, the Director of Staffordshire Polytechnic, who became chairman in June 1989, staying until 1993. The deputy from 1989 was Michael Goldstein, Director of Coventry Polytechnic. PCAS was at Fulton House on Jessop Avenue, near Cheltenham Waitrose. Also in the building was ECCTIS 2000 and UCCA, and it is now called Festival House.

The PCAS name was chosen as the Department for Education and Science grant was conditional upon the new scheme being made available for applications to Colleges of Higher Education later on. It was thought that the PCAS acronym could remain if the organization's name needed to be changed to Polytechnics' & Colleges' Admissions Service.

Applicants to courses were given the option to apply separately for universities or polytechnics, or for both.

The PCAS system came into effect in 1985. It was led by its first Chief Executive, Tony Higgins, later chief executive of UCAS from 1993, and in the first year it handled around 140,000 applications to polytechnic courses, of whom 40,000 a year went on to study at polytechnics.

Although many polytechnics offered art and design programmes, and some also offered teacher training courses, these admissions systems remained outside PCAS.

### Merger

UCCA and PCAS merged their form in 1992, whereby PCAS sorted postal applications, and UCCA ran the computer, then both merged in 1993.

## Merger with University Admissions System

Although the aim to create a unified application system for universities and polytechnics was not achieved in 1985, the Chief Executive of PCAS, Tony Higgins, continued to push for the merger of PCAS with UCCA. In 1992, following the change of status and name of most polytechnics to universities, the two bodies did combine under Higgins's leadership. Initially the application form was branded jointly UCCA/PCAS, but in 1994 the new merged body was renamed UCAS.


abstract: The Bronze Statuettes of Athletic Spartan Girl are bronze figurines depicting a Spartan young woman wearing a short tunic in a presumably running pose. These statuettes are considered Spartan manufacture dating from the 6th century B.C., and they were used as decorative attachments to ritual vessels as votive dedications, such as a cauldron, suggested by the bronze rivet on their feet. The figures typically have their hair hung down, right arm slightly bent, left hand lifted the hem of the chiton skirt and expose part of the left thigh, likely to facilitate the movement, and their legs in a wide stride. The style of the statuettes is attributed to Laconian workshops in the Archaic Period. The typical characteristics of Laconian bronzes are slender bodies with unproportional muscular legs, arched and swelling thighs, immature chests in female figures, and long faces with strongly marked facial features. Laconian bronzes were widely traded, which helps to explain why some of those Laconian manufacture were not discovered in the region. It may also suggest the possible presence of Laconian craftsmen at that site.

text:
# Bronze Statuette of Athletic Spartan Girl

The **Bronze Statuettes of Athletic Spartan Girl** are bronze figurines depicting a Spartan young woman wearing a short tunic in a presumably running pose. These statuettes are considered Spartan manufacture dating from the 6th century B.C., and they were used as decorative attachments to ritual vessels as votive dedications, such as a cauldron, suggested by the bronze rivet on their feet. The figures typically have their hair hung down, right arm slightly bent, left hand lifted the hem of the chiton skirt and expose part of the left thigh, likely to facilitate the movement, and their legs in a wide stride.

The style of the statuettes is attributed to Laconian (the region where Sparta is located) workshops in the Archaic Period. The typical characteristics of Laconian bronzes are slender bodies with unproportional muscular legs, arched and swelling thighs, immature chests in female figures, and long faces with strongly marked facial features. Laconian bronzes were widely traded, which helps to explain why some of those Laconian manufacture were not discovered in the region. It may also suggest the possible presence of Laconian craftsmen at that site.

## History

### Female athletic costume in ancient Greece

The statuette in British Museum depicts a girl wearing a short chiton affixed to the left shoulder, leaving the right shoulder and breast bare. This is the type of athletic costume especially for participants in the Heraean Games, the earliest recorded women's running competition held quadrennially in Olympic stadium. Although women in Ancient Greece (except Sparta) were not encouraged to participate in athletic activities and were excluded from the Olympic games, they could participate in the foot race at the Heraea, which was an athletic event for females of all ages. Thus, this particular piece depicts a participant in the Heraea. One speculation proposed that the costume is adapted from a light garment worn by men in hot weather or while performing hard labor.

The piece from the National Archaeological Museum, Athens, found at Dodona, is wearing a different kind of dress. Unlike the costume for Heraea Game, the bodice of the chiton covers both shoulders and breasts. It may suggest that this running costume is for girls at local ritual festivals in Sparta that are documented in ancient literature. During the festival, some Spartan maidens ran a special race in honor of Dionysus. This ritual celebrating the girls' rites of passage also involved dancing, singing and other athletic events.

### Athletic Spartan women

Women in Sparta led very different lives from their counterparts in the rest part of ancient Greece in terms of engagement in athletics. Spartan girls were offered a state-supervised educational system separated from the boys, including a physical training program. The aim of the program was to produce healthy mothers of healthy warriors. Spartan girls engaged in various athletic events including running and wrestling. They might even wrestle boys.

Spartan girls were said to wear very little when they did sports. Wearing short tunics exposing half of their thighs, Spartan females were called "thigh flashers" according to some accounts in ancient Greece. There were complaints that they left home "with bare thighs and loosened tunics" on their way to run and wrestle. Serving as supplements to those ancient literary sources, roughly forty bronze statuettes dating from the Archaic period are found showing young Spartan women dancing or running (including the two discussed ahead). There are even pieces depicting Spartan females playing sports in nudity, just as the Spartan males.

## Further reading


title: Quercus uxoris

abstract: Quercus uxoris is an uncommon species of oak. The tree is endemic to Mexico. It has been found in the states of Jalisco, Colima, Guerrero, Michoacán, and Oaxaca in southern Mexico.

text:
# Quercus uxoris

***Quercus uxoris*** is an uncommon species of oak.

The tree is endemic to Mexico. It has been found in the states of Jalisco, Colima, Guerrero, Michoacán, and Oaxaca in southern Mexico.

## Description

*Quercus uxoris* is a large deciduous tree up to 25 metres (82 feet) tall with a trunk often more than 100 centimetres (39 inches) in diameter.

The leaves can be as much as 26 cm (10 in) long, thick and leathery, broadly lance-shaped with numerous tapering teeth along the edges.

