# History of Geometry

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#1
I'm doing a project on incidence geometry, and for the introduction I'm trying to give it some historical context.

They key points I've got jotted down are
* rudimentary geometry is known in pre-history, from empirical observations necessary to make basic measurements, layout buildings and fields, etc.
* Thales of Miletus deduces new geometrical results from the empirical facts he learns in Egypt and Babylon. This effectively makes him the first (known) mathematician, and starts geometry as a field of inquiry in it's own right.
* Euclid sets out the first axiomatic system for the class of geometries which still bear his name. Archimedes, Apollonius, and various others further develop the field in the following centuries.
* in the seventeenth century Descartes develops coordinate systems and transforms, leading to analytic geometry. At around the same time Desargues considers idealised structures at infinity, which give some early results on the real projective plane.
* in the eighteenth century Euler sets out the basics of affine geometry
* in the early nineteenth century Bolyai and Lobachevsky independently develop hyperbolic geometry. Riemann establishes Riemannian geometry and incidentally elliptic geometry, and later Klein is able to unify elliptic, Euclidean, and parabolic geometries within projective geometry, as part of the Erlangen program.
* in part because of questions about the foundations of mathematics, and also because of the proliferation of geometries, people set about finding new axiomatic systems. The best known are Tarski's and Hilbert's axioms. The early recognition of relations such as incidence prompts the development of synthetic geometry, as purely formal systems.
* incidence geometry and ordered geometry continue to develop. Interest is bolstered by their close links to combinatorics, and in turn to computer science.

Is there anything fundamentally wrong, or any important point that I've missed in any of that? Can anyone recommend a decent book or article on all this?
0
6 years ago
#2
(Original post by mmmpie)
I'm doing a project on incidence geometry, and for the introduction I'm trying to give it some historical context.

They key points I've got jotted down are
* rudimentary geometry is known in pre-history, from empirical observations necessary to make basic measurements, layout buildings and fields, etc.
* Thales of Miletus deduces new geometrical results from the empirical facts he learns in Egypt and Babylon. This effectively makes him the first (known) mathematician, and starts geometry as a field of inquiry in it's own right.
* Euclid sets out the first axiomatic system for the class of geometries which still bear his name. Archimedes, Apollonius, and various others further develop the field in the following centuries.
* in the seventeenth century Descartes develops coordinate systems and transforms, leading to analytic geometry. At around the same time Desargues considers idealised structures at infinity, which give some early results on the real projective plane.
* in the eighteenth century Euler sets out the basics of affine geometry
* in the early nineteenth century Bolyai and Lobachevsky independently develop hyperbolic geometry. Riemann establishes Riemannian geometry and incidentally elliptic geometry, and later Klein is able to unify elliptic, Euclidean, and parabolic geometries within projective geometry, as part of the Erlangen program.
* in part because of questions about the foundations of mathematics, and also because of the proliferation of geometries, people set about finding new axiomatic systems. The best known are Tarski's and Hilbert's axioms. The early recognition of relations such as incidence prompts the development of synthetic geometry, as purely formal systems.
* incidence geometry and ordered geometry continue to develop. Interest is bolstered by their close links to combinatorics, and in turn to computer science.

Is there anything fundamentally wrong, or any important point that I've missed in any of that? Can anyone recommend a decent book or article on all this?
The BSHM might be of some use.
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