P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
For the following solids, try to visualise how best to pack lots of them together so as to use up the least space. Can you draw a clear diagram or give a clear explanation of your packing mechanism in each case?
Whilst it might seems relatively simple, the problem of 'shape packing' is very difficult mathematically to solve with certainty. Intuitive visualisation often works just as well as a strict mathematical analysis, and often is the only sensible possibility with packing together complicated shapes.
In reality, complex molecules such as proteins pack, or fold, together in very intricate ways..