He is remembered primarily for his cosmology based on water as the essence of all matter, with Earth a flat disk floating on a vast sea.

(a)  

He has been credited with the discovery of five geometric theorems: (1) that a circle is bisected by its diameter, (2) that angles in a triangle opposite two sides of equal length are equal, (3) that opposite angles formed by intersecting straight lines are equal, (4) that the angle inscribed inside a semicircle is a right angle, and (5) that a triangle is determined if its base and the two angles at the base are given.

(a)  

His questioning approach to the understanding of heavenly phenomena was the beginning of Greek astronomy.

(a)  

He seems to be the first known Greek philosopher, scientist and mathematician although his occupation was that of an engineer. He is believed to have been the teacher of Anaximander and he was the first natural philosopher in the Milesian School.

(a)  

It is reported that he predicted an eclipse of the Sun in 585 BC. The cycle of about 19 years for eclipses of the Moon was well known at this time but the cycle for eclipses of the Sun was harder to spot since eclipses were visible at different places on Earth. His prediction of the 585 BC eclipse was probably a guess based on the knowledge that an eclipse around that time was possible.

(a)  

Hieronymus says that he succeeded in measuring the pyramids by observation of the length of their shadow at the moment when our shadows are equal to our own height.

(a)  

It was he who first conceived the principle of explaining the multitude of phenomena by a small number of hypotheses for all the various manifestations of matter. He believed that the Earth floats on water and all things come to be from water. For him the Earth was a flat disc floating on an infinite ocean. It has also been claimed that he explained earthquakes from the fact that the Earth floats on water. Again the importance of his idea is that he is the first recorded person who tried to explain such phenomena by rational rather than by supernatural means.

(a)  

He is often described as the first pure mathematician. He is an extremely important figure in the development of mathematics yet we know relatively little about his mathematical achievements. Unlike many later Greek mathematicians, where at least we have some of the books which they wrote, we have nothing of his writings. The society which he led, half religious and half scientific, followed a code of secrecy which certainly means that today he is a mysterious figure.

(a)  

His father was Mnesarchus and his mother was Pythais.

(a)  

He was well educated, learning to play the lyre, learning poetry and to recite Homer. There were, among his teachers, three philosophers who were to influence him while he was a young man. They were Pherekydes, Thales and Anaximander.

(a)  

It is not difficult to relate many of his beliefs, ones he would later impose on the society that he set up in Italy, to the customs that he came across in Egypt. For example the secrecy of the Egyptian priests, their refusal to eat beans, their refusal to wear even clothes made from animal skins, and their striving for purity were all customs that he would later adopt.

(a)  

He founded a philosophical and religious school in Croton (now Crotone, on the east of the heel of southern Italy) that had many followers. He was the head of the society with an inner circle of followers known as mathematikoi. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians. They were taught by him and obeyed strict rules.

(a)  

The beliefs that he held were: (1) that at its deepest level, reality is mathematical in nature,(2) that philosophy can be used for spiritual purification,(3) that the soul can rise to union with the divine,(4) that certain symbols have a mystical significance, and(5) that all brothers of the order should observe strict loyalty and secrecy.

(a)  

He was interested in the principles of mathematics, the concept of number, the concept of a triangle or other mathematical figure and the abstract idea of a proof.

(a)  

He 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. In fact he made remarkable contributions to the mathematical theory of music. He was a fine musician, playing the lyre, and he used music as a means to help those who were ill.

(a)  

Each number had its own personality - masculine or feminine, perfect or incomplete, beautiful or ugly. This feeling modern mathematics has deliberately eliminated, but we still find overtones of it in fiction and poetry. Ten was the very best number: it contained in itself the first four integers - one, two, three, and four [1 + 2 + 3 + 4 = 10] - and these written in dot notation formed a perfect triangle.

(a)  

He was one of the most famous and controversial ancient Greek philosophers, lived from ca. 570 to ca. 490 BCE. He spent his early years on the island of Samos, off the coast of modern Turkey. At the age of forty, however, he emigrated to the city of Croton in southern Italy and most of his philosophical activity occurred there.

