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# Geometry Timeline

A Timeline of geometric discoveries, advances, etc

by

Tweet## Jackie Kulacz

on 14 September 2012#### Transcript of Geometry Timeline

People from the Stone Age in France and Europe record numbers on bones 30000 B.C early geometric shapes used 25000 B.C Egyptians use a form of decimal number system •5000 B.C The first symbols used

for numbers, simple

straight lines

are used in Egypt •3400 B.C The abacus is developed

in the Middle East and in areas

around the Mediterranean 3000 B.C. Egyptian Calendar is used 2770 B.C 1950 BC Babylonians solve quadratic equations The Moscow papyrus

(also called the Golenishev papyrus)

is written. It gives details of Egyptian geometry. 1900 B.C Babylonians know Pythagoras's Theorem. 1850 B.C. The Rhind papyrus

(sometimes called the Ahmes papyrus) is written. It shows that Egyptian mathematics has developed many techniques to solve problems. Multiplication is based on repeated doubling, and division uses successive halving. 1700 B.C Apastamba writes the most interesting

Indian Sulbasutra from a mathematical point of view. 600 B.C. Thales brings Babylonian mathematical knowledge to Greece.

He uses geometry to solve problems such as calculating

the height of pyramids and the

distance of ships from the shore. 575 B.C. Pythagoras of Samos moves to Croton

in Italy and teaches mathematics,

geometry, music, and reincarnation. 530 B.C Pythagoras of Samos was

credited for making the imfamous

"Pythagorian Theorem” 569-475 BC Hippocrates of Chios 470-410 BC worked on duplicating the cube which he showed equivalent to constructing two mean proportionals between a number and its double. Hippocrates was also the first to show that the ratio of the areas of two circles was equal to the ratio of the squares of their radii. Theaetetus of Athens

creator of solid geometry and constructed all five regular solids 417-369 BC Menaechmus was the first to show that ellipses, parabolas, and hyperbolas are obtained by cutting a cone in a plane not parallel to the base. 380-320 BC Euclid of Alexandria

collected the theorems of Pythagoras, Hippocrates, Theaetetus, Eudoxus and other predecessors into a logically connected whole in his 13 Book treatise "The Elements or The Thirteen Books of Euclid's Elements 325-265 BC

Archimedes of Syracuse greatest contributions to mathematics were in the area of Geometry. It was believed that he was actually the first to have invented integral calculus and scientific notation.

Also he created a formula to find the area under a curve, the amount of space that is enclosed by a curve. 287-212 BC

Apollonius of Perga determined the center of curvature and the evolute of the ellipse, parabola, and hyperbola. In another work "Tangencies", he showed how to construct the circle which is tangent to three objects (points, lines or circles). He also computed an approximation for better than the one of Archimedes. 262-190 BC Hipparchus of Rhodes made an early, extensive contribution to trigonometry producing a table of chords, an early example of a trigonometric table 190-120 BC 10-75 AD

Heron of Alexandria) wrote "Metrica" (3 Books) which gives methods for computing areas and volumes. Book I considers areas of plane figures and surfaces of 3D objects, and contains his now-famous formula for the area of a triangle = sqrt[s(s-a)(s-b)(s-c)] where s=(a+b+c)/2 [but some historians attribute this result to Archimedes]. Book II considers volumes of 3D solids. Book III deals with dividing areas and volumes according to a given ratio, and gives a method to find the cube root of a number.

