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.
Spherical Triangles on Very Big Spheres
Stage: 5 Challenge Level:
Large networks of pipes, cables and power lines are obviously of
great importance. Whilst small percentage errors may not appear to
be large they will have a significant impact on the cost of large
engineering projects, such as laying a new oil pipeline. Fuel
costings for international travel provide other applications of
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. More information on many of our other activities
can be found here.