What roles did Hipparchus and Claudius Ptolemy play in the development of trigonometry?
145859
check out the link below. Hope it helps!
567674
Blaise Pascal? He invented the calculator. Maybe Isaac Newton, the inventor of calculus, or Charles Babbage, the inventor of the computer. Perhaps John Napier, who discovered how to add, subtract, multiply, divide, and even extract square roots simply by moving pieces on a chessboard? Tell you what, pick René Descartes, he's the inventor of coordinate geometry. These are all excellent choices!
1159729
Euclid of Alexandria (Greek: Εὐκλείδης) (ca. 325 BC–265 BC), a Greek mathematician, who lived in Alexandria, Egypt almost certainly during the reign of Ptolemy I (323 BC–283 BC), is often considered to be the "father of geometry". \nhttp://en.wikipedia.org/wiki/Euclid\n\nIt seems Euclid is the father, by general consent! -\nhttp://mathforum.org/library/drmath/view/52508.html\n\nEuclid, who is considered the father of mathematics, taught in Egypt at Alexandria.\nhttp://everyschool.org/u/logan/culturalmath/afmathematicians.htm\n\nPythagoras (approximately 582 BC–507 BC, Greek: Πυθαγόρας) was an Ionian (Greek) mathematician and philosopher, founder of the mystic, religious and scientific society called Pythagoreans, and is known best for the Pythagorean theorem which bears his name. Known as "the father of numbers":\nhttp://en.wikipedia.org/wiki/Pythagoras\n\nArchimedes (Greek: Αρχιμήδης ) (c. 287 BC – 212 BC) was an ancient Greek mathematician, physicist, engineer, astronomer, and philosopher born in the seaport colony of Syracuse, Sicily. He is considered by some historians of mathematics to be one of the greatest mathematicians in antiquity; Carl Friedrich Gauss considered him one of the two greatest ever (the other being himself.)\nhttp://en.wikipedia.org/wiki/Archimedes\n\nAl-Khwarizmi is held to be the father of algebra:\nhttp://www.math.umd.edu/~czorn/hist_algebra.pdf\n\nRene Descartes (March 31, 1596 – February 11, 1650), also known as Cartesius, is considered to be the father of modern mathematics:\nhttp://en.wikipedia.org/wiki/Rene_Descartes\nhttp://www.hi.is/~joner/eaps/descart2.htm
248907
The Dioptra was another surveying instrument that was utilized by Roman Surveyors.  It was used to measure horizontal and vertical angles and could also be used as a leveling instrument and for astronomical observations as well.  As with most instruments used by the surveyors of the Roman Empire, the Dioptra was not an original invention of the Romans, but was developed by the Greeks and implemented by the Romans.  There are very few remains of the Dioptra and the estimation of the replication of this instrument vary from reference to reference.  The best recollection of the description of what the Dioptra may have looked like and its uses comes from the records of Hero of Alexandria.  Hero, a Greek, described the use of the Dioptra, however many of the important details regarding the construction of the instrument were either lost or destroyed.  Since there has not been any concrete evidence to the contrary, it is believed that the Romans used the Dioptra in much the same way as the Greeks did and the design of the Roman Dioptra was parallel to that of the Greek origin.\n\nThe staff of the Dioptra may have been a three-legged instrument, similar to today's tripod or possibly a monopole with three points at the base to assist in keeping it vertical.  Either of these types of staffs were approximately the equivalent of 7-7 U.S. Survey Feet in height.  At the top of the staff, was a circular plate with a cylinder attached to it.  This plate and cylinder allowed for rotation.  At the top of the cylinder was another circular plate, approximately 30 inches in diameter.  This plate was made of wood and was divided and marked into 360 degrees.  Although the Dioptra was divided into degrees, it is believed that these measurements were mainly used for astronomical observations.  