Difference between revisions of "Chapter 2: An ancient theorem and a modern question"

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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 jsut some constant.
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.
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