Ideal Triangles

When using the Poincaré disc model for hyperbolic geometry, the hyperbolic universe is inside a circle. The circle itself is at infinity. A triangle inside the circle will always have angle sum less than 180 degrees. As the vertices of a triangle approach the circle, the angle sum tends to 0, and the hyperbolic perimeter of the triangle tends to infinity. The limiting triangle is called an ideal triangle. The hyperbolic area of an ideal triangle is always π. All triangles in the animation have the same hyperbolic area.

Source:http://www.malinc.se/math/noneuclidean/mainen.php