What is Geometry?
"Geometry is the visual study of shapes, sizes, patterns, and positions"
It occurred in all cultures, through at least one of these five strands of human activities:
1. building/structures (building/repairing a house, laying out a garden, making a kite, …)
2. machines/motion (using a pry-bar, riding a bike, sawing a board, swinging, …)
3. navigating/star-gazing (How do I get from here to there?, using maps, …)
4. art/patterns (designs, symmetries, representations, …)
5. measurement (How big is it?, How far is it?, ...)
Historical Chronological Development
Geometric thought appears to have risen simultaneously somewhere around 2000 BC in both Egypt and Babylon. The ensuing development of geometric thinking seems to go something like this:
Egypt & Babylon - 2000 - 500 BC
An understanding of "Pi" and what was later termed the "Pythagorean" relationships.
Greece - 750 - 250 BC
An absorption of Egyptian and Babylonian invention and the development of experimental geometry leading to a formal mathematics bound by rules of logic culminating in Euclids' seminal book "The Elements" in 400 BC.
Arabia - 940 - 1274 AD
Beginning with Abul Wafa al-Buzjani in 940 AD, Omar Khayyam in 1048 AD and Nasir al-Din al-Tusi in 1201 AD, successive attempts to prove Euclids' fifth postulate resulted in the birth of plane and "spherical trigonometry" an independent branch of mathematics.
Europe - 1413 - 1639 AD
At the start of the "Renaissance" with Fillipo Brunelleschi and his "perspectival drawing" method in 1413 described by Leone Battista Alberti in his book in 1435 there is a gradual development of a "geometry of vision" in art. This is further developed by figures such as Piero della Francesca and Albrecht Durer with his book illustrating mechanical aids for drawing published in 1525. In 1639 Girard Desargues wrote his revolutionary treatise on "projective geometry" based on ideas of projection and section. For the first time terms such as "point at infinity," "cone of vision" and "pencils of lines" appear and rigid Euclidean shapes can be transformed into another similar shape by perspective transformation.
Europe - 1663 - 1872 AD
Starting with Girolamo Saccheri there is an ongoing attempt to resolve the problem of Euclids' fifth postulate developed further by Carl Friedrich Gauss and finally solved independently by János Bolyai in 1823 and Nikolai Ivanovich Lobachevski in 1829. In 1868 Eugenio Beltrami produced the first model and "hyperbolic geometry" was accepted into the mainstream. A few years later in 1872 Felix Klein produced his general view of geometry by combining Spherical, Perspective, Projective and Hyperbolic geometries together enabling mathematicians to see geometry abstractly as a set of axioms not necessarily linked to the physical world.
Geometric thought appears to have risen simultaneously somewhere around 2000 BC in both Egypt and Babylon. The ensuing development of geometric thinking seems to go something like this:
Egypt & Babylon - 2000 - 500 BC
An understanding of "Pi" and what was later termed the "Pythagorean" relationships.
Greece - 750 - 250 BC
An absorption of Egyptian and Babylonian invention and the development of experimental geometry leading to a formal mathematics bound by rules of logic culminating in Euclids' seminal book "The Elements" in 400 BC.
Arabia - 940 - 1274 AD
Beginning with Abul Wafa al-Buzjani in 940 AD, Omar Khayyam in 1048 AD and Nasir al-Din al-Tusi in 1201 AD, successive attempts to prove Euclids' fifth postulate resulted in the birth of plane and "spherical trigonometry" an independent branch of mathematics.
Europe - 1413 - 1639 AD
At the start of the "Renaissance" with Fillipo Brunelleschi and his "perspectival drawing" method in 1413 described by Leone Battista Alberti in his book in 1435 there is a gradual development of a "geometry of vision" in art. This is further developed by figures such as Piero della Francesca and Albrecht Durer with his book illustrating mechanical aids for drawing published in 1525. In 1639 Girard Desargues wrote his revolutionary treatise on "projective geometry" based on ideas of projection and section. For the first time terms such as "point at infinity," "cone of vision" and "pencils of lines" appear and rigid Euclidean shapes can be transformed into another similar shape by perspective transformation.
Europe - 1663 - 1872 AD
Starting with Girolamo Saccheri there is an ongoing attempt to resolve the problem of Euclids' fifth postulate developed further by Carl Friedrich Gauss and finally solved independently by János Bolyai in 1823 and Nikolai Ivanovich Lobachevski in 1829. In 1868 Eugenio Beltrami produced the first model and "hyperbolic geometry" was accepted into the mainstream. A few years later in 1872 Felix Klein produced his general view of geometry by combining Spherical, Perspective, Projective and Hyperbolic geometries together enabling mathematicians to see geometry abstractly as a set of axioms not necessarily linked to the physical world.
