How did the Egyptians create the perfectly round pillars of their buildings?
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We invented the concept of pi before the Greeks. Using higher math, we were able to create a perfect circle in three dimensions. Scultping the columns only required a complex circular leveling device using water which we invented in the 8th dynasty.
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It was believed that he saw the shadows of the pillars on the tiled temple floor, that looked like a right angled triangle with squares attached. \nFrom there he developed his theory that the square drawn on the hypotenuse of a right angled triangle, is equal in area to the sum of the squares drawn on the other two sides.\nPythagoras put forward a proof, but said proof contained errors to do with transient numbers, however it seemed the theory was sound.\nSome two centuries later the Great Euclid himself proved it, with his brilliant proof using congruent triangles, true poetry of geometry.
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They have pillars in the front area. There are three types of pillars, Doric, Ionic and Corinthian the latter is the most spectacular.
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Check this site:\nhttp://www.funsms.net/egypt.htm
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Angles associated with a Pyramid\n\ncheck out the site for the mathematical equation\n\n\n\n\n\n            In mathematics, the term pyramid refers to a rather general type of geometric solid.  One can find the definition here.  But the pyramids that one finds in different parts of the world generally have a rectangular base with the apex directly above the center of the base.  Most of the pyramids in Egypt actually have a square base and are therefore quite symmetrical. The four faces are isosceles triangles and are congruent to each other.  The shape of such a pyramid is determined by the angle that each face makes with the base, i.e. the angle formed by the horizontal line joining the midpoint of the base of a face to the center of the pyramid and the slanted line joining that midpoint to the apex of the pyramid.    That angle could be any angle between 0o and 90o. If that angle is close to 90o, then the pyramid would be very tall and would seem like a simple, pointed obelisk.  If that angle is close to 0o, then the pyramid would be almost flat and one would  probably be unhappy calling it a pyramid.  But the shape is also determined by various other quantities.  For example, the angle that each edge of the pyramid makes with the base would be sufficient.  (That angle is formed by the horizontal line joining a corner of the pyramid to the center and the edge joining that corner to the apex.)   Either of these angles is determined by its slope, or the inverse of its slope.  In modern Western Mathematics,  it would be customary to specify either angle by its slope, but the discussions of pyramids that one finds in the Egyptian Mathematical Papyri suggest that the Egyptian architect would have specified an angle by the inverse of its slope. For the slant-angle of the faces of a pyramid, the inverse-slope is referred to as the "seked" of the pyramid in the Rhind papyrus. \n\nhttp://www.math.washington.edu/~greenber/slope.html
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pyramids of egypt\nhanging gardens of babylon\nstatue of zeus\nTemple of Artemis (Diana) at Ephesus \nMausoleum at Halicarnassus \nColossus at Rhodes \nPharos (Lighthouse) of Alexandria \n\nmore explanations:\n\nSince ancient times, numerous “seven wonders” lists have been created. The content of these lists tends to vary, and none is definitive. The seven wonders that are most widely agreed upon as being in the original list are the Seven Wonders of the Ancient World, which was compiled by ancient Greek historians and is thus confined to the most magnificent structures known to the ancient Greek world. Of all the Ancient Wonders, the pyramids alone survive. \n\nThe Pyramids of Egypt are three pyramids at Giza, outside modern Cairo. The largest pyramid, built by Khufu (Cheops), a king of the fourth dynasty, had an original estimated height of 482 ft (now approximately 450 ft). The base has sides 755 ft long. It contains 2,300,000 blocks; the average weight of each is 2.5 tons. Estimated date of completion is 2680 B.C. \n\nThe Hanging Gardens of Babylon were supposedly built by Nebuchadnezzar around 600 B.C. to please his queen, Amuhia. They are also associated with the mythical Assyrian queen Semiramis. Archeologists surmise that the gardens were laid out atop a vaulted building, with provisions for raising water. The terraces were said to rise from 75 to 300 ft.\n\nThe Statue of Zeus (Jupiter) at Olympia was made of gold and ivory by the Greek sculptor Phidias (5th century B.C.). Reputed to be 40 ft high, the statue has been lost without a trace, except for reproductions on coins.\n\nThe Temple of Artemis (Diana) at Ephesus was begun about 350 B.C., in honor of a non-Hellenic goddess who later became identified with the Greek goddess of the same name. The temple, with Ionic columns 60 ft high, was destroyed by invading Goths in A.D. 262.\n\nThe Mausoleum at Halicarnassus was erected by Queen Artemisia in memory of her husband, King Mausolus of Caria in Asia Minor, who died in 353 B.C. Some remains of the structure are in the British Museum. This shrine is the source of the modern word mausoleum.\n\nThe Colossus at Rhodes was a bronze statue of Helios (Apollo), about 105 ft high. The work of the sculptor Chares, who reputedly labored for 12 years before completing it in 280 B.C., it was destroyed during an earthquake in 224 B.C.\n\nThe Pharos (Lighthouse) of Alexandria was built by Sostratus of Cnidus during the 3rd century B.C. on the island of Pharos off the coast of Egypt. It was destroyed by an earthquake in the 13th century.