## Range and habitat

*Quercus uxoris* is native to the mountains of southern Mexico, mostly in the Sierra Madre del Sur, with small outlier populations in the Chiapas Highlands and Sierra Madre de Chiapas of Chiapas in southeastern Mexico, and in the Sierra de Taxco and near Valle de Bravo in the Trans-Mexican Volcanic Belt of central Mexico. It is found in the states of Jalisco, Colima, Michoacán, Guerrero, Oaxaca, and Chiapas. Although it has a large range, its distribution is highly discontinuous.

It grows mostly in humid cloud forest pockets from 1,800 to 2,100 meters elevation, and occasionally in humid locations, like ravines and stream valleys, in oak forest, pine–oak forest, mountain mesophyll forest, deciduous tropical forest, and tropical sub-deciduous forest habitats. It prefers deep soils rich in organic matter.

Its populations are generally small, but it can be a dominant canopy tree under favorable conditions.

## Conservation and threats

The species is subject to habitat loss from deforestation. Its native cloud forests and other humid forests are exploited for timber, and are cleared for conversion to livestock pasture and agriculture, including coffee.

A population of the species in the montane mesophyll forest of Ojo de Agua del Cuervo, in Talpa de Allende municipality of Jalisco, is threatened by deforestation, illegal logging, and road-building which fragments habitat blocks.

## InfoBox

| *Quercus uxoris* | |
| --- | --- |
|  | |
| *Quercus uxoris* in Zapotitlán de Vadillo, Mexico | |
| Conservation status | |
|
Least Concern  (IUCN 3.1) | |
| Scientific classification | |
| Kingdom: | Plantae |
| *Clade*: | Tracheophytes |
| *Clade*: | Angiosperms |
| *Clade*: | Eudicots |
| *Clade*: | Rosids |
| Order: | Fagales |
| Family: | Fagaceae |
| Genus: | *Quercus* |
| Subgenus: | *Quercus subg. Quercus* |
| Section: | *Quercus sect. Lobatae* |
| Species: | ***Q. uxoris*** |
| Binomial name | |
| ***Quercus uxoris***
McVaugh | |
|


title: Razanaka

abstract: Razanaka or Vohipeno Razanaka is a rural municipality in the Brickaville district in the Atsinanana Region, Madagascar. It is located near on the banks of the Vohitra river.

text:
# Razanaka

**Razanaka** or **Vohipeno Razanaka** is a rural municipality in the Brickaville district (or Vohibinany) in the Atsinanana Region, Madagascar.

It is located near on the banks of the Vohitra river.

## Agriculture

Curcuma is widely planted in this municipality.

## InfoBox

| Razanaka Vohipeno Razanaka | |
| --- | --- |
| RazanakaLocation in Madagascar | |
| Coordinates: 18°46′10″S 48°52′54″E / 18.76944°S 48.88167°E / -18.76944; 48.88167 | |
| Country | Madagascar |
| Region | Atsinanana |
| District | Vohibinany (district) |
| Elevation | 24 m (79 ft) |
| Population (2018 Census) | |
| Total | 5,592 |
| Time zone | UTC3 (EAT) |
| Postal code | 508 |


title: Ted Karras (offensive lineman)

abstract: Theodore John Karras III is an American professional football center for the Cincinnati Bengals of the National Football League (NFL). He played college football at Illinois, and was selected in the sixth round of the 2016 NFL draft by the New England Patriots, with whom he won two Super Bowl championships. He spent the 2020 season with the Miami Dolphins before returning to New England the next season.

text:
# Ted Karras (offensive lineman)

**Theodore John Karras III** (born March 15, 1993) is an American professional football center for the Cincinnati Bengals of the National Football League (NFL). He played college football at Illinois, and was selected in the sixth round of the 2016 NFL draft by the New England Patriots, with whom he won two Super Bowl championships. He spent the 2020 season with the Miami Dolphins before returning to New England the next season.

## Professional career

Pre-draft measurables
| Height | Weight | Arm length | Hand span | 40-yard dash | 10-yard split | 20-yard split | 20-yard shuttle | Three-cone drill | Vertical jump | Broad jump | Bench press |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 6 ft 3+34 in
(1.92 m) | 307 lb
(139 kg) | 32+12 in
(0.83 m) | 9+12 in
(0.24 m) | 5.34 s | 1.88 s | 3.07 s | 4.70 s | 8.15 s | 26.5 in
(0.67 m) | 8 ft 10 in
(2.69 m) | 32 reps |
| All values from Pro Day | | | | | | | | | | | | |

### New England Patriots (first stint)

Karras was selected by the New England Patriots in the sixth round (221st overall) in the 2016 NFL draft. He made the Patriots 53-man roster and was the starting right guard in the season opener against the Cardinals due to the injuries of Shaq Mason and Jonathan Cooper. He split time with Mason in Week 2 but was reverted to a reserve role for the rest of the season after Mason resumed his starting role in Week 3. Karras contributed to the Patriots finishing with a 14–2 record and earning the top-seed for the AFC playoffs.

On February 5, 2017, Karras was part of the Patriots team that won Super Bowl LI. In the game, the Patriots defeated the Atlanta Falcons by a score of 34–28 in overtime.

On September 2, 2017, Karras was released by the Patriots and was signed to the practice squad the next day. He was promoted to the active roster on September 7, 2017. He made his first start of the season in Week 11 at center, filling in for starter David Andrews, who was out with an illness. Karras and the Patriots reached Super Bowl LII, but were defeated by the Philadelphia Eagles by a score of 41–33.

Karras entered 2018 as a backup guard and center. He started two games at right guard in place of an injured Shaq Mason. The Patriots reached Super Bowl LIII where they defeated the Los Angeles Rams 13–3.

Karras began the 2019 season as the Patriots' starting center after David Andrews was placed on season-ending injured reserve.

### Miami Dolphins

On March 20, 2020, Karras signed a one-year contract with the Miami Dolphins. He started all 16 games at center for the Dolphins in 2020.

### New England Patriots (second stint)

On March 19, 2021, Karras signed a one-year contract with the Patriots. After being named a backup guard to begin the season, he was named the starting left guard in Week 7 following a poor performance from Michael Onwenu and started the remainder of the season.

