Thoughts of higher things

As my year eight group were working through their exercises on calculating areas of compound shapes, one of the pupils approached me to have his work marked. After I marked his efforts he asked me if I could help him with a mathematical problem that he was working on. He then proceeded to outline the trouble he was experiencing with work on calculating the volume of a sphere in four dimensions! Not quite the sort of problem I was expecting from a year eight pupil! I had to admit to him that I was unable to help him at that moment, but that I would go away and give it some thought. This article summarizes those musings.