Geometry

Geometry is a form of mathematics which deals with shape, size, relative position of figures, and the properties of space. It was not officially "discovered" by one culture, and rose throughout a variety of societies (Mesopotamia/Egypt) as a means of dealing with lengths areas and volumes for architecture, works of art, and astronomy among other things.

Despite the varied nature of its origins, the Greeks pioneered much of Pre-Christ mathematical geometry. Pythagoras and Thales were some of the leading geometers of that time, with the Pythagoras school formulating the Pythagoras Theorem, which still bears much relevance in today's world. Around 300BC, after the work of Thales and others, Euclid revolutionized mathematical geometry at the time, writing a book called Elements. The script remained a key source of geometric knowledge for many years, and some of its principles are still taught today.

With the writing of this book, Euclid brought further mathematical insight into the geometric process. By use of the axiomatic method, ideas and calculations became more precise and rigorous. The introduction of a definition, axiom, theorem, and proof caused the format which we see today in modern mathematics. Through the introduction of a small number of accepted truths (axioms),a theorem can be introduced which in turn can be proved by other calculations and axioms.

During the Middle Ages, the mathematics of countries in the Middle East contributed greatly to the development of geometry as we know it. This is particularly true of algebra's role in geometry, and the development of analytic geometry. Analytic geometry was fully created in the 17th century by Rene Descartes and Pierre de Fermat. An example of analytic geometry is shown below. 

Analytic geometry functions through the use of equations and algebraic representation to represent certain points within a space. This form of representation functions on a co-ordinate system. Many elements of geometry can be seen to function in this way, as by using co-ordinates, distances and relativity can be made precise. Cartesian co-ordinates can be seen to have done this, as every point can be specified within a certain plane by a set of numbers.

Originally these numbers would have come in pairs, to function on 2 dimensional (2 plane) basis, however we have come to see how this Cartesian system can function on 3 planes. This knowledge allows for a far greater understanding of the world around us, and has lead to many discoveries in architecture and science, among other things.








Different types of contemporary geometry:

Euclidean geometry -

Differential geometry -

Topology and geometry -

Algebraic geometry -

http://mathworld.wolfram.com/Geometry.html