History of Geometry Timeline

(c. 3000 BCE – Present)

The history of geometry traces humanity's study of shapes, sizes, and spatial relationships from practical land measurement in ancient Egypt and Mesopotamia, through the rigorous axiomatic systematization by Greek mathematicians like Euclid, to revolutionary developments such as analytic geometry, non-Euclidean geometries, and modern computational and differential geometry. More Less

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Ancient Geometry

Earliest recorded beginnings of geometry

3000 BCE

The earliest recorded beginnings of geometry can be traced to early peoples, such as the ancient Indus Valley (see Harappan mathematics) and ancient Babylonia (see Babylonian mathematics) from around 3000 BCE.

Image source: History of geometry

Babylonian tablet with fifteen Pythagorean triples

1850 BCE

A Mesopotamian clay tablet from 1850 BCE contains fifteen Pythagorean triples with quite large entries, including (13500, 12709, 18541), a primitive triple, indicating sophisticated understanding of the topic.

Image source: Plimpton 322

Egyptians and Babylonians know Pythagorean theorem versions

1500 BCE

Both the Egyptians and the Babylonians were aware of versions of the Pythagorean theorem about 1500 years before Pythagoras, and the Egyptians had a correct formula for the volume of a frustum of a square pyramid.

Indian Sulba Sutras state the Pythagorean theorem

800 BCE

The Indian Sulba Sutras, composed around 800 BCE, contained the first statements of the Pythagorean theorem.

Image source: Shulba Sutras

Aristotle writes on deductive reasoning

384 BCE - 322 BCE

Aristotle, Plato's greatest pupil, wrote a treatise on methods of reasoning used in deductive proofs (see Logic) which was not substantially improved upon until the 19th century.

Image source: Aristotle

Euclid writes The Elements

300 BCE

Euclid's book The Elements is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.

Image source: Euclid's Elements

Decline of the Library of Alexandria

300 CE - 400 CE

Civil wars, decreasing investments in maintenance and acquisition of new scrolls, and generally declining interest in non-religious pursuits likely contributed to a reduction in the body of material available in the Library, especially in the 4th century.

Image source: Library of Alexandria

Destruction of Alexandria's pagan temples

391 CE

There is a growing consensus among historians that the Library of Alexandria likely suffered from several destructive events, but that the destruction of Alexandria's pagan temples in the late 4th century was probably the most severe and final one.

Chinese and Islamic Contributions

Zhou Li gives rough estimates for pi

100 BCE

Although rough estimates for pi were given in the Zhou Li, compiled in the 2nd century BCE, it was Zhang Heng who was the first to make a concerted effort at creating a more accurate formula for pi.

Image source: Rites of Zhou

Zhang Heng approximates pi

100 CE

Zhang Heng approximated pi as 730/232 (approximately 3.1466), although he used another formula of pi in finding a spherical volume, using the square root of 10 (approximately 3.162) instead.

Image source: Zhang Heng

Nine Chapters on the Mathematical Art appears by title

179 CE

The Nine Chapters on the Mathematical Art, the title of which first appeared by 179 CE on a bronze inscription, was edited and commented on by the 3rd century mathematician Liu Hui from the Kingdom of Cao Wei.

Image source: The Nine Chapters on the Mathematical Art

Wang Fan renders pi as 142/45

250 CE

Liu Hui's contemporary Wang Fan, a mathematician and astronomer from Eastern Wu, rendered pi as 3.1555 by using 142/45.

Liu Hui calculates pi with polygons

263 CE

Liu Hui listed pi as 3.141014 by using a 192-sided polygon, and then calculated pi as 3.14159 using a 3072-sided polygon.

Image source: Liu Hui

Transmission of Greek classics via the Islamic Golden Age

900 CE - 1200 CE

The transmission of the Greek Classics to medieval Europe via the Arabic literature of the 9th to 10th century Islamic Golden Age began in the 10th century and culminated in the Latin translations of the 12th century.

Image source: Transmission of the Greek Classics

Gerard of Cremona translates Ptolemy's Optics

1150 CE

Gerard of Cremona (1114–1187) translated Ptolemy's Optics into Latin, drawing on his knowledge of Arabic, Greek, and Latin in the task.

Image source: Gerard of Cremona

Gerard of Cremona translates Ptolemy's Optics

Gift of Greek manuscripts to King William I

1162

In 1162, Greek manuscripts were sent as a gift from the Emperor to King William I of Sicily, aiding the transmission of classical learning to medieval Europe.

Image source: William I of Sicily

Renaissance and Early Modern

Advances in perspective in Renaissance art

1300 - 1500

Advances in the treatment of perspective were made in Renaissance art of the 14th to 15th century which went beyond what had been achieved in antiquity.

Image source: Perspective (graphical)

Brunelleschi demonstrates the geometrical method of perspective

1413

In 1413 Filippo Brunelleschi demonstrated the geometrical method of perspective, used today by artists, by painting the outlines of various Florentine buildings onto a mirror.

Image source: Filippo Brunelleschi

Brunelleschi designs the Basilica di San Lorenzo

1419

A prime example of Renaissance use of geometrical principles is the Basilica di San Lorenzo in Florence by Filippo Brunelleschi (1377–1446).

Image source: Basilica of San Lorenzo, Florence

Alberti writes De pictura

1435 - 1436

Decades after Brunelleschi's demonstration, his friend Leon Battista Alberti wrote De pictura (1435/1436), a treatise on proper methods of showing distance in painting based on Euclidean geometry.

Image source: De pictura

Leonardo da Vinci draws the Vitruvian Man

1490

Leonardo da Vinci's Vitruvian Man (c. 1490) depicts a man in two superimposed positions with his arms and legs apart and inscribed in a circle and square.

Image source: Vitruvian Man

Vieta's formula for pi falls between Zu's approximations

1593

In comparison to later works, the formula for pi given by the French mathematician Franciscus Vieta (1540–1603) fell halfway between Zu Chongzhi's approximations.

Image source: François Viète

Creation of analytic geometry

1637

The first and most important development of the early 17th century was the creation of analytic geometry, or geometry with coordinates and equations, by René Descartes (1596–1650) and Pierre de Fermat (1601–1665).

Image source: Analytic geometry

Desargues studies projective geometry

1639

The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661).

Image source: Girard Desargues

Modern Geometry

Newton and Leibniz develop calculus

1665 - 1700

In the late 17th century, calculus was developed independently and almost simultaneously by Isaac Newton (1642–1727) and Gottfried Wilhelm Leibniz (1646–1716).

Image source: History of calculus

Work on Euclid's fifth postulate by 1700

1700

By 1700 a great deal had been discovered about what can be proved from the first four of Euclid's postulates, and what the pitfalls were in attempting to prove the fifth.

Image source: Parallel postulate

Saccheri, Lambert, and Legendre work on the parallel postulate

1733 - 1800

Saccheri, Lambert, and Legendre each did excellent work on the problem of the fifth postulate in the 18th century, but still fell short of success.

Gauss, Bolyai, and Lobachevsky develop non-Euclidean geometry

1829 - 1832

In the early 19th century, Gauss, Johann Bolyai, and Lobachevsky, each independently, took a different approach to the parallel postulate, developing non-Euclidean geometry.

Image source: Non-Euclidean geometry

Gauss, Bolyai, and Lobachevsky develop non-Euclidean geometry

Beltrami proves consistency of non-Euclidean geometry

1868

It remained to be proved mathematically that non-Euclidean geometry was just as self-consistent as Euclidean geometry, and this was first accomplished by Beltrami in 1868.

Image source: Eugenio Beltrami

Beltrami proves consistency of non-Euclidean geometry

Clifford introduces geometric algebra

1878

In 1878 William Kingdon Clifford introduced what is now termed geometric algebra, unifying William Rowan Hamilton's quaternions with Hermann Grassmann's algebra and revealing the geometric nature of these systems, especially in four dimensions.

Image source: Geometric algebra

Key Facts

Ancient Egyptians used practical geometry around 3000 BCE to re-survey farmland after the Nile's annual floods, as recorded in the Rhind Papyrus.
Euclid's 'Elements' (c. 300 BCE) organized geometry into an axiomatic-deductive system that remained the standard textbook for over 2,000 years.
René Descartes' invention of analytic geometry in 1637 linked algebra and geometry through coordinate systems, enabling the study of curves via equations.
In the 19th century, mathematicians such as Gauss, Lobachevsky, and Bolyai developed non-Euclidean geometries, overturning the assumption that Euclid's parallel postulate was necessary.
Modern geometry underpins contemporary science and technology, including Einstein's general relativity (based on Riemannian geometry), computer graphics, robotics, and GPS navigation.

Source

This History of Geometry timeline was generated with the help of AI, using information found on the internet.

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