Term Paper: Euclid's Fifth Postulate Philosophical

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[. . .] Whether the fifth postulate is true or false also affects the kind of geometry that is being used. For example, if the postulate is true, than Euclidian geometry works. If the postulate is false, then it creates a non-Euclidian type of geometry where similar triangles must always be congruent and the Pythagorean Theorem is no longer valid (Bennett, 2000).

Whether Euclid's fifth postulate is true, false, or both, it will continue to be debated by scholars and mathematicians for many years to come. Whether it will ever be 'solved' or proved remains to be seen. Either way, it is a fascinating and problematic piece of information that will carry on Euclid's legacy for centuries. If someday it is proven to be either true or false, and the decision is agreed upon, then it could change the way mathematics are done and the way geometry is looked at during the present time and also well into the future. Euclid would have likely enjoyed the attention his simple thoughts are receiving.

Works Cited

Bennett, Andrew G. The Axiomatic Method. 2000. Math 572 Home. 2 December 2002. http://www.math.ksu.edu/math572/notes/824.html.

Bogomolny, Alexander. The fifth postulate: attempts to prove. 2002. Cut the Knot. 2 December 2002. http://www.cut-the-knot.com/triangle/pythpar/Attempts.shtml.

Parallel lines and planes. 2002. Connecting Geometry. 2 December 2002. http://www.k12.hi.us/~csanders/ch_07Parallels.html.

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