View source for Timeline of geometry

{{Short description|Notable events in the history of geometry}}
{{more citations needed|date=October 2023}}
{{Use dmy dates|date=August 2019}}
The following is a timeline of key developments of [[geometry]]:

==Before 1000 BC==
* ca. 2000 BC – [[Scotland]], [[carved stone balls]] exhibit a variety of symmetries including all of the symmetries of [[Platonic solid]]s.
* 1800 BC – [[Moscow Mathematical Papyrus]], findings volume of a frustum
*1800 BC – [[Plimpton 322]] contains the oldest reference to the Pythagorean triplets.<ref>{{Cite web |editor-last=Jones |editor-first=Alexander |editor2-last=Proust |editor2-first=Christine |editor2-link=Christine Proust |title=Before Pythagoras: The Culture of Old Babylonian Mathematics |url=https://isaw.nyu.edu/exhibitions/before-pythagoras/items/plimpton-322/ |access-date=2023-04-04 |website=Institute for the Study of the Ancient World, [[New York University]]}}</ref>
* 1650 BC – [[Rhind Mathematical Papyrus]], copy of a lost scroll from around 1850 BC, the scribe [[Ahmes]] presents one of the first known approximate values of [[pi|π]] at 3.16, the first attempt at [[squaring the circle]], earliest known use of a sort of [[cotangent]], and knowledge of solving first order linear equations

==1st millennium BC==
* 800 BC – Baudhayana, author of the Baudhayana [[Sulba Sutras|Sulba Sutra]], a [[Vedic Sanskrit]] geometric text, contains [[quadratic equations]], and calculates the [[square root of 2]] correct to five decimal places
* ca. 600 BC – the other [[Vedic civilization|Vedic]] "[[Sulba Sutras]]" ("rule of chords" in [[Sanskrit]]) use [[Pythagorean triples]], contain a number of geometrical proofs, and approximate [[pi|π]] at 3.16
* 5th century BC – [[Hippocrates of Chios]] utilizes [[Lune (mathematics)|lunes]] in an attempt to [[squaring the circle|square the circle]]
* 5th century BC – [[Apastamba]], author of the Apastamba [[Sulba Sutras|Sulba Sutra]], another [[Vedic Sanskrit]] geometric text, makes an attempt at [[squaring the circle]] and also calculates the [[square root]] of 2 correct to five decimal places
* 530 BC – [[Pythagoras]] studies propositional [[geometry]] and vibrating lyre strings; his group also discover the [[irrational number|irrationality]] of the [[square root]] of [[two]],
* 370 BC – [[Eudoxus of Cnidus|Eudoxus]] states the [[method of exhaustion]] for [[area]] determination
* 300 BC – [[Euclid]] in his ''[[Euclid's Elements|Elements]]'' studies [[geometry]] as an [[axiomatic system]], proves the [[Infinite set|infinitude]] of [[prime number]]s and presents the [[Euclidean algorithm]]; he states the law of reflection in  ''Catoptrics'', and he proves the [[fundamental theorem of arithmetic]]
* 260 BC – [[Archimedes]] [[method of exhaustion|proved]] that the value of [[pi|π]] lies between 3&nbsp;+&nbsp;1/7 (approx. 3.1429) and 3&nbsp;+&nbsp;10/71 (approx. 3.1408), that the area of a circle was equal to π multiplied by the square of the radius of the circle and that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He also gave a very accurate estimate of the value of the square root of 3.
* 225 BC – [[Apollonius of Perga]] writes  ''On [[Conic section|Conic Sections]]'' and names the [[ellipse]], [[parabola]], and [[hyperbola]],
* 150 BC – [[Jainism|Jain]] mathematicians in [[History of India|India]] write the "Sthananga Sutra", which contains work on the theory of numbers, arithmetical operations, [[geometry]], operations with [[fractions]], simple equations, [[cubic equations]], quartic equations, and [[permutations]] and [[combinations]]
* 140 BC – [[Hipparchus]] develops the bases of [[trigonometry]].

