If a ball is rolled into the corner of a room how far is its centre
from the corner?
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.
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.
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?
Explain your answer.
Now imagine a sphere with diameter $OT$.
Do $P$ and $Q$ lie inside, or on, or outside this sphere?
Explain your answer. You may find an interactive hint in the second
To experiment further with this problem, download a copy of
Geometer's Sketch Pad .