### Cincinnati Bengals

On March 18, 2022, Karras signed a three-year, $18 million contract with the Cincinnati Bengals. Karras started was the starting center for the team during the 2022 season, and was named a captain. He would reprise both roles for the 2023 season. On June 13, 2024, Karras signed a one-year contract extension through the 2025 season.

## Personal life

Karras is a third-generation NFL player. His grandfather, Ted Karras Sr., and grand uncles, Lou Karras and Alex Karras, played in the NFL from the 1950s until Alex retired in 1970. His father Ted Karras Jr. played during the 1987 season. He is also the seventh family member over three generations to play football in the Big Ten. Ted attended the same school, Saint Matthew Catholic School in Indianapolis, Indiana, (K-8) as Nick Martin of the Houston Texans, Zack Martin of the Dallas Cowboys, and Cap Boso of the Chicago Bears. Karras is a self-proclaimed fan of and trivia expert on *The Office* TV series.

## InfoBox

Ted Karras
| Karras with the New England Patriots in 2019 | |
| --- | --- |
| No. 64 – Cincinnati Bengals | |
| Position: | Center |
| Personal information | |
| Born: | (1993-03-15) March 15, 1993
Chicago, Illinois, U.S. |
| Height: | 6 ft 4 in (1.93 m) |
| Weight: | 310 lb (141 kg) |
| Career information | |
| High school: | Cathedral
(Indianapolis, Indiana) |
| College: | Illinois (2011–2015) |
| NFL draft: | 2016 / round: 6 / pick: 221 |
| Career history | |
|  | |
|  | |
| Roster status: | Active |
| Career highlights and awards | |
|  | |
|  | |
| Career NFL statistics as of Week 1, 2024 | |
| Games played: 127  Games started: 83 | |
|  | |
| Player stats at **PFR** | |
|  | |


title: Only for the Lonely

abstract: Only for the Lonely is the second solo studio by American rhythm and blues and gospel singer Mavis Staples. It was released on October 12, 1970, by Volt Records.

text:
# Only for the Lonely

***Only for the Lonely*** is the second solo studio by American rhythm and blues and gospel singer Mavis Staples. It was released on October 12, 1970, by Volt Records.

## Critical reception

Professional ratings
| Review scores | |
| --- | --- |
| Source | Rating |
| AllMusic |  |

In the *Billboard* issue dated October 24, 1970, a review was published saying, "This album is at once dramatic and sensuous, and warm and appealing. Mavis Staples is cast in the same mold that produced recording greats like Aretha Franklin, Nancy Wilson and Etta James, and she can really deliver a song. Included here are "It Makes Me Want to Cry," "How Many Times," "Since I Fell for You" and "Endlessly".

*Cashbox* published a review of the album in the issue dated October 31, 1970, which said, "Mavis Staples is a brilliant songstress with an incredibly powerful voice. Listening to her perform on an album, one cannot help but feel that she is in fact performing live in your living room. "I Have Learned to Do Without You," "Endlessly," "Since I Fell for You," and "It Makes Me Wanna Cry," are among the more impressive cuts, but each is a gem in its own right. For Mavis, it's the second release in a bright, shining career."

## Track listing

Side one
| No. | Title | Writer(s) | Length |
| --- | --- | --- | --- |
| 1. | "I Have Learned to Live Without You" |  | 4:09 |
| 2. | "How Many Times" |  | 3:21 |
| 3. | "Endlessly" |  | 3:08 |
| 4. | "You're the Fool" | Sharon McMahan | 2:40 |

Side two
| No. | Title | Writer(s) | Length |
| --- | --- | --- | --- |
| 1. | "Since I Fell for You" | Buddy Johnson | 3:34 |
| 2. | "What Happened to the Real Me" | Helga Penzabene | 2:35 |
| 3. | "Since You Became a Part of My Life" |  | 3:30 |
| 4. | "It Makes Me Wanna Cry" |  | 2:50 |
| 5. | "Don't Change Me Now" | * Darryl Carter * Fred Briggs * Sam Ballard | 2:25 |

2001 CD reissue bonus tracks
| No. | Title | Writer(s) | Original release | Length |
| --- | --- | --- | --- | --- |
| 10. | "Security" | Otis Redding | *Mavis Staples* (1969) | 2:47 |
| 11. | "Son of a Preacher Man" |  | *Mavis Staples* (1969) | 2:17 |
| 12. | "You Send Me" | L.C. Cook | *Mavis Staples* (1969) | 2:56 |
| 13. | "A House Is Not a Home" |  | *Mavis Staples* (1969) | 4:27 |
| 14. | "That's the Way Love Is" (with Johnnie Taylor) | Deadric Malone | *Boy Meets Girl* (1969) | 2:24 |
| Total length: | | | | 43:03 |

## Personnel

Adapted from the album liner notes.

* Barry Beckett \- keyboards
* Joel Brodsky \- photography
* Vernon Bullock - guitar, keyboards
* Ron Capone - engineer
* Steve Cropper \- guitar
* Don Davis - engineer
* Donald "Duck" Dunn \- bass
* Eli Fountain - percussion, saxophone
* Marlin Greene - engineer
* Don Hahn - producer, engineer
* Roger Hawkins \- drums
* Isaac Hayes \- organ
* Eddie Hinton \- guitar
* David Hood \- bass
* Al Jackson Jr. \- drums
* David Krieger - art direction
* Herb Kole - art supervisor
* George McGregor - drums
* Ray Monette - guitar
* Tony Newton - bass
* Horace Ott \- string arrangements
* Paul Richmond - mastering
* Rudy Robinson - keyboards
* Mavis Staples - lead vocals
* Marvell Thomas - piano

## Charts

## InfoBox

| Only for the Lonely | |
| --- | --- |
|  | |
| Studio album by Mavis Staples | |
| Released | October 12, 1970 |
| Studio |  |
| Genre |  |
| Length | 28:12 |
| Label | Volt |
| Producer |  |
| Mavis Staples chronology | |
| *Mavis Staples*
(1969) ***Only for the Lonely***
(1970) *A Piece of the Action*
(1977) | |
|  | |
| Singles from  *Only for the Lonely* | |
| 1. "I Have Learned to Do Without You"
Released: June 1970 2. "Endlessly"
Released: August 1972 | |
|  | |


abstract: South Korea is competing at the 2013 World Aquatics Championships in Barcelona, Spain between 19 July and 4 August 2013.

text:
# South Korea at the 2013 World Aquatics Championships

**South Korea** is competing at the 2013 World Aquatics Championships in Barcelona, Spain between 19 July and 4 August 2013.

