Henri Poincaré (1854 - 1912) devised a model of a non-Euclidean geometry.

He wrote of his model as an imaginary universe occupying the interior of a disc in the Euclidean plane. The inhabitants are seen by us to 'shrink' as they approach the edge of the disc which to them seems to be an infinitely distant horizon. They do not register the effect, as their 'ruler' shrinks with them.

The sum of the angles of a triangle in this hypobolic space is always less than $180^o.$ An example of a triangle in this space is given in the diagram.

Poincaré said:

  • 'one geometry cannot be more true than another; it can only be more convenient'

(none) (none) AxiomOfChoice
ContinuumHypothesis
Euclid
EuclideanGeometry
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UncountableSet
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NonEuclideanGeometry Axiom
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PoincaresDisc
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HyperbolicFunction Axiom
EuclideanGeometry 		DedekindCut
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EuclideanAlgorithm
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HighestCommonFactor
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PerfectNumber
PrimeNumber

Local neighbourhood - D3

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