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Evidence showed that ancient Babylonians are responsible for the discovery that a circle contains 360 equal parts. They used the "Babylonian mile" to measure time, known as time-miles. 12 time-miles could be completed in an entire day, or revolution in the sky. Partitioning the Babylonian mile into 30 parts and multiplying that by the number of of time-miles in one day equates to 360.
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Though little is known about his life and the full extent of his mathematical works, we do know Pythagorus discovered the Pythagorean theorem, triangular numbers, introduced the study of musical scales with mathematics, and took the first steps in developing number theory.
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During his life time, Euclid founded Euclidean tools (the unmarked straightedge and compass), as his postulates in "Elements" are proved through the use of these tools. He explains how to use these tools and bases his proofs off the use of these tools.
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Abu al-Wafa' makes discoveries and advances in geometric constructions with a compass at a fixed opening, as well as trigonometric tables.
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In 1260 in China, Yung Hui gave the earliest surviving presentation of what is now known as Pascal’s arithmetic triangle.
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Chinese mathematician Chu Shih Chieh depicts the arithmetic triangle.
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At only 23 years old, Newton invents Calculus during his time away from Trinity College. He originally created calculus to prove planetary motion. When Robert Hooke and Newton disagreed on a particle being released into the center of the Earth, Newton refused to be wrong and then worked out the mathematics of planetary orbits.
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Gauss made noteworthy contributions to almost all areas of mathematics. His greatest contributions were those involving the complex number, as he introduced the standard notation (a+bi), promoted the practice of graphing complex numbers, and expanded the area of complex numbers. He is considered the first mathematician to coin the term “non-Euclidean geometry” and discovered that self-consistent non-Euclidean geometries could be constructed.
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Though multiple mathematicians contributed efforts into this revolution of mathematics, Karl Weierstrass created a program to rigorize the real number system, thus leading to all of analysis being logically derive from a postulate set that characterizes the real number system.