## Diving

South Korea qualified six quota places for the following diving events.

Men

| Athlete | Event | Preliminaries | | Semifinals | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank | Points | Rank |
| Kim Yeong-Nam | 1 m springboard | 276.95 | 36 |  | | did not advance | |
| Woo Ha-Ram | | 315.75 | 25 |  | | did not advance | |
| Cho Kwan-Hoon | 3 m springboard | 337.05 | 35 | did not advance | | | |
| Kim Yeong-Nam | | 373.20 | 22 | did not advance | | | |
| Kim Yeong-Nam | 10 m platform | 297.15 | 30 | did not advance | | | |
| Woo Ha-Ram | | 321.90 | 27 | did not advance | | | |
| Kim Yeong-Nam
Woo Ha-Ram | 3 m synchronized springboard | 378.24 | 10 **Q** |  | | 377.34 | 10 |
| | 10 m synchronized platform | 390.18 | 7 **Q** |  | | 386.22 | 8 |

Women

| Athlete | Event | Preliminaries | | Semifinals | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank | Points | Rank |
| Cho Eun-Bi | 1 m springboard | 221.50 | 24 |  | | did not advance | |
| Kim Chae-Hyon | | 215.65 | 27 |  | | did not advance | |
| Cho Eun-Bi | 3 m springboard | 205.45 | 35 | did not advance | | | |
| Kim Su-ji | | 223.20 | 29 | did not advance | | | |
| Cho Eun-Bi | 10 m platform | 245.45 | 29 | did not advance | | | |
| Kim Su-ji | | 235.20 | 32 | did not advance | | | |
| Cho Eun-Bi
Kim Su-ji | 3 m synchronized springboard | 229.74 | 18 |  | | did not advance | |
| | 10 m synchronized platform | 266.82 | 11 **Q** |  | | 259.80 | 11 |

## Swimming

South Korean swimmers earned qualifying standards in the following events (up to a maximum of 2 swimmers in each event at the A-standard entry time, and 1 at the B-standard):

Men

| Athlete | Event | Heat | | Semifinal | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Time | Rank | Time | Rank | Time | Rank |
| Chang Gyu-Cheol | 100 m butterfly | 54.09 | 34 | did not advance | | | |
| | 200 m butterfly | 2:03.32 | 31 | did not advance | | | |
| Choi Kyu-Woong | 100 m breaststroke | 1:02.58 | 43 | did not advance | | | |
| Im Tae-Jeong | 200 m backstroke | 2:01.23 | 23 | did not advance | | | |
| | 200 m individual medley | 2:03.61 | 36 | did not advance | | | |
| | 400 m individual medley | 4:34.69 | 37 |  | | did not advance | |
| Jang Sang-Jin | 800 m freestyle | 8:18.51 | 30 |  | | did not advance | |
| Jeong Jeong-Soo | 200 m freestyle | 1:51.86 | 43 | did not advance | | | |
| | 400 m freestyle | 3:56.68 | 30 |  | | did not advance | |
| Ju Jang-Hun | 200 m breaststroke | 2:14.79 | 26 | did not advance | | | |
| Shin Hee-Woong | 50 m backstroke | 25.84 | 22 | did not advance | | | |
| | 100 m backstroke | 56.95 | 35 | did not advance | | | |
| Shin Hyeong-Keun | 50 m breaststroke | 28.29 | 42 | did not advance | | | |
| Yang Jung-Doo | 50 m freestyle | 22.48 | 22 | did not advance | | | |
| | 50 m butterfly | 23.84 | 24 | did not advance | | | |
| Chang Gyu-Cheol
Jeong Jeong-Soo
Shin Hee-Woong
Yang Jung-Doo | 4×100 m freestyle relay | 3:25.50 | 15 |  | | did not advance | |
| Im Tae-Jeong
Jang Sang-Jin
Ju Jang-Hun
Jeong Jeong-Soo | 4×200 m freestyle relay | 7:32.83 | 17 |  | | did not advance | |
| Choi Kyu-Woong
Chang Gyu-Cheol
Shin Hee-Woong
Yang Jung-Doo | 4×100 m medley relay | 3:44.08 | 20 |  | | did not advance | |

Women

| Athlete | Event | Heat | | Semifinal | | Final | |
| --- | --- | --- | --- | --- | --- | --- | --- |
| | | Time | Rank | Time | Rank | Time | Rank |
| An Se-Hyeon | 200 m butterfly | 2:13.26 | 19 | did not advance | | | |
| Back Su-Yeon | 100 m breaststroke | 1:09.11 | 25 | did not advance | | | |
| | 200 m breaststroke | 2:27.47 | 13 **Q** | 2:25.61 | 10 | did not advance | |
| Han Na-Kyeong | 1500 m freestyle | 16:55.46 | 20 |  | | did not advance | |
| Hwang Seo-Jin | 50 m butterfly | 27.22 | 30 | did not advance | | | |
| Im Da-Sol | 200 m backstroke | 2:14.07 | 23 | did not advance | | | |
| Kim Go-Eun | 50 m breaststroke | 31.95 | 28 | did not advance | | | |
| Kim Ji-Hyun | 50 m backstroke | 29.18 | 29 | did not advance | | | |
| | 100 m backstroke | 1:04.66 | 37 | did not advance | | | |
| Park Jin-Young | 100 m butterfly | 1:00.78 | 31 | did not advance | | | |
| Yang Ji-Won | 200 m breaststroke | 2:27.78 | 14 **Q** | 2:27.67 | 14 | did not advance | |
| An Se-Hyeon
Han Na-Kyeong
Hwang Seo-Jin
Kim Ji-Hyun | 4×100 m freestyle relay | 3:55.67 | 15 |  | | did not advance | |
| | 4×200 m freestyle relay | 8:32.98 | 13 |  | | did not advance | |
| Back Su-Yeon
Hwang Seo-Jin
Kim Ji-Hyun
Park Jin-Young | 4×100 m medley relay | 4:10.75 | 16 |  | | did not advance | |

