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Mr Reasonable wrote:https://www.theonion.com/new-evidence-reveals-pythagoras-wrote-dozens-of-unhinge-1819655096
These conspiracy theorems shed new light on this historic figure, who was apparently suspicious of the fact that all triangles have interior angles adding up to 180 degrees, believing this was evidence that they were united in hiding some sort of covert agenda,” said Professor Janet Boisvert, who found among the artifacts an alternative version of the Pythagorean theorem in which Pythagoras concluded that the square of the hypotenuse of a right triangle was equal to the sum of “all the lies embodied by these cursed triangles!” “One scroll is 35 feet long and contains nothing but a rambling series of postulates attempting to demonstrate the existence of a triangle with three obtuse angles that he thought was being kept under wraps by the government.
gib wrote:Einstein proved that on the surface of a sphere, you could form a triangle with two right angles. Just draw two parallel lines going north starting from the equator and they will meet at the north pole. <-- Could that be considered a triangle? If so, is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm...
gib wrote:is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm...
Uccisore wrote:gib wrote:Einstein proved that on the surface of a sphere, you could form a triangle with two right angles. Just draw two parallel lines going north starting from the equator and they will meet at the north pole. <-- Could that be considered a triangle? If so, is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm...
What if I say you can't draw a triangle on a sphere at all, because anything drawn on a sphere is inherently a three dimensional figure, which violates the definition of 'triangle'?
James S Saint wrote:gib wrote:is there a spacetime geometry in which a triangle can be formed with three obtuse angles? Hmm...
Easily as long as you aren't talking about planer geometry. Wrapping things around a sphere allows for just about anything.
gib wrote:But I think to the beings who are confined to the sphere surface, any shape you draw enclosed by 3 angles would look like a triangle.
[/quote]Still, that doesn't mean the shape I described would look like a triangle to them either. At the equator, it would look like the beginning of a square and as they make their way to the north pole they'd wonder how the hell the two sides ended up crossing.
surreptitious75 wrote:The general definition of a triangle is a shape with three straight sides whose points touch and whose internal angles add up to I80 degrees. However this is only true
of triangles in two dimensional space.
gib wrote:If we are living in a 4D universe which is symbolized by the 3D sphere, then no geometric object we see is ever really flat.
If I understand where Ucci's going with this, he'd like to say that if we are analogues of 2D creatures bound to the surface of a sphere, then whatever looks flat to us is really curved.
Just as we would say that the surface of a sphere is really curved despite what the 2D creatures living on the surface think,
Thus, if we really are creatures living on a the surface of a 4D universe, we have never ever seen a triangle.
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