Two circles of equal size intersect and the centre of each circle
is on the circumference of the other. What is the area of the
intersection? Now imagine that the diagram represents two spheres
of equal volume with the centre of each sphere on the surface of
the other. What is the volume of intersection?
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.
Age 16 to 18 Challenge Level:
This requires some 3D geometry most easily visualised by using
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.