Tusi's writings influenced European mathematicians including Wallis; his revisions of the Ptolemaic model led him to the Tusi-couple, a special case of trochoids usually called Copernicus' Theorem, though historians have concluded Copernicus discovered this theorem by reading Tusi.

The earliest mathematician to whom definite teachings can be ascribed was Lagadha, who apparently lived about BC and used geometry and elementary trigonometry for his astronomy.

Youth and early work Allen Konigsberg grew up in Brooklyn in a family steeped in Jewish culture. I suspect that Archimedes accepted heliocentrism, but thought saying so openly would distract from his work.

While Europe was in its early "Dark Age," Aryabhata advanced arithmetic, algebra, elementary analysis, and especially plane and spherical trigonometry, using the decimal system. While some Greeks, notably Aristarchus and Seleucus of Seleucia and perhaps also Heraclides of Pontus or ancient Egyptiansproposed heliocentric models, these were rejected because there was no parallax among stars.

Gersonides was also an outstanding astronomer.

Al-Farisi made several other corrections in his comprehensive commentary on Alhazen's textbook on optics. Hippocrates is most famous for his work on the three ancient geometric quandaries: He studied under Philolaus of Croton, was a friend of Plato, and tutored Eudoxus. Eudoxus was the first great mathematical astronomer; he developed the complicated ancient theory of planetary orbits; and may have invented the astrolabe.

Ancient Persians and Mayans did have place-value notation with zero symbols, but neither qualify as inventing a base decimal system: For example, some of Euclid's more difficult theorems are easy analytic consequences of Archimedes' Lemma of Centroids. After a decade of working with United ArtistsAllen switched the financing of his films to Orion Pictures.

While Pythagoras had been horrified by the discovery of irrational numbers, Eudoxus is famous for incorporating them into arithmetic. There are many famous quotations about Euclid and his books.

Archytas introduced "motion" to geometry, rotating curves to produce solids. In mathematics, he popularized the use of the decimal system, developed spherical geometry, wrote on many other topics and was a pioneer of cryptography code-breaking. He defined congruums and proved theorems about them, including a theorem establishing the conditions for three square numbers to be in consecutive arithmetic series; this has been called the finest work in number theory prior to Fermat although a similar statement was made about one of Bhaskara II's theorems.

He preserved some of the teachings of Aryabhata which would otherwise have been lost; these include a famous formula giving an excellent approximation to the sin function, as well as, probably, the zero symbol itself.

Please send me e-mail if you believe there's a major flaw in my rankings or an error in any of the biographies. Apastambha ca BC India The Dharmasutra composed by Apastambha contains mensuration techniques, novel geometric construction techniques, a method of elementary algebra, and what may be an early proof of the Pythagorean Theorem.

Some of this may have been added after the time of Chang; some additions attributed to Liu Hui are mentioned in his mini-bio; other famous contributors are Jing Fang and Zhang Heng.

Archimedes' Equiarea Map Theorem asserts that a sphere and its enclosing cylinder have equal surface area as do the figures' truncations.

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