Classical Geometry & Axiomatic Proofs: From Nine Chapters to Euclid
Encyclopedia/1. The Cosmos & The Natural World/1. Mathematics & Formal Systems/01. Geometry & Spatial Systems • Curated by Admin Timeline.sg
This timeline traces the parallel development of geometric deduction and spatial calculation across ancient civilizations, highlighting key milestones from Chinese, Indian, Greek, and Islamic traditions, including the Zhoubi Suanjing, Euclid's Elements, Liu Hui's Pi algorithm, and other foundational contributions up to 1600 CE.
Plimpton 322 Tablet By photo author unknown - image copied from http://www.math.ubc.ca/~cass/courses/m446-03/pl322/pl322.html, Public domain, https://commons.wikimedia.org/w/index.php?curid=1170904
800 BCE
Baudhayana Sulba Sutras
Indian text contains a statement of the Pythagorean theorem for constructing altars. #math #india
600 BCE
Thales' Geometry
Thales of Miletus introduces deductive geometry, proving theorems about circles and triangles. #math #greece
Thales' Geometry By Wilhelm Meyer - own scan, Public domain, https://commons.wikimedia.org/w/index.php?curid=11037570
500 BCE
Pythagorean School
Pythagoras and his followers study geometry, numbers, and the Pythagorean theorem. #math #greece
Pythagorean School By Unknown author - Photo by Szilas, 2013-03-04, Public domain, https://commons.wikimedia.org/w/index.php?curid=36520519
430 BCE
Hippocrates Quadrature of Lunes
Hippocrates of Chios squares lunes, showing that certain curvilinear areas can be computed. #math #geometry
Hippocrates Quadrature of Lunes By No machine-readable author provided. Audriusa assumed (based on copyright claims). - No machine-readable source provided. Own work assumed (based on copyright claims)., CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=478595
350 BCE
Aristotle on Axioms
Aristotle discusses axioms and deductive reasoning in Posterior Analytics, influencing mathematical proof. #philosophy #math
Aristotle on Axioms By After Lysippos - Jastrow (2006), Public domain, https://commons.wikimedia.org/w/index.php?curid=1359807
350 BCE
Mozi's Geometric Definitions
Mozi (Mohist) text includes definitions of geometric concepts like point, line, square. #math #china
Mozi's Geometric Definitions By Vjacheslav Rublevskiy - https://www.flickr.com/photos/193162016@N04/51221161306/, CC0, https://commons.wikimedia.org/w/index.php?curid=106219380
300 BCE
Euclid's Elements Published
Euclid compiles the Elements, a systematic axiomatic treatment of geometry, used for over two millennia. #math #geometry
Euclid's Elements Published By University of Pennsylvania Museum of Archaeology and Anthropology - https://openn.library.upenn.edu/Data/0016/html/e2748.html, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=169166171
300 BCE
Euclid's Parallel Postulate
Euclid states his fifth postulate, later challenged and leading to non-Euclidean geometry. #math #geometry
Euclid's Parallel Postulate By Dickdock - Own work based on: Parallel postulate.svg by Harkonnen2, Public domain, https://commons.wikimedia.org/w/index.php?curid=4559984
250 BCE
Archimedes Measures Circle
Archimedes approximates pi using inscribed and circumscribed polygons. #math #geometry
Archimedes Measures Circle By Domenico Fetti - http://archimedes2.mpiwg-berlin.mpg.de/archimedes_templates/popup.htm, Public domain, https://commons.wikimedia.org/w/index.php?curid=146592
240 BCE
Eratosthenes Measures Earth
Eratosthenes uses geometry to estimate the Earth's circumference. #math #geography
Eratosthenes Measures Earth By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=494949
200 BCE
Apollonius Conics
Apollonius of Perga writes Conics, defining parabola, ellipse, and hyperbola. #math #geometry
Apollonius Conics By Giovanni Battista Memo - File:ApolloniiPergeiOpera1537.jpg, Public domain, https://commons.wikimedia.org/w/index.php?curid=70830662
150 BCE
Liu Xin's Standard Measures
Chinese scholar Liu Xin uses geometry for standard volume measures. #math #china
100 BCE