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Use clay and then you'll be able to form the 3d shapes
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Lots of slave labor, donkey carts, ropes, rolling logs, mules, wagons...the wheel was invented during the building of the time of the Pyramids.
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The shape of Egyptian pyramids is thought to represent the primordial mound from which the Egyptians believed the earth was created. The shape is also thought to be representative of the descending rays of the sun, and most pyramids were faced with polished, highly reflective white limestone, in order to give them a brilliant appearance when viewed from a distance. Pyramids were often also named in ways that made reference to solar luminescence. For example, the formal name of the Bent Pyramid at Dahshur was The Southern Shining Pyramid, and that of Senwosret at el-Lahun was Senwosret is Shining.\n\nWhile it is generally agreed that pyramids were burial monuments, there is continued disagreement on the particular theological principles that might have given rise to them. One theory that has gained a degree of acceptance is that they were designed as a type of "resurrection machine";[8] the Egyptians believed the dark area of the night sky around which the stars appear to revolve was the physical gateway into the heavens, and co-incidentally, one of the narrow shafts that extends from the main burial chamber through the entire body of the Great Pyramid points directly towards the centre of this part of the sky. This suggests the pyramid may have been designed to serve as a means to magically launch the deceased pharaoh's soul directly into the abode of the gods.\n\nAll Egyptian pyramids were built, without exception, on the west bank [9] of the Nile, which as the site of the setting sun was associated with the realm of the dead in Egyptian mythology.
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Pyramids in Egypt served as tombs, initially only for kings and close members of the royal family, but eventually came to be used (in much smaller forms) by the general populace.\n\nThe pyramid is thought to have developed out of the mastaba tomb. Mastaba is an Arabic word, meaning bench, which was applied to the flat-topped, slope sided superstructures of tombs. The pyramid is also thought to be associated with solar worship and the "ben-ben" stone which played a major role in sun worship and was vaguely pyramid shaped.\n\nIn the 3rd Dynasty, several mastabas were stacked forming the Step Pyramid of King Djoser. By the 4th Dynasty in the reign of Snefru attempts at building a true pyramid were underway. The pyramids of the 4th and 5th Dynasties, including those at Giza, essentially reflect the further refinement of the pyramid, the chambers within it, and the associated temple complexes. Eventually the standard style was an orientation of east to west (significant in Egyptian religion), with a pyramid temple, located directly on the east side of the pyramid, and a causeway leading to the "valley temple" located near the Nile at the edge of the cultivation.\nWhile it is accepted by reputable Egyptologists that pyramids served as burials for kings, the exact details of the theology behind them remains unclear. One idea, popularized I believe by Dr. Mark Lehner, one of the foremost experts on Egyptian pyramids, is that pyramids served as "resurrection machines" providing all the necessary means for eternal life with the gods for the dead king.\nIn the late 5th Dynasty in the Pyramid of Unas at Saqqara, we have the first appearance of formal texts within the pyramid itself - the appropriately-named Pyramid Texts. These texts are somewhat esoteric and are essentially a collection of spells, stories, and guides relating to the Underworld. Initially these texts were limited to royalty. In succeeding pyramids, elements of the Pyramid Texts were included in the "Coffin Texts" of the First Intermediate and Middle Kingdom and in the "Book of the Dead" of the New Kingdom - texts available to a broad spectrum of society.