Area of Hyperbolic Triangles Heldine Aguiluz Emily Ki Trinity Shen

The Hyperbolic Geometry Song LYRICS: Hyperbolic triangles
 Which sort of look like trees
 Are always curved strangely
 So that they're less than 180 degrees

 Not a regular line on a regular plane
 Shaped like a potato chip on a subway train
 A complicated challenge for the human brain

Background Check Triangle: Polygon with 3 corners/vertices & 3 sides/edges Euclidean geometry Sides/edges are straight lines Right, obtuse, & acute triangles  angles add up to 180° Area = ½ bh Look up images with angles and/or labeled area of a triangle with b, h

Hyperbolic Triangles In hyperbolic geometry, a hyperbolic triangle is a figure in the hyperbolic plane, consisting of three sides and three angles. The 3 sides are made of geodesics and the three angles sum up to less than 180°

Hyperbolic Area If D is a region in , hyperbolic area is defined as

Area of Hyperbolic Triangle In hyperbolic geometry, a hyperbolic quadrilateral has angle sum less than 2π, therefore cannot have four right angles. Instead, we use triangles as basic figures. The Gauss-Bonnet Formula If the hyperbolic triangle ABC has angles α, β,γ, then its area is

How to Have Hyperbolic Fun! http://www.geometrygames.org/HyperbolicGames/