(a)  

He presented a cosmos that was structured according to moral principles and significant numerical relationships and may have been akin to conceptions of the cosmos found in Platonic myths, such as those at the end of the Phaedo and Republic. In such a cosmos, the planets were seen as instruments of divine vengeance (“the hounds of Persephone”), the sun and moon are the isles of the blessed where we may go, if we live a good life, while thunder functioned to frighten the souls being punished in Tartarus. The heavenly bodies also appear to have moved in accordance with the mathematical ratios that govern the concordant musical intervals in order to produce a music of the heavens, which in the later tradition developed into “the harmony of the spheres.”

(a)  

He is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements. The long lasting nature of The Elements must make him the leading mathematics teacher of all time. However little is known of his life except that he taught at Alexandria in Egypt.

(a)  

He also wrote the following books which have survived: Data (with 94 propositions), which looks at what properties of figures can be deduced when other properties are given; On Divisions which looks at constructions to divide a figure into two parts with areas of given ratio; Optics which is the first Greek work on perspective; and Phaenomena which is an elementary introduction to mathematical astronomy and gives results on the times stars in certain positions will rise and set. His following books have all been lost: Surface Loci (two books), Porisms (a three book work with, according to Pappus, 171 theorems and 38 lemmas), Conics (four books), Book of Fallacies and Elements of Music.

(a)  

He is often referred to as the “Father of Geometry”, and he wrote perhaps the most important and successful mathematical textbook of all time, the “Stoicheion”, which represents the culmination of the mathematical revolution which had taken place in Greece up to that time. He also wrote works on the division of geometrical figures into into parts in given ratios, on catoptrics (the mathematical theory of mirrors and reflection), and on spherical astronomy (the determination of the location of objects on the “celestial sphere”), as well as important texts on optics and music.

(a)  

He was a Greek mathematician and astronomer who substantially advanced proportion theory, contributed to the identification of constellations and thus to the development of observational astronomy in the Greek world, and established the first sophisticated, geometrical model of celestial motion. He also wrote on geography and contributed to philosophical discussions in Plato's Academy. Although none of his writings survive, his contributions are known from many discussions throughout antiquity.

(a)  

His contributions to the early theory of proportions (equal ratios) forms the basis for the general account of proportions found in Book V of Elements (c. 300 BCE). Where previous proofs of proportion required separate treatments for lines, surfaces, and solids, he provided general proofs. It is unknown, however, how much later mathematicians may have contributed to the form found in the Elements. He certainly formulated the bisection principle that given two magnitudes of the same sort one can continuously divide the larger magnitude by at least halves so as to construct a part that is smaller than the smaller magnitude.

(a)  

Two of his proofs were based on the method of exhaustion: that the volumes of pyramids and cones are one-third the volumes of prisms and cylinders, respectively, with the same bases and heights. Various traces suggest that his proof of the latter began by assuming that the cone and cylinder are commensurable, before reducing the case of the cone and cylinder being incommensurable to the commensurable case.

(a)  

He also proved that the areas of circles are proportional to the squares of their diameters. He is also probably largely responsible for the theory of irrational magnitudes of the form a ± b (found in the Elements, Book X), based on his discovery that the ratios of the side and diagonal of a regular pentagon inscribed in a circle to the diameter of the circle do not fall into the classifications of Theaetetus of Athens. He also contributed a solution to the problem of doubling the cube — that is, the construction of a cube with twice the volume of a given cube.

(a)  

Perhaps his greatest fame stems from his being the first to attempt, in On Speeds, a geometric model of the motions of the Sun, the Moon, and the five planets known in antiquity. His model consisted of a complex system of 27 interconnected, geo-concentric spheres, one for the fixed stars, four for each planet, and three each for the Sun and Moon.

(a)  

He also wrote an ethnographical work (“Circuit of the Earth”) of which fragments survive. It is plausible that he also divided the spherical Earth into the familiar six sections (northern and southern tropical, temperate, and arctic zones) according to a division of the celestial sphere.

