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. Coins inserted into the machine slide down a chute into the machine and a drink is duly released. How many more revolutions does the foreign coin make over the 50 pence piece going down the chute? N.B. A 50 pence piece is a 7 sided polygon ABCDEFG with rounded edges, obtained by
replacing AB with arc centred at E and radius EA; replacing BC with arc centred at F radius FB ...etc..
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Any cube may be removed so imagine some uncoloured, transparent
cubes propping up anything that needs it.
If a 'perforated cube' has the three views (projections) below,
what is the most and the least cubes possible to make a
shape that has these three projections ? In other words what could
be the most and the least cubes left from the original 125 ?