Imagine you are suspending a cube from one vertex (corner) and
allowing it to hang freely. Now imagine you are lowering it into
water until it is exactly half submerged. What shape does the
surface of the water make around the cube?
What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?
Draw a square. A second square of the same size slides around the
first always maintaining contact and keeping the same orientation.
How far does the dot travel?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3
grid so that all the rows and columns add up to a prime number. Two
solutions are considered to be the same if, as in the example
shown, they contain the same six triples. How many different
solutions can you find?
Show that it is impossible to place the numbers 1, 2, 3,..., 9
one on each square of a 3 by 3 grid so that the diagonals, as well
as all the rows and columns, add up to prime numbers.