(a)  

He is the most innovative Greek mathematician before Archimedes. His work forms the foundation for the most advanced discussions in Elements and set the stage for Archimedes’ study of volumes and surfaces. The theory of proportions is the first completely articulated theory of magnitudes. Although most astronomers seem to have abandoned his astronomical views by the middle of the 2nd century BCE, his principle that every celestial motion is uniform and circular about the centre endured until the time of the 17th-century astronomer Johannes Kepler. Dissatisfaction with Ptolemy's modification of this principle (where he made the centre of the uniform motion distinct from the centre of the circle of motion) motivated many medieval and Renaissance astronomers, including Nicolaus Copernicus (1473–1543).

(a)  

He was a Greek geometer who compiled the first known work on the elements of geometry nearly a century before the Elements. Although the work is no longer extant, it may have been used in the Elements.

(a)  

According to tradition, he was a merchant whose goods had been captured by pirates. He went to Athens to prosecute them but met with little success in recovering his property. He remained in Athens, however, where he attended lectures on mathematics and finally took up teaching geometry to support himself. Aristotle (384–322 BC) recounts a different story, claiming that he was cheated by customs officers in Byzantium; he purportedly did so to show that, although he was a good geometer, he was incompetent to handle the ordinary affairs of life.

(a)  

In his attempts to square the circle, he was able to find the areas of certain lunes, or crescent-shaped figures contained between two intersecting circles. He based this work upon the theorem that the areas of two circles have the same ratio as the squares of their radii.

(a)  

The third of the achievements attributed to him was the discovery that, given a cube of side a, a cube with double its volume can be constructed if two mean proportionals, x and y, can be determined such that a:x = x:y = y:2a. It is also generally thought that he introduced the tactic of reducing a complex problem to a more tractable or simpler problem. His reduction of the problem of "doubling the cube" (a three-dimensional quantity) to finding two lengths (one-dimensional quantities) certainly fits this

(a)  

He was a Greek astronomer and mathematician who made fundamental contributions to the advancement of astronomy as a mathematical science and to the foundations of trigonometry. Although he is commonly ranked among the greatest scientists of antiquity, very little is known about his life, and only one of his many writings is still in existence. Knowledge of the rest of his work relies on second-hand reports, especially in the great astronomical compendium the Almagest, written by Ptolemy in the 2nd century CE.

(a)  

As a young man in Bithynia, he compiled records of local weather patterns throughout the year. Such weather calendars (parapēgmata), which synchronized the onset of winds, rains, and storms with the astronomical seasons and the risings and settings of the constellations, were produced by many Greek astronomers from at least as early as the 4th century BCE.

(a)  

He also wrote critical commentaries on some of his predecessors and contemporaries. In Tōn Aratou kai Eudoxou Phainomenōn exēgēseōs biblia tria (“Commentary on the Phaenomena of Aratus and Eudoxus”), his only surviving book, he ruthlessly exposed errors in Phaenomena, a popular poem written by Aratus and based on a now-lost treatise of Eudoxus of Cnidus that named and described the constellations. Apparently his commentary Against the Geography of Eratosthenes was similarly unforgiving of loose and inconsistent reasoning. Ptolemy characterized him as a “lover of truth” (philalēthēs) — a trait that was more amiably manifested in his readiness to revise his own beliefs in the light of new evidence. He communicated with observers at Alexandria in Egypt, who provided him with some times of equinoxes, and probably also with astronomers at Babylon.

(a)  

His most important astronomical work concerned the orbits of the Sun and Moon, a determination of their sizes and distances from Earth. and the study of eclipses. Like most of his predecessors — Aristarchus of Samos was an exception — he assumed a spherical, stationary Earth at the centre of the universe (the geocentric cosmology). From this perspective, the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn (all of the solar system bodies visible to the naked eye), as well as the stars (whose realm was known as the celestial sphere), revolved around Earth each day.

