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There are well-known non-euclidean models that are created in euclidean geometry, for example the Beltrami-Klein model. This "nesting" proves the consistency of non-euclidean geometry (it is consistent if euclidean geometry is consistent).

I have heard that it is possible to build a model of Euclidean geometry inside non-Euclidean geometry, but I couldn't find any examples. Could you please provide some.

Jean Marie
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veirab
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    Which kind of non-euclidean geometry do you target ? Hyperbolic or spherical ? If it is the spherical model, it is locally Euclidean... – Jean Marie Aug 08 '24 at 17:16
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    Take a look at https://math.stackexchange.com/questions/1347/studying-euclidean-geometry-using-hyperbolic-criteria – Steen82 Aug 09 '24 at 01:15

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