==1st millennium==
* ca 340 – [[Pappus of Alexandria]] states his [[Pappus's hexagon theorem|hexagon theorem]] and his [[Pappus's centroid theorem|centroid theorem]]
* 50 – [[Aryabhata]] writes the "Aryabhata-Siddhanta", which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of [[sine]] and [[cosine]], and also contains the [[Aryabhata's sine table|earliest tables of sine]] and cosine values (in 3.75-degree intervals from 0 to 90 degrees)
* 7th century – [[Bhaskara I]] gives a rational approximation of the sine function
* 8th century – [[Virasena]] gives explicit rules for the [[Fibonacci sequence]], gives the derivation of the [[volume]] of a [[frustum]] using an [[Infinity|infinite]] procedure.
* 8th century – [[Shridhara]] gives the rule for finding the volume of a sphere and also the formula for solving quadratic equations
* 820 – [[Al-Mahani]] conceived the idea of reducing [[Geometry|geometrical]] problems such as [[doubling the cube]] to problems in algebra.
* ca. 900 – [[Abu Kamil]] of Egypt had begun to understand what we would write in symbols as <math>x^n \cdot x^m = x^{m+n}</math>
* 975 – [[Al-Batani]] – Extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions. Derived the formula: <math> \sin \alpha = \tan \alpha / \sqrt{1+\tan^2 \alpha} </math> and <math> \cos \alpha = 1 / \sqrt{1 + \tan^2 \alpha}</math>.

==1000–1500==
* ca. 1000 – [[Law of sines]] is discovered by [[Islamic mathematics|Muslim mathematicians]], but it is uncertain who discovers it first between [[Abu-Mahmud al-Khujandi]], [[Abu Nasr Mansur]], and [[Abū al-Wafā' al-Būzjānī|Abu al-Wafa]].
* ca. 1100 – [[Omar Khayyám]] "gave a complete classification of [[cubic equation]]s with geometric solutions found by means of intersecting [[conic section]]s." He became the first to find general [[geometry|geometric]] solutions of [[cubic equation]]s and laid the foundations for the development of [[analytic geometry]] and [[non-Euclidean geometry]]. He also extracted [[root of a function|roots]] using the [[decimal]] system ([[Hindu–Arabic numeral system]]).
* 1135 – [[Sharafeddin Tusi]] followed al-Khayyam's application of algebra to geometry, and wrote a treatise on [[cubic equation]]s which "represents an essential contribution to another [[algebra]] which aimed to study [[curve]]s by means of [[equation]]s, thus inaugurating the beginning of [[algebraic geometry]]."<ref name=MacTutor>[http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html Arabic mathematics], ''[[MacTutor History of Mathematics archive]]'', [[University of St Andrews]], Scotland</ref>
* ca. 1250 – [[Nasir Al-Din Al-Tusi]] attempts to develop a form of [[non-Euclidean geometry]].
* 15th century – [[Nilakantha Somayaji]], a [[Kerala school of astronomy and mathematics|Kerala school]] mathematician, writes the "Aryabhatiya Bhasya", which contains work on infinite-series expansions, problems of algebra, and spherical geometry

==17th century==
* 17th century – Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series
* 1619 – [[Johannes Kepler]] discovers two of the [[Kepler-Poinsot polyhedra]].
* 1637 - [[René Descartes]] publishes [[La Géométrie]] which introduces [[analytic geometry]], which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations.

==18th century==
* 1722 – [[Abraham de Moivre]] states [[de Moivre's formula]] connecting [[trigonometric function]]s and [[complex number]]s,
* 1733 – [[Giovanni Gerolamo Saccheri]] studies what geometry would be like if [[parallel postulate|Euclid's fifth postulate]] were false,
* 1796 – [[Carl Friedrich Gauss]] proves that the [[heptadecagon|regular 17-gon]] can be constructed using only a [[compass and straightedge]]
* 1797 – [[Caspar Wessel]] associates vectors with [[complex number]]s and studies complex number operations in geometrical terms,
* 1799 – [[Gaspard Monge]] publishes Géométrie descriptive, in which he introduces [[descriptive geometry]].