(a)  

His most significant contribution to mathematics may have been to develop — if not actually invent — a trigonometry based on a table of the lengths of chords in a circle of unit radius tabulated as a function of the angle subtended at the centre. Such a table would, for the first time, allow a systematic solution of general trigonometric problems, and clearly he used it extensively for his astronomical calculations. Like so much of his work, his chord table has not survived.

(a)  

He was a Greek geometer and inventor whose writings preserved for posterity a knowledge of the mathematics and engineering of Babylonia, ancient Egypt, and the Greco-Roman world.

(a)  

His most important geometric work, Metrica, was lost until 1896. It is a compendium, in three books, of geometric rules and formulas that he gathered from a variety of sources, some of them going back to ancient Babylon, on areas and volumes of plane and solid figures. Book I enumerates means of finding the area of various plane figures and the surface areas of common solids. Included is a derivation of a formula bearing his name (actually, Archimedes formula) for the area A of a triangle. Book I also contains an iterative method known by the Babylonians (c. 2000 BC) for approximating the square root of a number to arbitrary accuracy. (A variation on such an iterative method is frequently employed by computers today.) Book II gives methods for computing volumes of various solids, including the five regular Platonic solids. Book III treats the division of various plane and solid figures into parts according to some given ratio.

(a)  

He was an important geometer and worker in mechanics who invented many machines including a steam turbine. His best known mathematical work is the formula for the area of a triangle in terms of the lengths of its sides.

(a)  

He was an Egyptian astronomer, mathematician, and geographer of Greek descent who flourished in Alexandria during the 2nd century CE. In several fields his writings represent the culminating achievement of Greco-Roman science, particularly his geocentric (Earth-centered) model of the universe.

(a)  

He also attempted to place astrology on a sound basis in Apotelesmatika (“Astrological Influences”), later known as the Tetrabiblos for its four volumes. He believed that astrology is a legitimate, though inexact, science that describes the physical effects of the heavens on terrestrial life. He accepted the basic validity of the traditional astrological doctrines, but he revised the details to reconcile the practice with an Aristotelian conception of nature, matter, and change. Of his writings, the Tetrabiblos is the most foreign to modern readers, who do not accept astral prognostication and a cosmology driven by the interplay of basic qualities such as hot, cold, wet, and dry.

(a)  

This mathematician was also an astronomer, philosopher, who lived in a very turbulent era in Alexandria's history. She is the earliest female mathematician of whose life and work reasonably detailed knowledge exists.

(a)  

(a)   is credited with commentaries on Apollonius of Perga's Conics (geometry) and Diophantus of Alexandria's Arithmetic (number theory), as well as an astronomical table. These works, the only ones listed as having written, have been lost, although there have been attempts to reconstruct aspects of them. In his time, he was the world's leading mathematician and astronomer, a popular teacher and lecturer in philosophical topics of a less-specialist nature, attracting many loyal students and large audiences.

He came to symbolze learning and science which the early Christians identified with paganism. However, among the pupils whom he taught in Alexandria there were many prominent Christians. One of the most famous is Synesius of Cyrene who was later to become the Bishop of Ptolemais. Many of the letters that Synesius wrote to him have been preserved and we see someone who was filled with admiration and reverence for his learning and scientific abilities.

(a)  

He was the most important mathematical author writing in Greek during the later Roman Empire, known for his Synagoge (“Collection”), a voluminous account of the most important work done in ancient Greek mathematics. Other than that he was born at Alexandria in Egypt and that his career coincided with the first three decades of the 4th century AD, little is known about his life. Judging by the style of his writings, he was primarily a teacher of mathematics. He seldom claimed to present original discoveries, but he had an eye for interesting material in his predecessors’ writings, many of which have not survived outside of his work. As a source of information concerning the history of Greek mathematics, he has few rivals.

(a)  

He wrote several works, including commentaries on Ptolemy's Almagest and on the treatment of irrational magnitudes in Euclid's Elements. His principal work, however, was the Synagoge (c. 340), a composition in at least eight books (corresponding to the individual rolls of papyrus on which it was originally written). The only Greek copy of the Synagoge to pass through the Middle Ages lost several pages at both the beginning and the end; thus, only Books 3 through 7 and portions of Books 2 and 8 have survived. A complete version of Book 8 does survive, however, in an Arabic translation. Book 1 is entirely lost, along with information on its contents. The Synagoge seems to have been assembled in a haphazard way from independent shorter writings of him. Nevertheless, such a range of topics is covered that the Synagoge has with some jsutice been described as a mathematical encyclopedia.

