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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 . Euclid e an Geometry in Egypt.

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Presentation Transcript
geometry

Geometry

Classical

Non-Euclidean

Analytic

Synthetic

euclidean geometry
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.
euclid e an geometry in egypt
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.

slide4

In Euclidean geometry

for instance the sum of

the anglesinside a

triangle is Always180

and a cube is always

360.

o

o

non euclidian geometry
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. 
slide6

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

slide7

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

analytic geometry
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.
slide9

In classical mathematics , analytic geometry also known as coordinate geometry , or cartesiangeometry,

is the study of geometry using a coordinate system and the principles of algebra and analysis .

slide10

Analytic Geometry:

The deferencesbetween AnalyticGeometryand SyntheticGeometry is AnalyticGeometry uses a coordinate system.

A coordinate system uses an X and Y or an X, Yand Z axe to locate a specific point on a flat or 3D plain.

ren descartes and pierre de fermat
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.

slide12

Made by:

Elif DEMİRLİ

JessicaBallon

HristiyanKolev

23.11.2011 UskudarGenclik Merkezi

BRIDGES THROUGH HISTORY WITH MATHS

Sources:

Wikipedia

Google

School materials