Claudius Ptolemy created"Ptolemy's Theorem", which states that for a quadrilateral inscribed in a circle, the product of its diagonals is equal to the sum of the products of its opposite sides. From this, he derived the (chord) formulas for sin(a+b), sin(a-b), and sin(a/2), and used these to compute detailed trigonometric tables. Geometry Timeline 100 B.C

Numerical notation, arithmetical computations, and counting rods were introduced. 100

Zhoubi suanjing writes the Arithmetical Classic of the Gnomon and the Circular Paths of Heaven 50

The Nine Chapters on the Mathematical Art ( written by Jiuzhang Suanshu) which collects mathematics to beginning of Han dynasty. It has 246 problems in 9 chapters. It is the Longest surviving and most influential Chinese math book. 250

Sun Zi wrote his mathematical manual 263

Liu Hui 450

Zhang Qiujian Wrote his mathematical manual 500

Zu Chongzhi 610

Liu Zhuo (544-610) Astronomer Introduced quadratic interpolation dies 625

Wang Xiaotong (fl. 625) Mathematician and astronomer. 600

Translations of Indian mathematical works. 727

Yi Xing (683-727) tangent table 1050

Jia Xian-Written work lost. 1261

Qin Jiushao 1279

Li Chih (a.k.a. Li Yeh) 1275

Yang Hui 1316

Guo Shoujing 1303

Zhu Shijie 953

Al-Karaji (born 953) is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. 1048

Omar Khayyam (born 1048) gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work. 1135

Sharaf al-Din al-Tusi (born 1135), although almost exactly the same age as al-Samawal, does not follow the general development that came through al-Karaji's school of algebra but rather follows Khayyam's application of algebra to geometry. He wrote a treatise on cubic equations, which [11] 58-165 AD 1637 In an appendix “La Geometrie” of hismanuscript “Discours de la method…”Rene Descartes applied algebra to geometry and created analytic geometry. Co-creator of analytic geometry which he first published in his paper “Ad Locos Planos et Solidos Isagoge”. Developed a method for determining maxima, minima, and tangents to curved lines foreshadowing calculus 1636 PIERRE DE FERMAT Leonhard Euler founded mathematical analysis and invented the idea of functions. 1752 Gaspard Monge is considered the father of both descriptive geometry in "Geometrie descriptive" and differential geometry in "Application de l'Analyse a la Geometrie" 1799 David Hilbert first worked on invariant theory and proved his famous "Basis Theorem" . He later did the most influential work in geometry since Euclid, publishing "Grundlagen der Geometrie" 1888 Donald Coxeter is regarded as the major synthetic geometer of the 20th century, and has made important contributions to the theory of polytopes, non-Euclidean geometry, group theory and combinatorics. 1907-2003

Full transcriptfor numbers, simple

straight lines

are used in Egypt •3400 B.C The abacus is developed

in the Middle East and in areas

around the Mediterranean 3000 B.C. Egyptian Calendar is used 2770 B.C 1950 BC Babylonians solve quadratic equations The Moscow papyrus

(also called the Golenishev papyrus)

is written. It gives details of Egyptian geometry. 1900 B.C Babylonians know Pythagoras's Theorem. 1850 B.C. The Rhind papyrus

(sometimes called the Ahmes papyrus) is written. It shows that Egyptian mathematics has developed many techniques to solve problems. Multiplication is based on repeated doubling, and division uses successive halving. 1700 B.C Apastamba writes the most interesting

Indian Sulbasutra from a mathematical point of view. 600 B.C. Thales brings Babylonian mathematical knowledge to Greece.

He uses geometry to solve problems such as calculating

the height of pyramids and the

distance of ships from the shore. 575 B.C. Pythagoras of Samos moves to Croton

in Italy and teaches mathematics,

geometry, music, and reincarnation. 530 B.C Pythagoras of Samos was

credited for making the imfamous

"Pythagorian Theorem” 569-475 BC Hippocrates of Chios 470-410 BC worked on duplicating the cube which he showed equivalent to constructing two mean proportionals between a number and its double. Hippocrates was also the first to show that the ratio of the areas of two circles was equal to the ratio of the squares of their radii. Theaetetus of Athens

creator of solid geometry and constructed all five regular solids 417-369 BC Menaechmus was the first to show that ellipses, parabolas, and hyperbolas are obtained by cutting a cone in a plane not parallel to the base. 380-320 BC Euclid of Alexandria

collected the theorems of Pythagoras, Hippocrates, Theaetetus, Eudoxus and other predecessors into a logically connected whole in his 13 Book treatise "The Elements or The Thirteen Books of Euclid's Elements 325-265 BC

Archimedes of Syracuse greatest contributions to mathematics were in the area of Geometry. It was believed that he was actually the first to have invented integral calculus and scientific notation.

