Synthetic geometry The human abstraction

Tu ne cede malis sed contra audentior ito

From Euclidean Geometry to Non-Euclidean Geometry

Euclidean geometry is one of the earliest geometry concepts known to man.

It works best when applied to 2D plains/objects. However when applied to 3D surfaces, 3D macro objects it becomes less functional thus Non-Euclidean geometry came to being.

Euclid Ipsa scientia potestas est

Gauss,Bolyai and Lobachevski

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.

Gauss Bolyai

Lobachevski Aut viam inveniam aut faciam

Hyperbolic Geometry

Elliptic Geometry

Veritas vos liberabit

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

Poincaré

Dimidium facti qui coepit habet

Poincaré disc

Docendo discimus

Poincaré disc

Icosahedron honeycomb

Adde parvum parvo

magnus acervus erit

Aftermath of the creation of Non-Euclidean geometry

Faber est quisque fortunae suae

Even though the discovery didn’t benefit the people of the 19th century immediately nowadays Non-Euclidean/Axiomatic Geometry is inseparable from our daily lives.

It is absolutely essential for scientists. Many of the science models are created in 3 dimensions (3D) so the classical Euclidean geometry is just not enough for an accurate model.

Nulli secundus /nulli secunda

Gravity

Electromagnetism

Per aspera ad astra!

The weak nuclear force

And the strong nuclear forceCrede quod habes, et habes

The shown above is referred to as Fundamental interaction or The 4 forces of nature. They are the 4 absolute laws of the universe and their Accurate representation in physical and mathematical models is Heavily dependent on Axiomatic Geometry!All terrestrial and celestial events can be represented with Axiomatic Geometry!

Credo ut intelligam

Credo quia absurdum est

Nihil obstat

De fumo in flammam

Created by Hristiyan Kolev Class 12-a year 2011

SOU Jeleznik, Stara Zagora

www.jeleznik.orgMaterial source:

http://www.wikipedia.org/http://www.wolframalpha.com/

Pictures: http://wall.alphacoders.com/

http://devianart.org/ http://www.google.com/

Dum spiro spero, Dum spiro scio

+ Tu ne cede malis sed contra audentior ito Yield not to misfortunes, but advance all the more boldly against them all+ Ipsa scientia potestas est Knowledge itself is power. + Aut viam inveniam aut faciam I'll either find a way or make one+ Veritas vos liberabit The truth shall set you free+ Dimidium facti qui coepit habet He conquers twice who in the hour of conquest conquers himself.

+ Docendo discimus Teach in order to learn (we learn by teaching)+ Adde parvum parvo magnus acervus eritAdd a little to a little and there will be a great heap+ Faber est quisque fortunae suae every man is an architect of his own fortune + Nulli secundus /nulli secunda Second to none + Per aspera ad astra! Through difficulties to the stars!

+ Crede quod habes, et habes Believe that you have it, and you do.+ Credo ut intelligam I believe so that I may understand + Credo quia absurdum est I believe it because it is absurd + Nihil obstatnothing stands in the way+ De fumo in flammam Out of the smoke into the flame+ Dum spiro spero. Dum spiro scio.While I breathe, I dream. While I breath, I learn.