You may also like

problem icon

Just Rolling Round

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

problem icon

At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

problem icon

Diophantine N-tuples

Can you explain why a sequence of operations always gives you perfect squares?

Gaudi's Design

Age 11 to 16 Challenge Level:
A regular octagon, with sides divided into three equal parts. The resulting points are joined to create a star.

The diagram shows a ceramic design by the Catalan architect Antoni Gaudi. It is formed by drawing eight lines connecting points which divide the edges of the outer regular octagon into three equal parts, as shown.

What fraction of the octagon is shaded?