Pink and White
The white square slides once around the pink square. Through what distance does the point P on the white square move?
Age
14 to 16
Challenge level
Problem
Image
A square of side 8cm, is painted pink and fixed to a table.
An identical square, painted white, is placed on the table alongside the pink square, and has a point P marked one quarter of the way along the diagonal as shown.
If the white square slides once around the pink square, keeping the same orientation and always remaining in contact with the pink square, through what distance does P move?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Image
The black line shows the locus of P as the white square slides around the pink square.
The locus is a square of side 16cm, and hence P moves through a distance of 64cm.