Ball Packing

If a ball is rolled into the corner of a room how far is its centre from the corner?

Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

When the Angles of a Triangle Don't Add up to 180 Degrees

This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the triangle.

Three Balls

Stage: 4 Challenge Level:

A circle has centre O and $\angle POR = \angle QOR.$

Construct tangents at $P$ and $Q$ meeting at $T$.
Draw a circle with diameter $OT$.
Do $P$ and $Q$ lie inside, or on, or outside this circle?
Now imagine a sphere with diameter $OT$.
Do $P$ and $Q$ lie inside, or on, or outside this sphere?