## Synchronized swimming

South Korea has qualified twelve synchronized swimmers.

| Athlete | Event | Preliminaries | | Final | |
| --- | --- | --- | --- | --- | --- |
| | | Points | Rank | Points | Rank |
| Gu Se-Ul | Solo free routine | 75.830 | 25 | did not advance | |
| Lim Hyun-Ji | Solo technical routine | 69.200 | 30 | did not advance | |
| Jung Young-Hee
Kong Do-Yeon | Duet free routine | 72.580 | 23 | did not advance | |
| Gu Se-Ul
Kim Ka-Young | Duet technical routine | 70.800 | 24 | did not advance | |

## InfoBox

| South Korea at the
2013 World Aquatics Championships | |
| --- | --- |
| Flag of South Korea | |
| FINA code | KOR |
| National federation | Korean Swimming Federation |
| Website | swimming.sports.or.kr |
| in Barcelona, Spain | |
| Medals | Gold 0 Silver 0 Bronze 0 Total 0 |
| World Aquatics Championships appearances | |
|  | |


title: Encompassment ordering

abstract:
In theoretical computer science, in particular in automated theorem proving and term rewriting,
the containment, or encompassment, preorder (≤) on the set of terms, is defined by
  - s ≤ t if a subterm of t is a substitution instance of s. It is used e.g. in the Knuth–Bendix completion algorithm.

text:
# Encompassment ordering

In theoretical computer science, in particular in automated theorem proving and term rewriting, the **containment**, or **encompassment**, preorder (≤) on the set of terms, is defined by

*s*  *t* if a subterm of *t* is a substitution instance of *s*.

It is used e.g. in the Knuth–Bendix completion algorithm.

## Properties

1. Gerard Huet (1981). "A Complete Proof of Correctness of the Knuth–Bendix Completion Algorithm". *J. Comput. Syst. Sci*. **23** (1): 11–21. doi:10.1016/0022-0000(81)90002-7.
2. N. Dershowitz, J.-P. Jouannaud (1990). Jan van Leeuwen (ed.). *Rewrite Systems*. Handbook of Theoretical Computer Science. Vol. B. Elsevier. pp. 243–320. Here:sect.2.1, p. 250
3. Dershowitz, Jouannaud (1990), sect.5.4, p. 278; somewhat sloppy, *R* is required to be a "terminating rewrite relation" there.


title: Pomba River

abstract: The Rio Pomba is a river of Minas Gerais and Rio de Janeiro states in southeastern Brazil, one of the principle tributaries of the Paraíba do Sul.

text:
# Pomba River

The **Rio Pomba** is a river of Minas Gerais and Rio de Janeiro states in southeastern Brazil, one of the principle tributaries of the Paraíba do Sul.

## Geography

The Rio Pomba begins in the city of Barbacena in Minas Gerais and flows south through the Zona da Mata to empty into the Paraíba do Sul between the towns of Cambuci and Itaocara, Rio de Janeiro. Its main tributaries are the rivers Piau, Xopotó, Pardo, and Formoso. The main cities along its banks are Cataguases in Minas Gerais and Santo Antônio de Pádua in Rio de Janeiro.

## Indigenous peoples

In the 18th century, Koropó speakers lived with Coroado Puri speakers along the Pomba River.

## Environmental issues

The lands of the Rio Pomba basin are severely deforested, a process that began throughout the Zona da Mata during the coffee era and did not spare even the headwaters of the river. It is a factor that contributes to the degradation of the river and is also affected by the release of industrial and domestic effluents. In 2003, a major spill of more than 1 billion liters of toxic chemical waste from one industry in Cataguases caused enormous environmental damage, and the effect was detected from the Paraiba do Sul River to its mouth in the Atlantic Ocean in the state of Rio de Janeiro.

## InfoBox

| Rio Pomba | |
| --- | --- |
| Rio Pomba valley in the region of Santa Bárbara do Tugúrio | |
|  | |
| Location | |
| Country | Brazil |
| State | Minas Gerais, Rio de Janeiro |
| Physical characteristics | |
|  | |
| Source |  |
| elevation | 1,100 m (3,600 ft) |
|  | |
| Mouth |  |
| location | Paraíba do Sul, MG, Brazil |
| coordinates | 21°38′18″S 42°2′59″W / 21.63833°S 42.04972°W / -21.63833; -42.04972 |
| Length | 305 km (190 mi) |


title: SS Orontes

abstract: SS Orontes was a passenger ship owned by Orient Line. The ship was built in 1929 by Vickers Armstrong at Barrow-in-Furness, England. Its sister ships were Orama (II), Orford, Oronsay, and Otranto (II). Orontes was the last of the "Orama" Class and great effort was taken to make the public rooms of Orontes the best of this class. The name had previously belonged to the RMS Orontes, an earlier ship owned by the Orient Line.

text:
# SS Orontes

**SS *Orontes*** was a passenger ship owned by Orient Line.

The ship was built in 1929 by Vickers Armstrong at Barrow-in-Furness, England.

Its sister ships were *Orama* (II), *Orford*, *Oronsay*, and *Otranto* (II). Orontes was the last of the "Orama" Class and great effort was taken to make the public rooms of *Orontes* the best of this class. The name had previously belonged to the *RMS Orontes*, an earlier ship owned by the Orient Line.

## Service

*Orontes* maiden voyage was a Mediterranean Cruise in June 1929. From 1929 to 1940, it served on the England to Australia route. It carried the England cricket team on the way to the Bodyline tour in 1932.

During World War II, *Orontes* became a troopship, serving that role from 1940 to 1947. In 1947 *Orontes* transported World War II prisoners of war from Melbourne to Cuxhaven, West Germany.

The ship served on the England to Australia route from 1948 to 1962, being refitted as a single class passenger ship at Thornycroft in 1953. In August 1958, *Orontes* was involved in a collision with SS *Empire Baltic*, a landing ship used as a ferry on the River Thames. The *Orontes* was scrapped at Valencia, Spain, in 1962.

