Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.
These pictures were made by starting with a square, finding the
half-way point on each side and joining those points up. You could
investigate your own starting shape.
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.
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
Derive a formula for finding the area of any kite.
Use the isometric grid paper to find the different polygons.
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. . . .
Remember that you want someone following behind you to see where
you went. Can yo work out how these patterns were created and
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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?
What shape and size of drinks mat is best for flipping and catching?
What mathematical words can be used to describe this floor
covering? How many different shapes can you see inside this