1. Area of Hyperbolic Triangles
Heldine Aguiluz
Emily Ki
Trinity Shen

2. 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

3. 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

4. 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°

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

7. 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

13. How to Have Hyperbolic Fun!