### How Far Does it Move?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

### Up and Across

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects its vertical and horizontal movement at each stage.

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

# Lying and Cheating

##### Age 11 to 14Challenge Level

Sheila Luk (Year 10, The Mount School, York) saw right through this 'deception' and gave an excellent explanation of the situation.

The cheat is that although each triangle has a side of length 1 cm, the side at right angles to it is of length 10/ 11 cm. The diagonal of the rectangle does not go through the corners of the squares if it's drawn on squared paper.

The new rectangle, shown dotted, is not 11 by 10, but 10 10/ 11 by 10 and the difference in area is exactly 10/ 11 square cm, the area of the two triangles which were removed.

10 10/ 11 x 10 = 109 1/ 11= 110 - 10/ 11