**Spherical Blackboard**

**What it shows:**

You can use a spherical blackboard for many things, including the teaching of geographical coordinates, as a model for a closed Universe, or simply as a mathematical shape.

In the non-Euclidean geometry of the sphere, a circle will have a circumference greater than 2πr and an area greater than πr^{2}. A triangle’s angles will add to more than 180°, and two parallel lines, called Great Circles, will converge.

A Universe with a density parameter Ω greater than unity will have too much mass to overcome its own gravitational...