Posted by Joel on October 29, 2002 at 00:10:47:
In Reply to: Re: geometry OR the world is flat in Non-Euclidian Geometry!! posted by MathBard on October 27, 2002 at 03:42:40:
: : : why do the angles of a triangle add up to 180*?
: I like the straight line thing very creative! Of course with that logic you could also "prove that a square, pentagon, or any other x-agon had 180* or for that matter even a circle... i am going to see if my students can find the flaw in that!
: : You had me stumped for a while...was ready to bs my way with:
: : a straight line has 180 degrees, and to make a triangle, you can
: : "fold or bend" that straight line, so the triangle HAS to have them
: : 180 degrees...but I knew damn well Mr G et al would have put a
: : stick in my spokes with: why has a straight line 180 degrees ?!
: : Then it came to me; ARE YOU READY?
: : A square or rectangle has 4 right angles, so 360 degrees, right?
: : Draw a corner to corner diagonal : that splits it in exactly 2 identical
: : triangles, right? So each s'got to have 180 degrees...
: : How you like them apples, Joel?
: The following contains no axioms or theorems so it is NOT an official proof, but i think this is how Einstein would do it.
: Imagine... <<< very Einsteinian eh?
: Imagine you made triangles out of construction paper or cardboard. I guess you could REALLY do that so much for the Einsteinian thingy...
: Make one of each kind of triangle you know: Right, obtuse, acute, equilateral, isosceles (realizing there is overlap here) THEN...
: Rip the corners off any one of them. Align them side-by-side with their vertices together. Do they form a 180* angle?
This is only valid when done on a moving train!
: until you've tried them all!
: and By the way Euclid is rolling over in his grave about MR. Smartypants' 270* triangle. What if a PLANE was spherical? THEN triangles have 270* and Columbus REALLY screwed up to! the world really IS "flat!"
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