However, the Greeks and Romans did have the knowledge and ability to use trigonometry, so it is possible that they used the Dioptra for horizontal angle measurement as well.\n\nAnother instrument used for leveling that could be placed on the tripod or monopole instead of the Dioptra was the water level.  This instrument was a linear bar made of wood and was approximately the equivalent of 6-7 U.S. Survey Feet in length, 1-1/2 inches thick and 2 inches in width.  In the center of the instrument, a groove was cut.  A vertical metal tube would be placed in the groove and the ends of the tube would protrude upwards approximately 1-1/2 inches from each end of the wooden bar.  A flat bar placed over the metal tube would assist in keeping the tube firmly in place.  In each end piece of the tubing, a glass cylinder would be fitted.  This cylinder was approximately the same height as the metal tube.  The glass cylindrical tube would be filled with water.  At the base of each end piece, a revolving rod or screw would be placed.  These screws would be used to move the instrument up or down until the surveyor determined it to be level.\n\nAn alternative method of leveling implemented by Roman Surveyors was by using an instrument call a Chorobate.  Since this instrument was made primarily of wood, there are virtually no remains still in existence today.  However, the descriptions for the design of the Chorobate and its use have been recovered.  It is believed that the Chorobate was used mainly for leveling in aqueducts.  Because of its massive size and weight, it would not have been as practical and appropriate as the Dioptra in laying out roadways.\n\nThe Chorobate was approximately 20 Roman Feet in length and was made predominantly of wood.  The Chorobate was elevated from the ground by wooden supports approximately 1-2 Roman Feet in height.  At the base of the supports were wooden braces, which had vertical marks across the face.  Plumb lines were hung from the supports and when the plumb lines on each end of the Chorobate touched the respective vertical marks simultaneously, the instrument would be level.  In windy conditions, a different method for using the Chorob
631440
The Ancient Greeks knew the world was round.  Their work in mathematics and geography allowed them to calculate the approximate curvature and circumference of the Earth.  The Romans also knew the world was round.  So much of the information from the Classical world was destroyed either during the burning of the library at Alexandria or during the many purges and book-burnings of the Dark Ages.  Much more information was hidden by the Church and forbidden.  Both the Renaissance and the Age of Exploration were about a return to the enlightened times of Classical Europe.  Christopher Columbus theorized that the Earth was not flat, and attempted to sail to Asia in 1492.  He thought he had reached Asia, but it turns out that the Earth was much larger than expected.  He simply re-discovered the Western Hemisphere.
182867
The basic observations were done thousands of years ago. THe ancient Greeks knew that the direction of the pole changes over time (also known as the progression of the equinoxes). Of course, it wasn't until recently that this effect was explained by the wobble of the earths axis. It used to be seen as just another cosmic cycle.
259099
calculations or math actually started way back ,no reference to an exact time but the indians during the 3rd century B.C were well advanced in maths , and so were the greeks,egyptians and chinese.
473889
Since ancient history regarding the concept.\n\nHistory of the notation:\n\nThe symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler. In either case, 'π' is the first letter of περιφέρεια (periphereia, the Greek word for periphery) or περίμετρον (perimetron), meaning 'measure around' in Greek.
1012191
It started with the Egyptians, expanded by Greeks, Indians and Romans and united with Algebra by Descartes. Riemann unseated Euclid and his geometry was used by Einstien for the Relativity theory.