(a)  

He is the last of the great Greek geometers and one of his theorems is cited as the basis of modern projective geometry. He wrote commentaries on Euclid's Elements and Ptolemy's Almagest.

(a)  

He was a Greek mathematician known as 'The Great Geometer'. His works had a very great influence on the development of mathematics and his famous book Conics introduced the terms parabola, ellipse and hyperbola.

(a)  

He was also an important founder of Greek mathematical astronomy, which used geometrical models to explain planetary theory. Ptolemy in his book Syntaxis says that this mathematician introduced systems of eccentric and epicyclic motion to explain the apparent motion of the planets across the sky. This is not strictly true since the theory of epicycles certainly predates him. Nevertheless, he did make substantial contributions particularly using his great geometric skills. In particular, he made a study of the points where a planet appears stationary, namely the points where the forward motion changes to a retrograde motion or the converse.

(a)  

There were also applications made by him, using his knowledge of conics, to practical problems. He developed the hemicyclium, a sundial which has the hour lines drawn on the surface of a conic section giving greater accuracy.

(a)  

He was a mathematician, known by his contemporaries as “the Great Geometer,” whose treatise Conics is one of the greatest scientific works from the ancient world. Most of his other treatises are now lost, although their titles and a general indication of their contents were passed on by later writers. His work inspired much of the advancement of geometry in the Islamic world in medieval times, and the rediscovery of his Conics in Renaissance Europe formed a good part of the mathematical basis for the scientific revolution.

(a)  

He was a Greek mathematician sometimes known as 'the father of algebra' who is best known for his Arithmetica. This had an enormous influence on the development of number theory.

(a)  

He also appears to know that every number can be written as the sum of four squares. If indeed he did know this result it would be truly remarkable for even Fermat, who stated the result, failed to provide a proof of it and it was not settled until Lagrange proved it using results due to Euler.

(a)  

Two works have come down to us under his name, both incomplete. The first is a small fragment on polygonal numbers (a number is polygonal if that same number of dots can be arranged in the form of a regular polygon). The second, a large and extremely influential treatise upon which all the ancient and modern fame of Diophantus reposes, is his Arithmetica. Its historical importance is twofold: it is the first known work to employ algebra in a modern style, and it inspired the rebirth of number theory.

(a)  

After some generalities about numbers, he explains his symbolism — he uses symbols for the unknown (corresponding to our x) and its powers, positive or negative, as well as for some arithmetic operations — most of these symbols are clearly scribal abbreviations. This is the first and only occurrence of algebraic symbolism before the 15th century. After teaching multiplication of the powers of the unknown, he explains the multiplication of positive and negative terms and then how to reduce an equation to one with only positive terms (the standard form preferred in antiquity). With these preliminaries out of the way, he proceeds to the problems.

(a)  

Although he had limited algebraic tools at his disposal, he managed to solve a great variety of problems, and the Arithmetica inspired Arabic mathematicians such as al-Karaji (c. 980–1030) to apply his methods. The most famous extension of his work was by Pierre de Fermat (1601–65), the founder of modern number theory who wrote various remarks, proposing new solutions, corrections, and generalizations of his methods as well as some conjectures such as Fermat's Last Theorem, which occupied mathematicians for generations to come. Indeterminate equations restricted to integral solutions have come to be known, though inappropriately, as an equation bearing his name.

(a)  

He was a Greek scientific writer, astronomer, and poet, who made the first measurement of the size of Earth for which any details are known.