Zhoubi Suanjing
Chinese mathematical text, 'The Arithmetical Classic of the Gnomon and Circular Paths', contains early geometry and the Gougu theorem. #math #china
Zhoubi Suanjing By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=104738
1 CE
Nine Chapters on the Mathematical Art
Chinese classic covering practical geometry, area calculations, and the Gougu theorem. #math #china
Nine Chapters on the Mathematical Art By 中國書店海王邨公司 - https://pmgs.kongfz.com/detail/1_158470/, Public domain, https://commons.wikimedia.org/w/index.php?curid=22913440
75 CE
Heron's Formula
Heron of Alexandria derives formula for triangle area using side lengths. #math #geometry
Heron's Formula By Jamgoodman - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=74872701
263 CE
Liu Hui's Pi Algorithm
Liu Hui improves pi approximation to 3.1416 using a 192-sided polygon. #math #china
Liu Hui's Pi Algorithm By Unknown - "Liu Hui (220 - 280) - Biography - MacTutor History of Mathematics" https://mathshistory.st-andrews.ac.uk/Biographies/Liu_Hui/, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=130481910
480 CE
Zu Chongzhi's Pi
Chinese mathematician Zu Chongzhi calculates pi between 3.1415926 and 3.1415927. #math #china
Zu Chongzhi's Pi By 三猎 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=54922069
499 CE
Aryabhata's Geometry
Indian mathematician Aryabhata gives accurate approximations of pi and area of a triangle. #math #india
Aryabhata's Geometry By Cpjha13 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=49883192
628 CE
Brahmagupta on Cyclic Quadrilaterals
Brahmagupta's Brāhmasphuṭasiddhānta provides formula for cyclic quadrilaterals. #math #india
820 CE
Al-Khwarizmi's Geometry
Al-Khwarizmi writes on geometry and algebra, influencing Islamic mathematics. #math #islam
Al-Khwarizmi's Geometry By Zarateman - Own work, CC0, https://commons.wikimedia.org/w/index.php?curid=162213187
900 CE
Thabit ibn Qurra's Geometry
Thabit ibn Qurra works on geometry of sections and translation of Greek works. #math #islam
1020 CE
Alhazen's Optics
Ibn al-Haytham (Alhazen) uses geometry in optics, analyzing reflection and refraction. #math #physics
Alhazen's Optics By Adolph Boÿ, engraved by Jeremias Falck. Used as the frontispiece to Johannes Hevelius, Selenographia, 1647 - https://www.loc.gov/resource/rbctos.2017rosen1321/?sp=9&r=0.059,0.617,0.327,0.182,0, Public domain, https://commons.wikimedia.org/w/index.php?curid=165125519
1025 CE
Al-Biruni's Geodesy
Al-Biruni measures Earth's radius using trigonometry and geometry. #math #geodesy
Al-Biruni's Geodesy By The original uploader was Romanm at Slovenian Wikipedia. - Originally from sl.wikipedia; description page is/was here., Public domain, https://commons.wikimedia.org/w/index.php?curid=2590841
1070 CE
Omar Khayyam's Geometric Algebra
Omar Khayyam solves cubic equations using conic sections. #math #islam
Omar Khayyam's Geometric Algebra By Alireza Javaheri - https://web.archive.org/web/20161024154356/http://www.panoramio.com/photo/85093358, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=55909539
1150 CE
Bhaskara II's Geometry
Bhaskara II writes Lilavati, covering geometry, trigonometry, and calculus-related ideas. #math #india
Bhaskara II's Geometry By Unknown author - Own work, Public domain, https://commons.wikimedia.org/w/index.php?curid=150275955
Fibonacci's Practica Geometriae By Taty2007 - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=5809387
1202 CE
Fibonacci's Liber Abaci
Fibonacci introduces Hindu-Arabic numerals but also includes geometric problems. #math #europe
Fibonacci's Liber Abaci By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=720501
1240 CE
Yang Hui's Magic Squares
Yang Hui develops magic squares and geometric puzzles. #math #china
Yang Hui's Magic Squares By Yáng Huī (楊輝), ca. 1238–1298) - w:en:Image:Yanghui_triangle.gif, Public domain, https://commons.wikimedia.org/w/index.php?curid=1189650
1247 CE
Qin Jiushao's Mathematical Treatise