\n\nPyramid construction continued in the Middle Kingdom - again limited to royalty, but not on the grand scale of the Old Kingdom. The last known royal pyramids located in Egypt are that of King Ahmose, founder of the 18th Dynasty of the New Kingdom (ca. 1550 BCE) and the pyramid-cenotaph constructed for his grandmother, Queen Tetisheri. Both are located at Abydos.\n\nIn the New Kingdom, pyramids came to be part of tombs for reasonably wealthy private individuals - frequently added to the exterior portico area of rock-cut cliff tombs or appearing as architectural elements of brick constructed tombs in varous parts of Egypt.\n\nThe Napatan and Meroitic kingdoms in Nubia (modern Sudan) also used the pyramid for royal burials at sites such as El-Kurru and Nuri. While the Napatan kings ruled Egypt for a time during the 25th Dynasty and were buried in pyramids, those pyramids were located in Nubia proper.\n\nPyramid construction relied on highly skilled teams of workmen who were housed nearby the pyramid fields - in the Old Kingdom located in the general vicinity of the ancient capital Memphis at sites now knows as Giza, Saqqara, Meidum, and Dashur. A few pyramids in the Middle Kingdom were located near the Fayum, roughly Middle Egypt.\nIn addition to the full-time workmen, there was likely a seasonal labor requirement asked of the lower classes of Egyptian society - a sort of taxation, often referred to by the French term "corvee" labor. This is distinct from slavery. While the ancient Greek historian Herodotus (writing over a thousand years after the construction of the pyramids at Giza) reported that he was told the pyramids at Giza were constructed by slaves, Herodotus was wrong about any number of things in his reports and may not even have visited Egypt in perso
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I'm thinking of the Moorish architecture in Spain that was built in the Middle Ages.  They are the ones with domed ceilings and arched doorways.  Their architectural achievements were copied throughout Europe.\n\nSue
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Nor inside ANY of the ancient egyptian monuments made prior to the Roman invasion in 52 B.C. The egyptians used another mechanism:Mirrors!\nYes they used a complicated system of mirrors to reflect the day light all the way inside the huge monuments they've built, which were siometimes several hundereds of feet high (like the pryamids, which aremore than 80 pyramids, the most famous of which,the biggest, but not the oldest, are the 3 giza pyramids) or far below the ground(tutemoses grave and other similarly fabulous graves in valley of the kings, or dug several meters deep inside solid granite mountains (like "Dir El Bahary" temple of hatshipsut)\nYes, as agatha christie said,they did it with mirrors :)
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I'm not entirely sure to what it is you're referring.  Most Egyptian pyramids are built of stone blocks or slabs - roughly dressed on the interior and smoothed on the exterior.  Typically the stone is limestone for the exterior, with the occasional use of granite on lower courses.  Interior chambers in the pyramid itself or subterranean chambers were frequently lined with a different type of stone - granite was a popular choice.\n\nThe peaks of the larger (ie. royal) pyramids are now large flat spaces now that stone has been robbed out and the pyramidia (capstones) have been removed.  The capstones, from what we know from contemporary inscriptions and a few examples that have actually been found were essentially little pyramids in miniature, each face was inscribed with the name of the pyramid  - each royal pyramid was named, usually a name including the nomen and/or prenomen of the king for whom it was built.  Additional inscriptions usually concerned the sun god and/or were specific to the cardinal direction that face of the pyramid faced.\n\nIt is extraordinarily unlikely that Egyptian pyramids serve as radio receivers and even more unlikely that they were designed to do so.  They were tombs.
