Mathematics Non-euclidian Maths. Powerpoint Templates. Once upon a time Euclid had 5 axioms It shall be possible to draw a straight line joining any 2 points. A finite straight line may be extended without limit in either direction.
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a. All perpendiculars to a straight line meet at one point.
b. Two straight lines enclose an area.
c. The sum of the angles of any triangle is greater than 180 degrees.
Neither have even been proven wrong, and yet they contradict each other???
Systems work within their own axiom sets
Godel (1906-78), Austrian
It is impossible to prove that any mathematical system is free from contradiction
He didn’t prove that Maths has contraditions, just that it’s impossible to prove it doesn’t
Maths hasn’t had any contraditions since it’s formalisation 2500 yrs ago – so most mathematicians mostly ignore Godel’s theorm
So if Riemann, Godel & Einstien have contradicted Euclidian maths, why do we still use it?
Because it works!
Why does it work?