## Further reading

* Geddes, FL (24 June 1948), "The Reconditioned "Orontes"", *Shipbuilding and Shipping Record*: 774 \- article about the post-war refit
* McCart, Neil (1987), *Passenger Ships of the Orient Line*, P. Stephens, ISBN 978-0-85059-891-9

## InfoBox

| SS Orontes in Tilbury Docks, circa 1957, about to sail for Sydney on a single-class voyage with (mainly) migrant passengers on the Ten Pound Poms scheme. | |
| --- | --- |
| History | |
| United Kingdom | |
| Name | SS Orontes |
| Owner | Orient Line (P & O) |
| Port of registry | Tilbury, Essex, United Kingdom |
| Route | * England - Australia (1929-1940) * England - Australia (1948-1962) |
| Builder | Vickers Armstrong Ltd. at Barrow-in-Furness, England |
| Launched | 26 February 1929 |
| Maiden voyage | June 1929 |
| Refit | 1947-1948 |
| Identification | * Code Letters and radio callsign GBXM * |
| Fate | Scrapped at Valencia, Spain in 1962 |
| General characteristics | |
| Type | Passenger |
| Tonnage | 20,097 grt |
| Length | 664 ft (202 m) |
| Beam | 75 ft 2 in (22.91 m) |
| Draft | 29 ft 8 in (9.04 m) |
| Installed power | 2 steam turbines, 20,000 shaft horsepower (15,000 kW) |
| Propulsion | 2 screws |
| Speed | 20 knots (37 km/h) |
| Capacity | * 1st: 500 passengers * 3rd: 1,112 passengers * Total: 1,612 passengers |


title: Sada Mee Sevalo

abstract: Sadaa Mee Sevalo is a 2005 Indian Telugu-language family drama film directed by G. Neelakanta Reddy starring Venu Thottempudi and Shriya Saran.

text:
# Sada Mee Sevalo

***Sadaa Mee Sevalo*** (transl.Always at your service) is a 2005 Indian Telugu-language family drama film directed by G. Neelakanta Reddy starring Venu Thottempudi and Shriya Saran.

## Plot

Tilak is a mind games expert and tries to help people in need. He and his friend, who is a lawyer, and a former police officer help needy people who are in the public. Tilak falls in love with Suryakantham. He follows her and they both fall in love. Suryakantham has difficulty adjusting to help people in need. Suryakantham gets kidnapped by Tilak's enemies. Tilak saves her.

## Cast

## Soundtrack

The music was composed by Vandemataram Srinivas and released by Aditya Music.

| Sada Mee Sevalo | |
| --- | --- |
| Soundtrack album by Vandemataram Srinivas | |
| Released | 2005 |
| Recorded | 2005 |
| Genre | Soundtrack |
| Length | 27:41 |
| Label | Aditya Music |
| Producer | Vandemataram Srinivas |

Track list
| No. | Title | Lyrics | Singer(s) | Length |
| --- | --- | --- | --- | --- |
| 1. | "Ee Dooram" | Kandikonda | Sonu Nigam, Shreya Ghoshal | 4:22 |
| 2. | "Yem Navvulivile" | Sirivennela Seetharama Sastry | KK, Shreya Ghoshal | 4:56 |
| 3. | "Hello Hello" | Kandikonda | Abhijeet Bhattacharya | 5:09 |
| 4. | "O Meghamala" | Kandikonda | Udit Narayan, Usha | 4:14 |
| 5. | "Lub Dub" | Chaitanya Prasad | Shankar Mahadevan | 4:35 |
| 6. | "Cheli Cherumari" | Kandikonda | Karthik, Kousalya | 4:25 |
| Total length: | | | | 27:41 |

## Reception

A critic from *The Hindu* wrote that "Venu and Shreya make a good team. Vandemataram's music is in sync with scenes and the background score, equally enjoyable." A critic from *Rediff.com* wrote that "Barring a few good comic moments, promising director Neelakantha gets it all wrong this time." A critic from *Idlebrain* wrote that "Plus points of the film are noble storyline and Shriya. The main drawbacks of the film are inconsistent graph of emotions, slow narration and music. As this film has the background of middle-class family values, it would have more reach to the family crowds."

## InfoBox

| Sadaa Mee Sevalo | |
| --- | --- |
|  | |
| Directed by | G. Neelakanta Reddy |
| Written by | G. Neelakanta Reddy |
| Produced by | Venkata Shyam Prasad |
| Starring | Venu Thottempudi <br>Shriya Saran |
| Cinematography | K. Prasad |
| Edited by | Marthand K. Venkatesh |
| Music by | Vandemataram Srinivas |
| Release date | * March 25, 2005 (2005-03-25) |
| Country | India |
| Language | Telugu |


title: Sada Cowan

abstract: Sada Louise Cowan (1882–1943) was an American writer who began her career as a playwright. She soon switched to writing feature films and is best known for her work on the films Don't Change Your Husband and Why Change Your Wife?. Cowan worked closely with director Cecil B. DeMille throughout her career.

text:
# Sada Cowan

**Sada Louise Cowan** (1882–1943) was an American writer who began her career as a playwright. She soon switched to writing feature films and is best known for her work on the films *Don't Change Your Husband* and *Why Change Your Wife?*. Cowan worked closely with director Cecil B. DeMille throughout her career.

## Early life

Sada Louise Cowan was born on September 8, 1882, in Boston, Massachusetts. She attended a private boarding school in the Boston area. However, as a teenager Cowan moved to Germany to study music. After finding that writing music was not fulfilling enough for her she switched to writing plays. In Frankfurt, Germany, she wrote her first hit play from start to finish in two hours titled, *Sintram of Skagerrak*. Cowan's inspiration for writing this play was hearing Frederick Lamond’s piano recital of Chopin. She started to write plays that got her name on the map. These were titled *The State Forbids*, *In the Morgue*, *Playing the Game*, *The Moonlit Way*, *The Wonder of the Age*, *The Honor of America* and *Pomp,* respectively.

## Silent film

After success writing plays, Cowan switched over to writing full length silent films. In 1919, at thirty-six years old, her first film, *The Woman Under Cover*, starring Fritzi Brunette, was completed. The film was described by the *Exhibitors Herald* as heavily dramatic but with frequent and smartly placed bits of humor dispersed within it. This successful film led to Cowan’s writing of numerous others, in which she worked with directors such as Harry Garson and Cecil B. DeMille. Some of Cowan’s most popular films include *The Reckless Lady* and *The Charmer*.

