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What sort of geometry results from allowing two parallels through any external point?

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The second alternative, which allows no parallels through any external point, leads to the elliptic geometry developed by the German Bernhard Riemann in 1854.

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Get more facts and information about non-Euclidean geometry . Or, view the full encyclopedia entry from The Columbia Encyclopedia, Sixth Edition.

Similar questions: How is elliptic geometry achieved? What alternative to Euclid's fifth postulate leads to the elliptic geometry developed by the German Bernhard Riemann in 1854? [ Hide these questions ]

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