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The following is a timeline of key developments ofgeometry:

• ca. 2000 BC –Scotland,carved stone balls exhibit a variety of symmetries including all of the symmetries ofPlatonic solids.
• 1800 BC –Moscow Mathematical Papyrus, findings volume of a frustum
• 1800 BC –Plimpton 322 contains the oldest reference to the Pythagorean triplets.^[1]
• 1650 BC –Rhind Mathematical Papyrus, copy of a lost scroll from around 1850 BC, the scribeAhmes presents one of the first known approximate values ofπ at 3.16, the first attempt atsquaring the circle, earliest known use of a sort ofcotangent, and knowledge of solving first order linear equations

• 800 BC – Baudhayana, author of the BaudhayanaSulba Sutra, aVedic Sanskrit geometric text, containsquadratic equations, and calculates thesquare root of 2 correct to five decimal places
• ca. 600 BC – the otherVedic "Sulba Sutras" ("rule of chords" inSanskrit) usePythagorean triples, contain a number of geometrical proofs, and approximateπ at 3.16
• 5th century BC –Hippocrates of Chios utilizeslunes in an attempt tosquare the circle
• 5th century BC –Apastamba, author of the ApastambaSulba Sutra, anotherVedic Sanskrit geometric text, makes an attempt atsquaring the circle and also calculates thesquare root of 2 correct to five decimal places
• 530 BC –Pythagoras studies propositionalgeometry and vibrating lyre strings; his group also discover theirrationality of thesquare root oftwo,
• 370 BC –Eudoxus states themethod of exhaustion forarea determination
• 300 BC –Euclid in hisElements studiesgeometry as anaxiomatic system, proves theinfinitude ofprime numbers and presents theEuclidean algorithm; he states the law of reflection inCatoptrics, and he proves thefundamental theorem of arithmetic
• 260 BC –Archimedesproved that the value ofπ lies between 3 + 1/7 (approx. 3.1429) and 3 + 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 writesOnConic Sections and names theellipse,parabola, andhyperbola,
• 150 BC –Jain mathematicians inIndia write the "Sthananga Sutra", which contains work on the theory of numbers, arithmetical operations,geometry, operations withfractions, simple equations,cubic equations, quartic equations, andpermutations andcombinations
• 140 BC –Hipparchus develops the bases oftrigonometry.

• ca 340 –Pappus of Alexandria states hishexagon theorem and hiscentroid 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 ofsine andcosine, and also contains theearliest 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 theFibonacci sequence, gives the derivation of thevolume of afrustum using aninfinite 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 reducinggeometrical problems such asdoubling the cube to problems in algebra.
• ca. 900 –Abu Kamil of Egypt had begun to understand what we would write in symbols as${\displaystyle x^n\cdot x^m=x^{m+n}}$
• 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:${\displaystyle \sin \alpha =\tan \alpha /\sqrt{1+{\tan }^2\alpha }}$ and${\displaystyle \cos \alpha =1/\sqrt{1+{\tan }^2\alpha }}$.

• ca. 1000 –Law of sines is discovered byMuslim mathematicians, but it is uncertain who discovers it first betweenAbu-Mahmud al-Khujandi,Abu Nasr Mansur, andAbu al-Wafa.
• ca. 1100 –Omar Khayyám "gave a complete classification ofcubic equations with geometric solutions found by means of intersectingconic sections." He became the first to find generalgeometric solutions ofcubic equations and laid the foundations for the development ofanalytic geometry andnon-Euclidean geometry. He also extractedroots using thedecimal system (Hindu–Arabic numeral system).
• 1135 –Sharafeddin Tusi followed al-Khayyam's application of algebra to geometry, and wrote a treatise oncubic equations which "represents an essential contribution to anotheralgebra which aimed to studycurves by means ofequations, thus inaugurating the beginning ofalgebraic geometry."^[2]
• ca. 1250 –Nasir Al-Din Al-Tusi attempts to develop a form ofnon-Euclidean geometry.
• 15th century –Nilakantha Somayaji, aKerala school mathematician, writes the "Aryabhatiya Bhasya", which contains work on infinite-series expansions, problems of algebra, and spherical geometry

• 17th century – Putumana Somayaji writes the "Paddhati", which presents a detailed discussion of various trigonometric series
• 1619 –Johannes Kepler discovers two of theKepler-Poinsot polyhedra.
• 1637 -René Descartes publishesLa Géométrie which introducesanalytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations.

• 1722 –Abraham de Moivre statesde Moivre's formula connectingtrigonometric functions andcomplex numbers,
• 1733 –Giovanni Gerolamo Saccheri studies what geometry would be like ifEuclid's fifth postulate were false,
• 1796 –Carl Friedrich Gauss proves that theregular 17-gon can be constructed using only acompass and straightedge
• 1797 –Caspar Wessel associates vectors withcomplex numbers and studies complex number operations in geometrical terms,
• 1799 –Gaspard Monge publishes Géométrie descriptive, in which he introducesdescriptive geometry.

• 1806 –Louis Poinsot discovers the two remainingKepler-Poinsot polyhedra.
• 1829 –Bolyai,Gauss, andLobachevsky invent hyperbolicnon-Euclidean geometry,
• 1837 –Pierre Wantzel proves that doubling the cube andtrisecting the angle are impossible with only a compass and straightedge, as well as the full completion of the problem ofconstructibility of regular polygons
• 1843 –William Hamilton discovers the calculus ofquaternions and deduces that they are non-commutative,
• 1854 –Bernhard Riemann introducesRiemannian geometry,
• 1854 –Arthur Cayley shows thatquaternions can be used to represent rotations in four-dimensionalspace,
• 1858 –August Ferdinand Möbius invents theMöbius 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 thate 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 theKlein bottle,
• 1899 –David Hilbert presents a set of self-consistent geometric axioms inFoundations of Geometry

• 1901 –Élie Cartan develops theexterior derivative,
• 1912 –Luitzen Egbertus Jan Brouwer presents theBrouwer fixed-point theorem,
• 1916 –Einstein's theory ofgeneral relativity.
• 1930 –Casimir Kuratowski shows that thethree-cottage problem has no solution,
• 1931 –Georges de Rham develops theorems incohomology andcharacteristic classes,
• 1933 –Karol Borsuk andStanislaw Ulam present theBorsuk-Ulam antipodal-point theorem,
• 1955 –H. S. M. Coxeter et al. publish the complete list ofuniform polyhedron,
• 1975 –Benoit Mandelbrot,fractals theory,
• 1981 –Mikhail Gromov develops the theory ofhyperbolic groups, revolutionizing both infinite group theory and global differential geometry,
• 1983 – theclassification of finite simple groups, a collaborative work involving some hundred mathematicians and spanning thirty years, is completed,
• 1991 –Alain Connes andJohn Lott developnon-commutative geometry,
• 1998 –Thomas Callister Hales proves theKepler conjecture,

• 2003 –Grigori Perelman proves thePoincaré conjecture,
• 2007 – a team of researchers throughout North America and Europe used networks of computers to mapE8 (mathematics).^[3]

• History of geometry – Historical development of geometry
• Timeline of ancient Greek mathematicians
• Timeline of mathematical logic
• Timeline of mathematics

• Mathematics timelines
• Algebra
• Geometry

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