1075126
Descartes made one of the greatest advances in geometry by connecting algebra and geometry. A myth is that he was watching a fly on the ceiling when he conceived of locating points on a plane with a pair of numbers. Maybe this has something to do with the fact that he stayed in bed everyday until 11:00 A.M. Fermat also discovered coordinate geometry, but it's Descartes' version that we use today.\n\nCo-ordinate Geometry\nCo-ordinate geometry was introduced by Fermat and Descartes, ignoring rather than solving the foundational problems which had prevented the Greeks from taking this step (viz: the lack of any well understood number system which could account for incommensurable ratios). \nThis development is important to science because it makes geometry quantitative and permits the use of algebraic methods. Geometry must be quantitative for it to be useful in science and engineering, and algebraic methods permit more rapid development of mathematics than the less systematic (if more rigourous) methods required by the Greek axiomatic approach to geometry. \n \nIn co-ordinate geometry the points of a plane are labelled by 2 co-ordinates, its distances from the 2 axes, and familiar figures become the loci of points satisfying an algebraic equation. Thus, geometry is incorporated into algebra and the way is opened for the introduction of spaces of arbitrarily large dimension, important in mechanics. Curvature, in its simplest form, is a number attached to a surface at a point. The flatter the surface, the smaller the number (positive for a sphere, negative for a saddle-shaped surface). \nFrench mathematician who is often called the founder of the modern theory of numbers. Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. Independently of Descartes, Fermat discovered the fundamental principle of analytic geometry. His methods for finding tangents to curves and their maximum and minimum points led him to be regarded as the inventor of the differential calculus. Through his correspondence with Blaise Pascal he was a co-founder of the theory of probability.\n\n\nhttp://people.bath.ac.uk/jm255/Geometry.htm this website will help u aswell!\n\nAnalytic geometry, also called coordinate geometry and earlier referred to as Cartesian geometry, is the study of geometry using the principles of algebra. Usually the Cartesian coordinate system is applied to manipulate equations for planes, lines, curves, and circles, often in two and sometimes in three dimensions of measurement. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining geometrical shapes in a numerical way, and extracting numerical information from that representation. The numerical output, however, might also be a vector or a shape. Some consider that the introduction of analytic geometry was the beginning of modern mathematics.\n\nRené Descartes is popularly regarded as having introduced the foundation for the methods of analytic geometry in 1637 in the appendix titled Geometry of the titled Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences, commonly referred to as Discourse on Method. This work, written in his native language (French), and its philosophical principles, provided the foundation for calculus in Europe.\n\nThe relationship between algebra and geometry is nontrivial. There exist proofs of this relationship based on the theory of geometry and notions of geometric length.\n\n\n\nwrite this down and im finding more info ......
603384
you are rght about aristotle as it was Pythagoras (you know the theorem) 570 BC who hypothesised the curvature of the earth and the heavenly bodies,later the most notable writers on the positioning and behaviour of the planets were copernicus, gallaleio, kepler and newton
612662
Do a biography of Pythagoroas.
1022973
"Pythagoras of Samos was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music. He left Samos because of the tyrant who ruled there and went to southern Italy about 532 BC. He founded a philosophical and religious school in Croton that had many followers.\n\nAlthough the theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier he may have been the first to prove it.\n\nOf his actual work nothing is known. His school practised secrecy and communalism making it hard to distinguish between the work of Pythagoras and that of his followers. His school made outstanding contributions to mathematics.\n\nPythagoreans believed that all relations could be reduced to number relations. This generalisation stemmed from observations in music, mathematics and astronomy.\n\nThe Pythagoreans noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments.\n\nThe most important discovery of this school was the fact that the diagonal of a square is not a rational multiple of its side. This result showed the existence of irrational numbers. Not only did this disturb Greek mathematics but the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties was challenged by their own results.\n\nIn astronomy Pythagoras taught that the Earth was a sphere at the centre of the Universe. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star. "\n\nThere is some more on Pythagoras at\nhttp://www-history.mcs.st-and.ac.uk/~history.\nGo to the search menu and search for "pythagoras". Hope this answers your question.
170764
Plato, I guess. the Question is too vague. Plato's geocentric system was refuted by Copernicus, but the Catholic Church refused to accept Copernicus's findings.
730807
René Descartes is regarded as having invented analytic or coordinate geometry in 1637.  I can't find any information on who invented simultaneous equations.  However, the reason for this is clearly because they are much more ancient than Cartesian geometry.  The Indian mathematician Baudhayana was solving simultaneous equations as early as 800 BCE!  It is true that simultaneous equations have a relationship with coordinate geometry, because a system of equations is solved by a point that is the intersection of the curves represented by the equations.  However, this aspect of simultaneous equations is not fundamental to solving them.
24073
It was Pythagoras who was the first to question the flat earth theory, although probably just the most famous....incidently it was considered heracy at the time.
572647
SAGE VARAHA MIHIRA the father of ASTROLOGY . Even at a time when there were no telescopes developed and long before any other astronomers , he was able to observe the celestial beings and draw a chart on sand and make calculations and predict to the seconds what is going to take place,