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:

Chris, age 15, was able to solve the first part:

As $OP$ is a radius and $PT$ is a tangent, the angle between them is a right angle. So the triangle $OPT$ is right angled, and the hypotenuse is the diameter of the circle, so $P$ lies on the circle. In the same way, $Q$ lies on the circle.