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Chapter 2: An ancient theorem and a modern question: Difference between revisions
Chapter 2: An ancient theorem and a modern question (edit)
Revision as of 21:43, 16 May 2020
, 16 May 2020→Hyperbolic Geometry
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<math> \pi - (\alpha + \beta + \gamma) = C \triangle </math> | <math> \pi - (\alpha + \beta + \gamma) = C \triangle </math> | ||
where <math> C </math> is just some constant determined by the ''units'' by which we measure a give length or area. The ''units'' we use can always be chosen such that <math> C=1</math> | where <math> C </math> is just some constant determined by the ''units'' by which we measure a give length or area. The ''units'' we use can always be chosen such that <math> C=1</math>. | ||
In contrast to euclidean geometry where the angels of a triangle alone don’t tell you anything about its size - in hyperbolic geometry if you know the sum of the angels of a triangle, you can calculate its area using the formula above. | In contrast to euclidean geometry where the angels of a triangle alone don’t tell you anything about its size - in hyperbolic geometry if you know the sum of the angels of a triangle, you can calculate its area using the formula above. | ||