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About 500BC

The Babylonian sexagesimal number system is used to record and predict the positions of the Sun, Moon and planets. (See this History Topic.)

About 500BC

Panini's work on Sanskrit grammar is the forerunner of the modern formal language theory.

About 465BC

Hippasus writes of a "sphere of 12 pentagons", which must refer to a dodecahedron.

About 450BC

Greeks begin to use written numerals. (See this History Topic.)

About 450BC

Zeno of Elea presents his paradoxes.

About 440BC

Hippocrates of Chios writes the *Elements* which is the first compilation of the elements of geometry.

About 430BC

Hippias of Elis invents the quadratrix which may have been used by him for trisecting an angle and squaring the circle.

About 425BC

Theodorus of Cyrene shows that certain square roots are irrational. This had been shown earlier but it is not known by whom.

About 400BC

Babylonians use a symbol to indicate an empty place in their numbers recorded in cuneiform writing. There is no indication that this was in any way thought of as a number. (See this History Topic.)

387BC

Plato founds his Academy in Athens

About 375BC

Archytas of Tarentum develops mechanics. He studies the "classical problem" of doubling the cube and applies mathematical theory to music. He also constructs the first automaton.

About 360BC

Eudoxus of Cnidus develops the theory of proportion, and the method of exhaustion.

About 340BC

Aristaeus writes Five Books concerning Conic Sections.

About 330BC

Autolycus of Pitane writes *On the Moving Sphere* which studies the geometry of the sphere. It is written as an astronomy text.

About 320BC

Eudemus of Rhodes writes the *History of Geometry*.

About 300BC

Euclid gives a systematic development of geometry in his *Stoicheion* (*The Elements*). He also gives the laws of reflection in *Catoptrics*.

About 290BC

Aristarchus of Samos uses a geometric method to calculate the distance of the Sun and the Moon from Earth. He also proposes that the Earth orbits the Sun.

About 250BC

In *On the Sphere and the Cylinder*, Archimedes gives the formulae for calculating the volume of a sphere and a cylinder. In *Measurement of the Circle* he gives an approximation of the value of π with a method which will allow improved approximations. In *Floating Bodies* he presents what is now called "Archimedes' principle" and begins the study of hydrostatics. He writes works on two- and three-dimensional geometry, studying circles, spheres and spirals. His ideas are far ahead of his contemporaries and include applications of an early form of integration.

About 235BC

Eratosthenes of Cyrene estimates the Earth's circumference with remarkable accuracy finding a value which is about 15% too big.

About 230BC

Nicomedes writes his treatise *On conchoid lines* which contain his discovery of the curve known as the "Conchoid of Nicomedes".

About 230BC

Eratosthenes of Cyrene develops his sieve method for finding all prime numbers. (See this History Topic.)

About 225BC

Apollonius of Perga writes *Conics* in which he introduces the terms "parabola", "ellipse" and "hyperbola".

About 200BC

Diocles writes *On burning mirrors*, a collection of sixteen propositions in geometry mostly proving results on conics.

About 200BC

Possible earliest date for the classic Chinese work *Jiuzhang suanshu* or *Nine Chapters on the Mathematical Art*. (See this History Topic.)

About 180BC

Date of earliest Chinese document *Suanshu shu* (A Book on Arithmetic). (See this History Topic.)

About 150BC

Hypsicles writes *On the Ascension of Stars*. In this work he is the first to divide the Zodiac into 360 degrees.

127BC

Hipparchus discovers the precession of the equinoxes and calculates the length of the year to within 6.5 minutes of the correct value. His astronomical work uses an early form of trigonometry.

About 1AD

Chinese mathematician Liu Hsin uses decimal fractions.

List of mathematicians alive in 500BC.

List of mathematicians alive in 1AD.

JOC/EFR May 2015
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