Poincares Disc
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Poincares Disc |
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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 above.
Poincaré said 'one geometry cannot be more true than another; it can only be more convenient'