Visualising and representing

Can you find a rule which connects consecutive triangular numbers?

Weekly Problem 37 - 2013
Which of the statements about diagonals of polygons is false?

Can you mark 4 points on a flat surface so that there are only two different distances between them?

A huge wheel is rolling past your window. What do you see?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

A solid 'star' shape is created. How many faces does it have?

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?

I found these clocks in the Arts Centre at the University of Warwick intriguing - do they really need four clocks and what times would be ambiguous with only two or three of them?