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Over the years, people tried to prove the fifth postulate, thinking
that something so complex must somehow follow from the simpler
postulates. They failed. examples on math forum; In the nineteenth century, mathematicians
tried a different tack: try changing the postulate, and see what
happens.
They found that they ended up with several varieties of
"non-Euclidean" geometry that were completely self-consistent, but
different from Euclid's geometry. Changing the "rules" made a new but
perfectly good game. read more on online math forum.
Over the years, people tried to prove the fifth postulate, thinking
that something so complex must somehow follow from the simpler
postulates. They failed. examples on math forum; In the nineteenth century, mathematicians
tried a different tack: try changing the postulate, and see what
happens.
They found that they ended up with several varieties of
"non-Euclidean" geometry that were completely self-consistent, but
different from Euclid's geometry. Changing the "rules" made a new but
perfectly good game. read more on online math forum.
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