Chinese mathematician Qin Jiushao solves polynomial equations and geometry. #math #china
Qin Jiushao's Mathematical Treatise By Qin Jiushao 秦九韶 - 1842 printing Shu Shu Jiu Zhang, Public domain, https://commons.wikimedia.org/w/index.php?curid=3414657
1250 CE
Nasir al-Din al-Tusi's Trigonometry
Al-Tusi separates trigonometry from astronomy and proves the law of sines. #math #trigonometry
Nasir al-Din al-Tusi's Trigonometry By Unknown author - scan of stamp 30 May 2006, Public domain, https://commons.wikimedia.org/w/index.php?curid=829461
1300 CE
Bradwardine on Geometry
Thomas Bradwardine writes on geometry and the continuum, influencing medieval mathematics. #math #europe
Bradwardine on Geometry By Dorieo - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=69888631
1350 CE
Oresme's Geometry of Motion
Nicole Oresme uses geometry to represent motion and functions, foreshadowing coordinate geometry. #math #europe
Oresme's Geometry of Motion By Nicole Oresme / Aristotle - Nicole Oresme (1400-1420) Traité de la sphère; Aristote, De caelo et de mundo, traduction française par Nicole Oresme, p. 1r OCLC: 1177977521., Public domain, https://commons.wikimedia.org/w/index.php?curid=436922
1400 CE
Madhava's Pi Series
Madhava of Sangamagrama discovers infinite series for pi, a precursor to calculus. #math #india
1420 CE
Al-Kashi's Pi Calculation
Persian mathematician Jamshid al-Kashi computes pi to 16 decimal places using polygons. #math #islam
Al-Kashi's Pi Calculation By Christies.com - https://www.christies.com/lot/lot-6162908, Public domain, https://commons.wikimedia.org/w/index.php?curid=115212624
1482 CE
First Printed Euclid
Erhard Ratdolt prints the first edition of Euclid's Elements in Venice. #math #printing
1525 CE
Dürer's Geometry for Artists
Albrecht Dürer publishes 'The Painter's Manual' on geometry for artists, including constructions. #art #math
Dürer's Geometry for Artists By Albrecht Dürer - https://www.sammlung.pinakothek.de/de/artwork/Qlx2QpQ4Xq, Public domain, https://commons.wikimedia.org/w/index.php?curid=63803877
1550 CE
Recorde's Geometry Textbook
Robert Recorde's 'The Pathway to Knowledge' introduces geometric reasoning in English. #math #education
Recorde's Geometry Textbook By Basher Eyre - This file was derived from: St Mary, Tenby- memorial (13) (geograph 6264760).jpg, CC BY-SA 2.0, https://commons.wikimedia.org/w/index.php?curid=124709772
1570 CE
Commandino's Euclid Edition
Federico Commandino translates and comments on Euclid's works, aiding Renaissance mathematics. #math #renaissance
Commandino's Euclid Edition By Scuola del Barocco - www.urbinoelaprospettiva.it/commandino.asp, Public domain, https://commons.wikimedia.org/w/index.php?curid=7043617
1572 CE
Vieta's New Geometry
François Viète develops analytic geometry and trigonometric solutions, introducing symbolic notation. #math #europe
Vieta's New Geometry By Unknown author, Public domain, https://commons.wikimedia.org/w/index.php?curid=81021
Bombelli's Imaginary Geometry By Unknown author - Book printed by editor Giovanni Rossi, Public domain, https://commons.wikimedia.org/w/index.php?curid=1591687
1585 CE
Stevin's Decimal Fractions
Simon Stevin introduces decimal fractions and works on geometry in The Principles of the Art of Weighing. #math #europe
Stevin's Decimal Fractions By Unknown author - Digitool Leiden University Library, http://digitalcollections.universiteitleiden.nl, Public domain, https://commons.wikimedia.org/w/index.php?curid=72690
1591 CE
Viète's Analytic Geometry
François Viète introduces symbolic algebra and applies it to geometric problems. #math #algebra
1595 CE
Van Roomen's Pi
Adriaan van Roomen computes pi to 15 decimals using geometric methods. #math #europe
1600 CE
Kepler's Geometric Astronomy
Johannes Kepler uses geometric models to describe planetary motion, leading to his laws. #math #astronomy
Kepler's Geometric Astronomy By August Köhler [1] - Kepler-Museum in Weil der Stadt, Public domain, https://commons.wikimedia.org/w/index.php?curid=9406242