(a)  

At Syene (now Aswān), some 800 km (500 miles) southeast of Alexandria in Egypt, the Sun's rays fall vertically at noon at the summer solstice. He noted that at Alexandria, at the same date and time, sunlight fell at an angle of about 7.2° from the vertical. (Writing before the Greeks adopted the degree, a Babylonian unit of measure, he actually said “a fiftieth of a circle.”) He correctly assumed the Sun’s distance to be very great; its rays therefore are practically parallel when they reach Earth. Given an estimate of the distance between the two cities, he was able to calculate the circumference of Earth, obtaining 250,000 stadia.

(a)  

He also measured the degree of obliquity of the ecliptic (in effect, the tilt of Earth’s axis) and wrote a treatise on the octaeteris, an eight-year lunar-solar cycle. He is credited with devising an algorithm for finding prime numbers called a sieve bearing his name, in which one arranges the natural numbers in numerical order and strikes out one, every second number following two, every third number following three, and so on, which just leaves the prime numbers.

(a)  

His only surviving work is Catasterisms, a book about the constellations, which gives a description and story for each constellation, as well as a count of the number of stars contained in it, but the attribution of this work has been doubted by some scholars. His mathematical work is known principally from the writings of the Greek geometer Pappus of Alexandria, and his geographical work from the first two books of the Geography of the Greek geographer Strabo.

(a)  

After study in Alexandria and Athens, he settled in Alexandria about 255 BCE and became director of the great library there. He tried to fix the dates of literary and political events since the siege of Troy. His writings included a poem inspired by astronomy, as well as works on the theatre and on ethics. He was afflicted by blindness in his old age, and he is said to have committed suicide by voluntary starvation.

(a)  

He was the most famous mathematician and inventor in ancient Greece. He is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. He is known for his formulation of a known hydrostatic principle and a known device for raising water, still used.

(a)  

He published his works in the form of correspondence with the principal mathematicians of his time, including the Alexandrian scholars Conon of Samos and Eratosthenes of Cyrene. He played an important role in the defense of Syracuse against the siege laid by the Romans in 213 BCE by constructing war machines so effective that they long delayed the capture of the city. When Syracuse eventually fell to the Roman genera Marcus Claudius Marcellus in the autumn of 212 or spring of 211 BCE, he was killed in the sack of the city.

(a)  

He said "Give me a place to stand and I will move the Earth."

(a)  

While it is true that — apart from a dubious reference to a treatise, “On Sphere-Making”—all of his known works were of a theoretical character, his interest in mechanics nevertheless deeply influenced his mathematical thinking. Not only did he write works on theoretical mechanics and hydrostatics, but his treatise Method Concerning Mechanical Theorems shows that he used mechanical reasoning as a heuristic device for the discovery of new mathematical theorems.

(a)  

He was the greatest mathematician of his age. His contributions in geometry revolutionized the subject and his methods anticipated the integral calculus. He was a practical man who invented a wide variety of machines including pulleys and his known screw pumping device.

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

Who is this mathematician?

(a)  

He was a medieval Italian mathematician who wrote Liber abaci (1202; “Book of the Abacus”), the first European work on Indian and Arabian mathematics, which introduced Hindu-Arabic numerals to Europe. His name is mainly known because of a known sequence.

(a)  

When his Liber Abaci first appeared, Hindu-Arabic numerals were known to only a few European intellectuals through translations of the writings of the 9th-century Arab mathematician al-Khwarizmi. The first seven chapters dealt with the notation, explaining the principle of place value, by which the position of a figure determines whether it is a unit, 10, 100, and so forth, and demonstrating the use of the numerals in arithmetical operations. The techniques were then applied to such practical problems as profit margin, barter, money changing, conversion of weights and measures, partnerships, and interest. Most of the work was devoted to speculative mathematics — proportion (represented by such popular medieval techniques as the Rule of Three and the Rule of Five, which are rule-of-thumb methods of finding proportions), the Rule of False Position (a method by which a problem is worked out by a false assumption, then corrected by proportion), extraction of roots, and the properties of numbers, concluding with some geometry and algebra. In 1220 he produced a brief work, the Practica geometriae (“Practice of Geometry”), which included eight chapters of theorems based on Euclid's Elements and On Divisions.

(a)