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What sort of geometry results from allowing no parallels through any external point?

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Allowing two parallels through any external point, the first alternative to Euclid 's fifth postulate, leads to the hyperbolic geometry developed by the Russian N. I. Lobachevsky in 1826 and independently by the Hungarian Janos Bolyai in 1832 ...

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Similar questions: How is hyperbolic geometry achieved? What alternative to Euclid's fifth postulate leads to the hyperbolic geometry developed by the Russian N. I. Lobachevsky in 1826 and independently by the Hungarian Janos Bolyai in 1832? [ Hide these questions ]

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