## *Why Change Your Wife?*

*Why Change Your Wife?*, directed by Cecil B. DeMille, was one of Cowan’s most successful films. This film blazed a trail of “light and merry” films to follow it and included the wealth, clothing, and romance for which the 1920s are remembered. The film starred Gloria Swanson and Bebe Daniels and depicted the story of a man's marriage trials and tribulations between his first and second wives. The film cost $130,000 to produce and made $1,000,000. This was Cowan's first film that she wrote under director Cecil B. DeMille. At the time she was making only $25 a week, which was eventually raised to $60 per week. At first, DeMille dismissed her as a “failed writer” and believed her to be not capable of success. However, after the success of this film, and the many others she worked on with DeMille, she became one of his top writers and highest-paid staff members.

## Impact on the industry

The majority of Cowan's films revolve around the themes of marriage, divorce, love and infidelity. Cowan was a pioneer for women's writers in film. She was joined in her time by two other prominent women writers in the industry, Frances Marion and June Mathis. Cowan was one of the first American writers to travel abroad to Europe and work with foreign directors. She has written and received writing credit on numerous famous films from the 1920s and '30s.

## Personal life

Cowan was married two times, with both marriages resulting in divorce. Her first marriage was to Frederick James Pitt. In 1929, Cowan remarried to Dr. Ernest L. Commons. After her second marriage, Cowan's whereabouts were relatively unknown, with many speculating she was traveling around Europe or the Orient. However, in 1932 that she came back into the picture of American writers.

## Death

Cowan died on July 31, 1943, at the age of 60, in Los Angeles. The final film that she worked on was *Samson and Delilah* was released in 1950, seven years after her passing.

## Filmography

Media related to Sada Cowan at Wikimedia Commons

## InfoBox

| Sada Cowan | |
| --- | --- |
| Cowan in 1921 | |
| Born | Sada Louise Cowan
(1882-09-08)September 8, 1882
Boston, Massachusetts |
| Died | July 31, 1943(1943-07-31) (aged 60)
Los Angeles, California |
| Occupation | Playwright, screenwriter |
| Notable works |  |


title: Brooke A. Flinders

abstract: Brooke A. Flinders is an American nurse midwife and academic administrator who is the incoming president of Frontier Nursing University.

text:
# Brooke A. Flinders

**Brooke A. Flinders** is an American nurse midwife and academic administrator who is the incoming president of Frontier Nursing University.

## Life

Flinders earned an A.S. (1994) and B.S. (2003) in nursing from Miami University. She completed a M.S. in nursing and a doctor of nursing practice from Frontier Nursing University.

Flinders is a certified nurse-midwife. She became a fellow of the American College of Nurse-Midwives in 2021. She was a professor of nursing and an associate provost for faculty affairs at Miami University. On August 1, 2024, Flinders starts her role as the president of Frontier Nursing University.

## InfoBox

| Brooke A. Flinders | |
| --- | --- |
|  | |
| President of Frontier Nursing University | |
| **Incumbent** | |
| **Assumed office**
August 1, 2024 | |
| Preceded by | Susan Stone |
|  | |
| Personal details | |
| Education | Miami University
Frontier Nursing University |
|  | |


title: Brooke Abel

abstract: Brooke Abel is an American synchronized swimmer who competed in the women's team event at the 2008 Summer Olympics. Brooke began swimming with the Riverside AQuettes as a child and trained under Sue Baross Nesbitt. In 2003, Brooke Abel, Meryl Grandia, and Caitlin Stewart were Junior National Trio Champions. She went on to swim with the American team at the IX Junior World Championships in Moscow, Russia, in 2004, where they placed 4th. Brooke Abel also appeared on an episode of the television series Switched in 2003.

text:
# Brooke Abel

**Brooke Abel** (born February 15, 1988) is an American synchronized swimmer who competed in the women's team event at the 2008 Summer Olympics.

Brooke began swimming with the Riverside AQuettes as a child and trained under Sue Baross Nesbitt. In 2003, Brooke Abel, Meryl Grandia, and Caitlin Stewart were Junior National Trio Champions. She went on to swim with the American team at the IX Junior World Championships in Moscow, Russia, in 2004, where they placed 4th.

Brooke Abel also appeared on an episode of the television series Switched in 2003.

## InfoBox

Brooke Abel
| Personal information | |
| --- | --- |
| Full name | Brooke Abel |
| National team | United States |
| Born | (1988-02-15) February 15, 1988<br>Northridge, California |
| Height | 5 ft 4 in (1.63 m) |
| Weight | 115 lb (52 kg) |
| Sport | |
| Sport | Swimming |
|  | |
| Strokes | Synchronized swimming |
| Club | Riverside Aquettes |
|  | |


title: Brookula charleenae

abstract: Brookula charleenae is a species of sea snail, a marine gastropod mollusk unassigned in the superfamily Seguenzioidea.

text:
# Brookula charleenae

***Brookula charleenae*** is a species of sea snail, a marine gastropod mollusk unassigned in the superfamily Seguenzioidea.

## Description

The size of the shell varies between 0.8 mm and 1.4 mm.

## Distribution

This marine species occurs off the South Sandwich Islands, found at a depth of 2700 m.

* Schwabe E. & Engl W. (2008). *Description of two new deep-water species of the genus Brookula Iredale, 1912 (Mollusca, Gastropoda, Trochoidea), with a revision of the genus for the Subantarctic and Arctic Sector of the Atlantic Ocean*. Zootaxa, 1866: 187–204
* Engl W. (2012) *Shells of Antarctica*. Hackenheim: Conchbooks. 402 pp.

