Can you prove that the sum of the distances of any point inside a
square from its sides is always equal (half the perimeter)? Can you
prove it to be true for a rectangle or a hexagon?
What shape and size of drinks mat is best for flipping and catching?
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Polygons drawn on square dotty paper have dots on their perimeter
(p) and often internal (i) ones as well. Find a relationship
between p, i and the area of the polygons.
Find the ratio of the outer shaded area to the inner area for a six
pointed star and an eight pointed star.
Draw a pentagon with all the diagonals. This is called a pentagram.
How many diagonals are there? How many diagonals are there in a
hexagram, heptagram, ... Does any pattern occur when looking at. . . .
Derive a formula for finding the area of any kite.