Timeline
Antiquity to 500 CE
| Date | Event | Who | Where | Sources |
|---|---|---|---|---|
| c. 490 BCE | Zeno of Elea born; his paradoxes of motion and plurality state the problems limits and measure theory would later address Disputed: Date inferred from the dramatic setting of Plato's Parmenides, not from a document | Zeno of Elea | Elea, southern Italy | Source 7, Huggett |
| c. 460 BCE | Democritus born; he asserts that a cone is one third of its cylinder, treating a solid as a stack of indivisible slices Disputed: Known only from Archimedes' Method (recovered 1906) and Plutarch, De Comm. Not. adv. Stoicos xxxix.3 | Democritus | Abdera, Thrace | Source 2, Heath |
| c. 370 BCE | Eudoxus makes the method of exhaustion rigorous and defines equal ratios (Euclid, Elements V, Def. 5) Disputed: All of Eudoxus' own works are lost; dated from his floruit | Eudoxus | Cnidus / Athens | Source 1, Heath; Source 8, O'Connor |
| c. 250 BCE | Archimedes writes The Method of Mechanical Theorems to Eratosthenes, explaining how he discovers theorems by weighing infinitesimal slices Disputed: Heath's approximate dating | Archimedes | Syracuse | Source 2, Heath |
| c. 250 BCE | Archimedes proves a parabolic segment is 4/3 of the inscribed triangle (Quadrature of the Parabola) and brackets pi between 3+10/71 and 3+1/7 using a 96-gon | Archimedes | Syracuse | Source 1, Heath |
| 212 BCE | Archimedes killed in the sack of Syracuse; he had asked for a sphere in a cylinder on his tomb | Archimedes | Syracuse | Source 1, Heath |
| 263 CE | Liu Hui completes his commentary on the Nine Chapters, supplying proofs, cutting the circle to a 3072-gon for pi, and admitting he cannot find the sphere's volume | Liu Hui | Kingdom of Wei, China | Source 20, Guo; Source 22, O'Connor; Source 23, Wagner |
| 462 CE | Zu Chongzhi proposes the Daming calendar, the first Chinese calendar to allow for precession of the equinoxes | Zu Chongzhi | Jiankang (Nanjing) | Source 21, O'Connor |
| late 5th c. CE | Zu Gengzhi states the equal-cross-sections principle and derives the volume of a sphere, about 1100 years before Cavalieri | Zu Gengzhi | Liang dynasty China | Source 23, Wagner |
| 499 CE | Aryabhata completes the Aryabhatiya at age 23, containing the first known sine table and pi = 62832/20000, expressly called approximate | Aryabhata I | Kusumapura, India | Source 50, Ramasubramanian; Source 59, O'Connor |