# Convex Optimization in Normed Spaces by Juan Peypouquet download in ePub, pdf, iPad

He is less famous in part because he lived in a remote part of the Islamic empire. There is some evidence that the Hindus borrowed the decimal system itself from books like Nine Chapters. Other discoveries known only second-hand include the Archimedean semiregular solids reported by Pappus, and the Broken-Chord Theorem reported by Alberuni. Most famous was the Problem of Apollonius, which is to find a circle tangent to three objects, with the objects being points, lines, or circles, in any combination.

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. In addition to discoveries always attributed to him, he may be the source of several of Euclid's theorems, and some works attributed to Eudoxus and perhaps Pythagoras. He requested that a representation of such a sphere and cylinder be inscribed on his tomb. Hipparchus himself was influenced by Babylonian astronomers. The decimal place-value system with zero symbol seems to be an obvious invention that in fact was very hard to invent.

There are ingenious solutions available with other tools. Some think his best inspiration was recognizing that the Parallel Postulate must be an axiom rather than a theorem. Aryabhata made several important discoveries in astronomy, e.

Book I starts with an elegant proof that rigid-compass constructions can be implemented with a collapsing compass. Earlier Hindus, including Brahmagupta, contributed to this method.

Only fragments survive but it apparently used axiomatic-based proofs similar to Euclid's and contains many of the same theorems. He invented pharmaceutical methods, perfumes, and distilling of alcohol. Heliocentrism The mystery of celestial motions directed scientific inquiry for thousands of years.

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