Geometry Classical NonEuclidean Analytic Synthetic Euclidean geometry Euclidean

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Geometry Classical Non-Euclidean Analytic Synthetic

Geometry Classical Non-Euclidean Analytic Synthetic

Euclidean geometry � Euclidean geometry is one of the earliest geometry concepts known to

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

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 o triangle

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

Non-Euclidian Geometry The axiomatic study of Euclidean geometry in the 19 th Century led

Non-Euclidian Geometry The axiomatic study of Euclidean geometry in the 19 th 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

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

� Poincaré soon discovered the first physical geometric model of hyperbolic geometry, in a

� 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.

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

� 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

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 3 D plain.

René Descartes and Pierre de Fermat They are the so called father of analytic

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. 2011 Uskudar Genclik Merkezi

Made by: Elif DEMİRLİ Jessica Ballon Hristiyan Kolev 23. 11. 2011 Uskudar Genclik Merkezi BRIDGES THROUGH HISTORY WITH MATHS Sources: Wikipedia Google School materials

1 Analytic Function Analytic Function Analytic Function Analytic1 Analytic Function Analytic Function Analytic Function Analytic
1 Analytic Function Analytic Function Analytic Function Analytic1 Analytic Function Analytic Function Analytic Function Analytic
Analytic Geometry Chapter 4 Analytic Geometry Unites geometryAnalytic Geometry Chapter 4 Analytic Geometry Unites geometry
Chapter 28 Euclidean Algorithm Euclidean Algorithm Extended EuclideanChapter 28 Euclidean Algorithm Euclidean Algorithm Extended Euclidean
Euclidean geometry and trigonometry Euclidean geometry means flatEuclidean geometry and trigonometry Euclidean geometry means flat
Euclidean geometry and trigonometry Euclidean geometry means flatEuclidean geometry and trigonometry Euclidean geometry means flat
Heisenberg STFT Analytic Signal Analytic Wavelets Analytic WaveletHeisenberg STFT Analytic Signal Analytic Wavelets Analytic Wavelet
THE ANALYTIC HIERARCHY PROCESS Analytic Hierarchy Process AnalyticTHE ANALYTIC HIERARCHY PROCESS Analytic Hierarchy Process Analytic
ROMANIAN ACADEMY FROM THE EUCLIDEAN TO THE NONEUCLIDEANROMANIAN ACADEMY FROM THE EUCLIDEAN TO THE NONEUCLIDEAN
2 March Analytic Synthetic Distinction Examples of analytic2 March Analytic Synthetic Distinction Examples of analytic
Synthetic Networks Synthetic Networks as Models Why syntheticSynthetic Networks Synthetic Networks as Models Why synthetic