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Mathmajik

Thinking Too Much
Jan 9 '14
Non - Euclidean Geometry

The geometry most of us are familiar with from school is called Euclidean geometry, and it’s based on five rather simple self-evident truths, or axioms. It’s the regular geometry of lines and points that we can draw on a blackboard, and for a long time it was considered the only way geometry could work.The problem, however, is that the self-evident truths that Euclid outlined over 2000 years ago weren’t so self-evident to everyone. There was one axiom (known as the parallel postulate) that never sat right with mathematicians, and for centuries many people tried to reconcile it with the other axioms. 
At the beginning of the 18th century a bold new approach was tried: the fifth axiom was simply changed to something else. Instead of destroying the whole system of geometry, a new one was discovered which is now called hyperbolic (or Bolyai-Lobachevskian) geometry. This caused a complete paradigm shift in the scientific community, and opened the gates for many different types of non-Euclidean geometry. One of the more prominent types is called Riemannian geometry, which is used to describe none other than Einstein’s Theory of Relativity (our universe, interestingly enough, doesn’t abide by Euclidean geometry!).

Made me think of CFW who tried to sneak past yesterday….


Source: listverse.com

Non - Euclidean Geometry

The geometry most of us are familiar with from school is called Euclidean geometry, and it’s based on five rather simple self-evident truths, or axioms. It’s the regular geometry of lines and points that we can draw on a blackboard, and for a long time it was considered the only way geometry could work.The problem, however, is that the self-evident truths that Euclid outlined over 2000 years ago weren’t so self-evident to everyone. There was one axiom (known as the parallel postulate) that never sat right with mathematicians, and for centuries many people tried to reconcile it with the other axioms.
At the beginning of the 18th century a bold new approach was tried: the fifth axiom was simply changed to something else. Instead of destroying the whole system of geometry, a new one was discovered which is now called hyperbolic (or Bolyai-Lobachevskian) geometry. This caused a complete paradigm shift in the scientific community, and opened the gates for many different types of non-Euclidean geometry. One of the more prominent types is called Riemannian geometry, which is used to describe none other than Einstein’s Theory of Relativity (our universe, interestingly enough, doesn’t abide by Euclidean geometry!).

Made me think of CFW who tried to sneak past yesterday….


Source: listverse.com

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