Timeline of geometry

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Timeline of geometry" – news · newspapers · books · scholar · JSTOR (October 2023) (Learn how and when to remove this template message)

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 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 –
  cotangent
  , and knowledge of solving first order linear equations

1st millennium BC

• 800 BC – Baudhayana, author of the Baudhayana
  quadratic equations, and calculates the square root of 2
  correct to five decimal places
• ca. 600 BC – the other
  Pythagorean triples, contain of a number of geometrical proofs, and approximate π
  at 3.16
• 5th century BC –
  lunes in an attempt to square the circle
• 5th century BC –
  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 –
  two
  ,
• 370 BC – Eudoxus states the method of exhaustion for area determination
• 300 BC – Euclid in his Elements studies geometry as an axiomatic system, proves the infinitude of prime numbers and presents the Euclidean algorithm; he states the law of reflection in Catoptrics, and he proves the fundamental theorem of arithmetic
• 260 BC – Archimedes proved that the value of π 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 writes On Conic Sections and names the ellipse, parabola, and hyperbola,
• 150 BC –
  combinations
• 140 BC – Hipparchus develops the bases of trigonometry.

1st millennium

• ca. 340 – Pappus of Alexandria states his hexagon theorem and his centroid theorem
• 500 –
  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 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 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 ${\displaystyle x^{n}\cdot x^{m}=x^{m+n}}$
• 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 ${\displaystyle \cos \alpha =1/{\sqrt {1+\tan ^{2}\alpha }}}$.

1000–1500

• ca. 1000 –
  Abu al-Wafa
  .
• ca. 1100 –
  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 equations which "represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry."^[2]
• ca. 1250 –
  Nasir Al-Din Al-Tusi attempts to develop a form of non-Euclidean geometry
  .
• 15th century – Nilakantha Somayaji, a 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 –
  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 –
  trigonometric functions and complex numbers
  ,
• 1733 –
  Giovanni Gerolamo Saccheri studies what geometry would be like if Euclid's fifth postulate
  were false,
• 1796 –
  compass and straightedge
• 1797 – Caspar Wessel associates vectors with complex numbers and studies complex number operations in geometrical terms,
• 1799 – Gaspard Monge publishes Géométrie descriptive, in which he introduces descriptive geometry.

19th century

• 1806 –
  Kepler-Poinsot polyhedra
  .
• 1829 –
  Lobachevsky invent hyperbolic non-Euclidean geometry
  ,
• 1837 –
  trisecting the angle are impossible with only a compass and straightedge, as well as the full completion of the problem of constructibility
  of regular polygons
• 1843 – William Hamilton discovers the calculus of quaternions and deduces that they are non-commutative,
• 1854 – Bernhard Riemann introduces Riemannian geometry,
• 1854 – Arthur Cayley shows that quaternions 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 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 – Einstein's theory of general relativity.
• 1930 –
  three-cottage problem
  has no solution,
• 1931 – Georges de Rham develops theorems in cohomology and characteristic classes,
• 1933 –
  Borsuk-Ulam antipodal-point theorem
  ,
• 1955 –
  H. S. M. Coxeter et al. publish the complete list of uniform polyhedron
  ,
• 1975 – Benoit Mandelbrot, fractals theory,
• 1981 –
  Mikhail Gromov develops the theory of hyperbolic groups
  , 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 –
  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).^[3]

See also

• Geometry and topology – branch of mathematics at the intersection between geometry and topologyPages displaying wikidata descriptions as a fallback
• History of geometry – Historical development of geometry
• Timeline of ancient Greek mathematicians
• Timeline of mathematical logic
• Timeline of mathematics

References