Schwarz triangle function: Difference between revisions

Revision as of 19:54, 15 February 2017

Revision as of 19:55, 15 February 2017

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:<math>{1\over a} + {1\over b} + {1\over c} < 1.</math>

The construction of a tessallationtessellation will first be carried out for the case when ''a'', ''b'' and ''c'' are greater than 2.<ref> {{harvnb|Caratheodory|1954|pages=177–181}}</ref>

The equality above implies that if one of the angles is a right angle, say ''a'' = 2, then both ''b'' and ''c'' are greater than 2 and one of them, ''b'' say, must be greater than 3. In this case, reflecting the triangle across the side AB gives an isosceles hyperbolic triangle with angles {{pi}}/''c'', {{pi}}/''c'' and 2{{pi}}/''b''. The construction of the tessallationtessellation that is given below applies equally well in this case because the doubled triangle is isosceles.<ref>{{harvnb|Caratheodory|1954|pages=181–182}}</ref>

===Triangles with one or two ideal vertices===