==19th century==
* 1806 – [[Louis Poinsot]] discovers the two remaining [[Kepler-Poinsot polyhedra]].
* 1829 – [[Bolyai]], [[Carl Friedrich Gauss|Gauss]], and [[Nikolai Ivanovich Lobachevsky|Lobachevsky]] invent hyperbolic [[non-Euclidean geometry]],
* 1837 – [[Pierre Wantzel]] proves that doubling the cube and [[trisecting the angle]] are impossible with only a compass and straightedge, as well as the full completion of the problem of [[Constructible polygon|constructibility]] of regular polygons
* 1843 – [[William Rowan Hamilton|William Hamilton]] discovers the calculus of [[quaternion]]s and deduces that they are non-commutative,
* 1854 – [[Bernhard Riemann]] introduces [[Riemannian geometry]],
* 1854 – [[Arthur Cayley]] shows that [[quaternion]]s can be used to represent rotations in four-dimensional [[space]],
* 1858 – [[August Ferdinand Möbius]] invents the [[Möbius strip]],
* 1870 – [[Felix Klein]] constructs an analytic geometry for Lobachevski's geometry thereby establishing its self-consistency and the logical independence of Euclid's fifth postulate,
* 1873 – [[Charles Hermite]] proves that [[e (mathematical constant)|e]] is transcendental,
* 1878 – Charles Hermite solves the general quintic equation by means of elliptic and modular functions
* 1882 – [[Ferdinand von Lindemann]] proves that π is transcendental and that therefore the circle cannot be squared with a compass and straightedge,
* 1882 – Felix Klein discovers the [[Klein bottle]],
* 1899 – [[David Hilbert]] presents a set of self-consistent geometric axioms in ''Foundations of Geometry''

==20th century==
* 1901 – [[Élie Cartan]] develops the [[exterior derivative]],
* 1912 – [[Luitzen Egbertus Jan Brouwer]] presents the [[Brouwer fixed-point theorem]],
* 1916 – [[Albert Einstein|Einstein's]] theory of [[general relativity]].
* 1930 – [[Casimir Kuratowski]] shows that the [[three-cottage problem]] has no solution,
* 1931 – [[Georges de Rham]] develops theorems in [[cohomology]] and [[characteristic class]]es,
* 1933 – [[Karol Borsuk]] and [[Stanislaw Ulam]] present the [[Borsuk-Ulam Theorem|Borsuk-Ulam antipodal-point theorem]],
* 1955 – [[H. S. M. Coxeter]] et al. publish the complete list of [[uniform polyhedron]],
* 1975 – [[Benoit Mandelbrot]], [[fractal]]s theory,
* 1981 – [[Mikhail Gromov (mathematician)|Mikhail Gromov]] develops the theory of [[hyperbolic group]]s, revolutionizing both infinite group theory and global differential geometry,
* 1983 – the [[classification of finite simple groups]], a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,
* 1991 – [[Alain Connes]] and [[John Lott (mathematician)|John Lott]] develop [[non-commutative geometry]],
* 1998 – [[Thomas Callister Hales]] proves the [[Kepler conjecture]],

==21st century==
* 2003 – [[Grigori Perelman]] proves the [[Poincaré conjecture]],
* 2007 – a team of researchers throughout North America and Europe used networks of computers to map [[E8 (mathematics)]].<ref>{{Cite news |last=Thomson |first=Elizabeth A. |date=2007-03-18 |title=Math research team maps E8: Calculation on paper would cover Manhattan |url=https://news.mit.edu/2007/e8 |access-date=2024-02-19 |work=[[MIT]] News}}</ref>

==See also==

* {{annotated link|Geometry and topology}}
* {{annotated link|History of geometry}}
* {{annotated link|Timeline of ancient Greek mathematicians}}
* {{annotated link|Timeline of mathematical logic}}
* {{annotated link|Timeline of mathematics}}

==References==

{{reflist}}<!--added above categories/infobox footers by script-assisted edit-->

{{Ancient Greek mathematics}}
{{History of mathematics}}
{{DEFAULTSORT:Timeline Of Algebra And Geometry}}
[[Category:Mathematics timelines|Algebra and geometry]]
[[Category:Algebra| Timeline]]
[[Category:Geometry| ]]