Regular polygons and circles

article
Using GeoGebra

Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.
problem
Circular area

Age

7 to 11

Challenge level

How could you find out the area of a circle? Take a look at these ways.
project
Flip your mat!

What shape and size of drinks mat is best for flipping and catching?
problem
Gaudi's design

Age

11 to 16

Challenge level

Eight lines are drawn in a regular octagon to form a pattern. What fraction of the octagon is shaded?
problem
Olympic rings

Age

5 to 7

Challenge level

Can you design your own version of the Olympic rings, using interlocking squares instead of circles?
problem
A rational search

Age

16 to 18

Challenge level

Investigate constructible images which contain rational areas.
problem
Sports equipment

Age

7 to 11

Challenge level

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?
problem
Shaping it

Age

5 to 11

Challenge level

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.
problem
Contact circles

Age

14 to 16

Challenge level

These four touching circles have another circle hiding amongst them...
problem
Circle time

Age

14 to 16

Challenge level

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?