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If there was sand under the Egyptian pyramids they would have fallen down by now.  Some that were built on poor foundations already have fallen down.  The Great Pyramids near Cairo were built on a rocky plateau and that is why they are still in good condition.  They have burial chambers under them cut into the rock but the chamber under the biggest was not used.  \n\nBy the time these big pyramids were built the ancient Egyptians had a few hundred years experience in building them so they knew just exactly what they were doing.  You can see some of their earlier efforts in this site.\n\nhttp://www.touregypt.net/featurestories/dsteppyramid1.htm\n\nThe only real mystery attached to the Egyptian pyramids is why they put so much resources into them. \n\nThe answer is "rock".
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When you put your parts together, make them in the shape of triangles. Triangles are the strongest shape for building a simple construction like the one you're making. Make your structure with many triangles. For example, if you can, make your entire structure in the shape of a triangle, and also connect the sides of the big triangle with lots of smaller ones.
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"In antiquity, jewellery often contains, in the form of chains and applied decoration, large amounts of wire that is accurately made and which must have been produced by some efficient, if not technically advanced, means. In some cases, strips cut from metal sheet were made by pulling them through perforations in stone beads. This causes the strips to fold round on themselves to form thin tubes. This strip drawing technique was in use in Egypt by the 2nd Dynasty. From the middle of the 2nd millennium BC most of the gold wires in jewellery are characterised by seam lines that follow a spiral path along the wire. Such twisted strips can be converted into solid round wires by rolling them between flat surfaces or the strip wire drawing method. Strip and block twist wire manufacturing methods were still in use in Europe in the 7th century AD, but by this time there seems to be some evidence of wires produced by true drawing. Square and hexagonal wires were possibly made using a swaging technique. In this method a metal rod was struck between grooved metal blocks, or between a grooved punch and a grooved metal anvil. Swaging is of great antiquity, possibly dating to the beginning of the 2nd millennium BC in Egypt and in the Bronze and Iron Ages in Europe for torcs and fibulae. Twisted square section wires are a very common filigree decoration in early Etruscan jewellery. In about the middle of the 2nd millennium BC a new category of decorative wires was introduced which imitated a line of granules. Perhaps the earliest such wire is the notched wire which first occurs from the late 3rd, early 2nd millennium BC in Anatolia and occasionally later.\n\n"Wire was drawn in England from the medieval period. The wire was used to make wool cards and pins, manufactured goods whose import was prohibited by Edward IV in 1463. The first wire mill in Great Britain was established at Tintern in about 1568 by the founders of the Company of Mineral and Battery Works, who had a monopoly on this. Apart from their second wire mill at nearby Whitebrook, there were no other wire mills before the second half of the 17th century. Despite the existence of mills, the drawing of wire down to fine sizes continued to be done manually.\n\n"Wire is usually drawn of cylindrical form; but it may be made of any desired section by varying the outline of the holes in the draw-plate through which it is passed in the process of manufacture. The draw-plate or die is a piece of hard cast-iron or hard steel, or for fine work it may be a diamond or ruby. The object of utilizing precious stones is to enable the dies to be used for a considerable period without losing their size, and so producing wire of incorrect diameter. Diamond dies must be rebored when they have lost their original diameter of hole, but the metal dies are brought down to size again by hammering up the hole and then drifting it out to correct diameter with a punch."
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Make right triangles with the height as one leg, a radius (segment from center of base to one of its vertices) as the other leg, and lateral edge as the hypotenuse.  The radius will equal the length of the base edge as it's a side of an equilateral triangle.  So 10^2 + 15^2 will equal lateral edge squared.\n\nSlant height would be the hypotenuse of a right triangle with legs of the pyramid's height, and the apothem (distance from center of base to midpoint of a side.)  You can get the apothem from Pythagorean theorem from the right triangle formed by half a base edge, a radius, and the apothem.  Then use the apothem in another Pythagorean theorem to get slant height.\n\nLateral area = 6 times the area of any one triangle.  Each triangle's area is 1/2 times 10 times slant height.\n\nVolume = 1/3 (area of base)(height).  The area of the base is 1/2 (apothem)(perimeter).\n\nThose are the steps.  Hope you can figure them out from this typing!