Hyperbolic Triangle
 In the upper half-plane model of hyperbolic geometry, the hyperbolic straight lines are the vertical rays and the semicircles touching the  axis.The measure of the angle formed by the intersection of two semicircles is calculated by measuring the angle of the tangents to the circles at that point. The angle sum of a hyperbolic triangle is less than 180 degrees. The Gauss–Bonnet formula states that the area of a hyperbolic triangle is the difference of  (or 180°) and the sum of the interior angles of the triangle.C. Walkden, "The Gauss-Bonnet Theorem," lecture notes, Feb. 13, 2009. S. Weintraub, "Tiling the Poincaré Disk," American Mathematical Society Feature Column, Feb. 1998. R. E. Schwartz, "Ideal Triangle Groups, Dented Tori, and Numerical Analysis," Annals of Mathematics, 153, 2001 pp. 533–598.   "Hyperbolic Triangle" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/HyperbolicTriangle/ Contributed by: Michael Rach and Ron Grosz | ||||||||||||||
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