You are Here: Home >< Maths

# History of Geometry watch

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?
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.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 22, 2014
Today on TSR

### Exam Jam 2018

Join thousands of students this half term

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams