What shape is made when you fold using this crease pattern? Can you make a ring design?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

Explain how to construct a regular pentagon accurately using a straight edge and compass.

A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.

ABCDE is a regular pentagon of side length one unit. BC produced meets ED produced at F. Show that triangle CDF is congruent to triangle EDB. Find the length of BE.

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

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