Classical Non-Euclidean Analytic Synthetic Geometry Classical Non-Euclidean Analytic Synthetic

Euclidean geometry Euclidean geometry is one of the earliest geometry concepts known to man. Civilization from early history have been aware of these simple concepts.

Euclidean Geometry in Egypt The basic geometry concepts were used by the Egyptians in pyramid construction sites. This knowledge was transcribed mainly inside the pyramids. We have evidence that they were aware of Pythagoras’ theorem, the number π, basic calculations, figures such as spheres, triangles, cubes and so on.

In Euclidean geometry for instance the sum of the angles inside a triangle is Always 180 and a cube is always 360. o o

Non-Euclidian Geometry The axiomatic study of Euclidean geometry in the 19th Century led to the discovery of non-Euclidean geometries with different axioms. Gauss, Bolyai and  Lobachevski independently discovered Hyperbolic Geometry, in which the Euclidean axiom of parallelism is replaced by an alternative. 

For example the sum of a cube’s angles when applied to a non-Euclidean surface is not necessary 360 the sum can exceed this number. o o o o =180 >180 <180

Poincaré soon discovered the first physical geometric model of hyperbolic geometry, in a form known as the Poincaré disc.

Analytic geometry Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning.

In classical mathematics , analytic geometry also known as coordinate geometry , or cartesian geometry, is the study of geometry using a coordinate system and the principles of algebra and analysis .

Analytic Geometry: The deferences between Analytic Geometry and Synthetic Geometry is Analytic Geometry uses a coordinate system. A coordinate system uses an X and Y or an X, Y and Z axe to locate a specific point on a flat or 3D plain.

René Descartes and Pierre de Fermat They are the so called father of analytic geometry, trough it’s discovery algebra and geometry were bridge together for the first time. The Cartesian coordinate system got it’s name from the Descartes signature.

Made by: Elif DEMİRLİ Jessica Ballon Hristiyan Kolev 23. 11 Made by: Elif DEMİRLİ Jessica Ballon Hristiyan Kolev 23.11.2011 Uskudar Genclik Merkezi BRIDGES THROUGH HISTORY WITH MATHS Sources: Wikipedia Google School materials