1. Rolling Polygons A dynamic PowerPoint introduction to the “Rolling Polygons Investigation” created by Mrs A. Furniss.

2. Polygons A polygon is a 2D (flat) shape with many sides. Regular Polygons (all side lengths and angles equal) Irregular Polygons (different side lengths)

3. An Introduction to Rolling Polygons Roll an equilateral triangle around a regular hexagon. How many rolls does it take to get the triangle back to its starting position? Answer = 6

4. Now try rolling a square around a regular hexagon. How many rolls does it take to get the square back to its starting position? Keep going ; the dot needs to finish at the top! Answer = 12

5. Recording Your Results Try other combinations of polygons. Write down your results using a table like the one below. Can you find a link between the number of sides on the polygons you have used and the number of rolls it takes? Write this down under the subheading of “Conclusion” Shape 1 (stationary) Shape 2 (rolled) Number of Rolls hexagontriangle6

6. Extension Task: Investigating The Loci of Rolling Polygons A locus (plural : loci) is the path something travels Sketch the locus of the dot as one regular polygon rolls around another. Here is an example: Try changing the position of the dot. Investigate with other combinations of regular polygons.