## InfoBox

| *Brookula charleenae* | |
| --- | --- |
|
| Scientific classification | |
| Domain: | Eukaryota |
| Kingdom: | Animalia |
| Phylum: | Mollusca |
| Class: | Gastropoda |
| Subclass: | Vetigastropoda |
| Family: | *incertae sedis* |
| Genus: | *Brookula* |
| Species: | ***B. charleenae*** |
| Binomial name | |
| ***Brookula charleenae***<br>Schwabe & Engl, 2008 | |
|


title: British flag theorem

abstract:
In Euclidean geometry, the British flag theorem says that if a point P is chosen inside a rectangle ABCD then the sum of the squares of the Euclidean distances from P to two opposite corners of the rectangle equals the sum to the other two opposite corners.
As an equation: A P 2 + C P 2 = B P 2 + D P 2. The theorem also applies to points outside the rectangle, and more generally to the distances from a point in Euclidean space to the corners of a rectangle embedded into the space. Even more generally, if the sums of squares of distances from a point P to the two pairs of opposite corners of a parallelogram are compared, the two sums will not in general be equal, but the difference between the two sums will depend only on the shape of the parallelogram and not on the choice of P. The theorem can also be thought of as a generalisation of the Pythagorean theorem. Placing the point P on any of the four vertices of the rectangle yields the square of the diagonal of the rectangle being equal to the sum of the squares of the width and length of the rectangle, which is the Pythagorean theorem.

text:
# British flag theorem

In Euclidean geometry, the **British flag theorem** says that if a point *P* is chosen inside a rectangle *ABCD* then the sum of the squares of the Euclidean distances from *P* to two opposite corners of the rectangle equals the sum to the other two opposite corners. As an equation: $AP^{2}+CP^{2}=BP^{2}+DP^{2}.$

The theorem also applies to points outside the rectangle, and more generally to the distances from a point in Euclidean space to the corners of a rectangle embedded into the space. Even more generally, if the sums of squares of distances from a point *P* to the two pairs of opposite corners of a parallelogram are compared, the two sums will not in general be equal, but the difference between the two sums will depend only on the shape of the parallelogram and not on the choice of *P*.

The theorem can also be thought of as a generalisation of the Pythagorean theorem. Placing the point *P* on any of the four vertices of the rectangle yields the square of the diagonal of the rectangle being equal to the sum of the squares of the width and length of the rectangle, which is the Pythagorean theorem.

## Proof

Drop perpendicular lines from the point *P* to the sides of the rectangle, meeting sides *AB*, *BC*, *CD*, and *AD* at points *W*, *X*, *Y* and *Z* respectively, as shown in the figure. These four points *WXYZ* form the vertices of an orthodiagonal quadrilateral. By applying the Pythagorean theorem to the right triangle *AWP*, and observing that *WP* = *AZ*, it follows that

$$AP^{2}=AW^{2}+WP^{2}=AW^{2}+AZ^{2}$$

and by a similar argument the squares of the lengths of the distances from *P* to the other three corners can be calculated as

$$PC^{2}=WB^{2}+ZD^{2},$$

$BP^{2}=WB^{2}+AZ^{2},$ and

$$PD^{2}=ZD^{2}+AW^{2}.$$

Therefore:

$$\begin{aligned}AP^{2}+PC^{2}&=\left(AW^{2}+AZ^{2}\right)+\left(WB^{2}+ZD^{2}\right)\\\\[4pt\]&=\left(WB^{2}+AZ^{2}\right)+\left(ZD^{2}+AW^{2}\right)\\\\[4pt\]&=BP^{2}+PD^{2}\end{aligned}$$

## Isosceles trapezoid

The British flag theorem can be generalized into a statement about (convex) isosceles trapezoids. More precisely for a trapezoid $ABCD$ with parallel sides $AB$ and $CD$ and interior point $P$ the following equation holds:

$$|AP|^{2}+{\frac {|AB|}{|CD|}\cdot |PC|^{2}=|BP|^{2}+{\frac {|AB|}{|CD|}\cdot |PD|^{2}}}$$

In the case of a rectangle the fraction $\tfrac {|AB|}{|CD|}$ evaluates to 1 and hence yields the original theorem.

## Naming

This theorem takes its name from the fact that, when the line segments from *P* to the corners of the rectangle are drawn, together with the perpendicular lines used in the proof, the completed figure resembles a Union Flag.

## Further reading


title: Bruce Warner

abstract: David Bruce Warner is a South African alpine skier. He is the only person ever to have represented South Africa at the Winter Paralympic Games, and he is one of only two Africans to have competed at the Games to date. Warner lost a leg in a car crash in 1988. Having previously intended to make a career in hockey, he subsequently embarked on a career in skiing. In addition to the Paralympic Games, he has competed in events such as the Disabled World Championships. He is an electrical engineer by profession.

text:
# Bruce Warner

**David Bruce Warner** (born 5 June 1971, in Bloemfontein) is a South African alpine skier. He is the only person ever to have represented South Africa at the Winter Paralympic Games, and he is one of only two Africans (along with Ugandan Tofiri Kibuuka) to have competed at the Games to date.

Warner lost a leg in a car crash in 1988. Having previously intended to make a career in hockey, he subsequently embarked on a career in skiing. In addition to the Paralympic Games, he has competed in events such as the Disabled World Championships.

He is an electrical engineer by profession.

## Paralympic career

### 1998

South Africa made its Paralympic Games début at the 1998 Winter Paralympics in Nagano, Japan. Warner was his country's sole representative. He entered four events, all in alpine skiing, in the LW2 category.

* In the Men's downhill, he finished 25th (out of 30), with a calculated time of 1:19.25.
* In the Men's giant slalom, he finished 19th (out of 37), with a calculated time of 3:08.90. Only 21 competitors out of 37, however, successfully completed the event.
* In the Men's slalom, he finished 20th (out of 38), with a calculated time of 2:21.57. Only 25 competitors reached the finish line.
* In the Men's super-G, he finished 21st (out of 34), with a calculated time of 1:25.61. 26 competitors reached the finish line.

### 2002

Warner was, for the second time, his country's sole representative. He entered the same four events.

* In the Men's downhill, he finished 15th (out of 21), with a calculated time of 1:32.30.
* In the Men's giant slalom, he failed to finish.
* In the Men's slalom, he finished 9th (out of 27), with a calculated time of 1:40.29.
* In the Men's super-G, he finished 12th (out of 23), with a calculated time of 1:23.17.

### 2006

Warner was, for the third time, his country's sole representative. He entered the same four events, in the standing category.

* In the Men's downhill, he finished 36th (out of 49), with a calculated time of 1:31.18.
* In the Men's giant slalom, he finished 45th (out of 66), with a calculated time of 2:19.39.
* In the Men's slalom, he finished 27th (out of 64), with a calculated time of 1:33.29.
* In the Men's super-G, he finished 38th (out of 55), with a calculated time of 1:18.33.

### 2010

Warner was, once again, his country's only representative at the 2010 Winter Paralympics in Vancouver.