Also he created a formula to find the area under a curve, the amount of space that is enclosed by a curve. 287-212 BC

Apollonius of Perga determined the center of curvature and the evolute of the ellipse, parabola, and hyperbola. In another work "Tangencies", he showed how to construct the circle which is tangent to three objects (points, lines or circles). He also computed an approximation for better than the one of Archimedes. 262-190 BC Hipparchus of Rhodes made an early, extensive contribution to trigonometry producing a table of chords, an early example of a trigonometric table 190-120 BC 10-75 AD

Heron of Alexandria) wrote "Metrica" (3 Books) which gives methods for computing areas and volumes. Book I considers areas of plane figures and surfaces of 3D objects, and contains his now-famous formula for the area of a triangle = sqrt[s(s-a)(s-b)(s-c)] where s=(a+b+c)/2 [but some historians attribute this result to Archimedes]. Book II considers volumes of 3D solids. Book III deals with dividing areas and volumes according to a given ratio, and gives a method to find the cube root of a number.

Claudius Ptolemy created"Ptolemy's Theorem", which states that for a quadrilateral inscribed in a circle, the product of its diagonals is equal to the sum of the products of its opposite sides. From this, he derived the (chord) formulas for sin(a+b), sin(a-b), and sin(a/2), and used these to compute detailed trigonometric tables. Geometry Timeline 100 B.C

Numerical notation, arithmetical computations, and counting rods were introduced. 100

Zhoubi suanjing writes the Arithmetical Classic of the Gnomon and the Circular Paths of Heaven 50

The Nine Chapters on the Mathematical Art ( written by Jiuzhang Suanshu) which collects mathematics to beginning of Han dynasty. It has 246 problems in 9 chapters. It is the Longest surviving and most influential Chinese math book. 250

Sun Zi wrote his mathematical manual 263

Liu Hui 450

Zhang Qiujian Wrote his mathematical manual 500

Zu Chongzhi 610

Liu Zhuo (544-610) Astronomer Introduced quadratic interpolation dies 625

Wang Xiaotong (fl. 625) Mathematician and astronomer. 600

Translations of Indian mathematical works. 727

Yi Xing (683-727) tangent table 1050

Jia Xian-Written work lost. 1261

Qin Jiushao 1279

Li Chih (a.k.a. Li Yeh) 1275

Yang Hui 1316

Guo Shoujing 1303

Zhu Shijie 953

Al-Karaji (born 953) is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. 1048

Omar Khayyam (born 1048) gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. Khayyam also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work. 1135

Sharaf al-Din al-Tusi (born 1135), although almost exactly the same age as al-Samawal, does not follow the general development that came through al-Karaji's school of algebra but rather follows Khayyam's application of algebra to geometry. He wrote a treatise on cubic equations, which [11] 58-165 AD 1637 In an appendix “La Geometrie” of hismanuscript “Discours de la method…”Rene Descartes applied algebra to geometry and created analytic geometry. Co-creator of analytic geometry which he first published in his paper “Ad Locos Planos et Solidos Isagoge”. Developed a method for determining maxima, minima, and tangents to curved lines foreshadowing calculus 1636 PIERRE DE FERMAT Leonhard Euler founded mathematical analysis and invented the idea of functions. 1752 Gaspard Monge is considered the father of both descriptive geometry in "Geometrie descriptive" and differential geometry in "Application de l'Analyse a la Geometrie" 1799 David Hilbert first worked on invariant theory and proved his famous "Basis Theorem" . He later did the most influential work in geometry since Euclid, publishing "Grundlagen der Geometrie" 1888 Donald Coxeter is regarded as the major synthetic geometer of the 20th century, and has made important contributions to the theory of polytopes, non-Euclidean geometry, group theory and combinatorics. 1907-2003