The parallel evolution of spatial measurement and deductive proofs: Liu Hui's Pi enclosure algorithm, Gougu (Pythagorean) theorem, and Euclidean axiomatic geometry.
The Zhoubi Suanjing, an ancient Chinese astronomical and mathematical text, is compiled. It contains the earliest known proof of the Gougu theorem (Pythagorean theorem) and discusses right triangle geometry. #geometry #history
Thales of Miletus introduces deductive reasoning to geometry, proving theorems such as that a circle is bisected by its diameter. He is considered one of the first to use logical deduction in mathematics. #geometry #philosophy
Pythagoras establishes a school in Croton, where his followers study mathematics and geometry, including the Pythagorean theorem and properties of numbers. The school contributes to the development of deductive geometry. #geometry #mathematics
The Sulba Sutras, part of Vedic literature, contain geometric rules for altar construction, including Pythagorean triples and approximations of square roots. They represent early Indian contributions to geometry. #geometry #history
Hippocrates of Chios writes the first known geometry textbook, 'Elements', and works on the quadrature of lunes. He attempts to square the circle and contributes to the method of exhaustion. #geometry #mathematics
Plato founds the Academy in Athens, where geometry is considered essential for philosophical education. The motto 'Let no one ignorant of geometry enter' underscores its importance. #geometry #philosophy
Eudoxus of Cnidus formalizes the method of exhaustion, a precursor to integral calculus, used to compute areas and volumes. His work influences Euclid and Archimedes. #geometry #mathematics
Euclid of Alexandria compiles 'Elements', a 13-book treatise that becomes the foundation of geometry. It introduces axiomatic method, definitions, postulates, and proofs, influencing mathematics for over two millennia. #geometry #mathematics
Archimedes of Syracuse uses inscribed and circumscribed polygons to approximate pi, establishing bounds between 3.1408 and 3.1429. He also develops formulas for areas and volumes. #geometry #mathematics
Apollonius of Perga writes 'Conics', an eight-book work on conic sections (ellipse, parabola, hyperbola). He introduces terms like 'parabola' and 'hyperbola' and studies their properties. #geometry #mathematics
Chinese mathematician Liu Xin calculates pi as 3.1547, one of the earliest Chinese approximations. His work contributes to the development of pi calculations in China. #geometry #history
Heron of Alexandria writes 'Metrica', a treatise on geometry and measurement. He derives Heron's formula for the area of a triangle and describes methods for geometric constructions. #geometry #mathematics
Claudius Ptolemy writes 'Almagest', which includes geometric models for planetary motion and a table of chords (trigonometry). His work synthesizes Greek geometric astronomy. #geometry #astronomy
Liu Hui publishes a commentary on 'The Nine Chapters on the Mathematical Art', providing proofs for geometric formulas. He uses the method of exhaustion to calculate pi as 3.1416 and develops the Gougu theorem. #geometry #history
Pappus of Alexandria compiles 'Mathematical Collection', summarizing Greek geometry and including Pappus's theorem and the Pappus chain. His work preserves many lost treatises. #geometry #mathematics
Theon of Alexandria produces an edition of Euclid's 'Elements', which becomes the basis for many later translations. His daughter Hypatia also contributes to mathematical commentary. #geometry #history
Indian mathematician Aryabhata calculates pi as 3.1416 in his work 'Aryabhatiya', and provides rules for area and volume calculations. He also works on trigonometry and astronomy. #geometry #mathematics
Brahmagupta writes a treatise on mathematics and astronomy, including formulas for cyclic quadrilaterals and the Brahmagupta theorem. He also gives rules for zero and negative numbers. #geometry #mathematics
Al-Khwarizmi writes 'The Compendious Book on Calculation by Completion and Balancing', which includes geometric methods for solving quadratic equations. His work introduces algebraic reasoning to geometry. #geometry #algebra
Caliph Al-Ma'mun establishes the House of Wisdom in Baghdad, where Greek mathematical texts, including Euclid's 'Elements', are translated into Arabic. This preserves and transmits Greek geometry to the Islamic world. #geometry #history
Thabit ibn Qurra translates Greek works and writes on geometry, including the generalization of the Pythagorean theorem and work on amicable numbers. He also studies parabolas and volumes. #geometry #mathematics
Alhazen (Ibn al-Haytham) writes 'Book of Optics', using geometric methods to study light and vision. He also works on spherical geometry and the problem of Alhazen's problem. #geometry #optics
Omar Khayyam writes 'Treatise on Demonstration of Problems of Algebra', classifying cubic equations and solving them using geometric methods involving conic sections. He also works on the parallel postulate. #geometry #algebra
Bhaskara II writes 'Lilavati', a treatise on arithmetic and geometry, including problems on volumes, areas, and the Pythagorean theorem. He also gives a proof of the Pythagorean theorem by dissection. #geometry #mathematics
Leonardo Fibonacci publishes 'Liber Abaci', introducing Hindu-Arabic numerals to Europe. The book includes geometric problems and the famous Fibonacci sequence, which appears in nature. #geometry #mathematics
Chinese mathematician Qin Jiushao writes a treatise that includes methods for solving polynomial equations and geometric problems. He uses the Chinese remainder theorem and works on areas and volumes. #geometry #history
Nasir al-Din al-Tusi writes a treatise on the parallel postulate, attempting to prove it from other postulates. His work anticipates non-Euclidean geometry and influences later mathematicians. #geometry #mathematics
Zhu Shijie publishes a mathematical work that includes polynomial equations and geometric series. He uses the method of celestial element and solves problems in plane and solid geometry. #geometry #history
Persian mathematician Jamshid al-Kashi calculates pi to 16 decimal places using inscribed polygons, a record for the time. He also writes 'Key of Arithmetic', covering geometry and trigonometry. #geometry #mathematics
Euclid's 'Elements' is first printed in Venice, translated from Arabic by Campanus of Novara. This makes the text widely available in Europe, spurring geometric study. #geometry #history
Albrecht Dürer publishes a treatise on geometry and perspective, including methods for constructing regular polygons and curves. His work bridges art and mathematics. #geometry #art
Nicolaus Copernicus publishes his heliocentric model, which relies on geometric reasoning and circular orbits. His work uses Euclidean geometry to describe planetary motion. #geometry #astronomy
Robert Recorde publishes an algebra book that introduces the equals sign (=) and includes geometric problems. He also writes on arithmetic and geometry in English. #geometry #mathematics
Henry Billingsley publishes the first English translation of Euclid's 'Elements', with a preface by John Dee. This makes Euclidean geometry accessible to English readers. #geometry #history
Simon Stevin publishes 'De Thiende' (The Tenth), introducing decimal fractions and their use in geometry and measurement. He also works on statics and hydrostatics. #geometry #mathematics
François Viète publishes his work on symbolic algebra, introducing letters for unknowns and constants. He applies algebra to geometry, solving geometric problems analytically. #geometry #algebra
Galileo Galilei uses geometric methods to study the motion of falling bodies and projectiles. His work 'Two New Sciences' lays the foundation for kinematics and mathematical physics. #geometry #physics
