Nick Lord says "This problem encapsulates for me the best features of the NRICH collection."
Explain how to construct a regular pentagon accurately using a straight edge and compass.
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.
A voyage of discovery through a sequence of challenges exploring properties of the Golden Ratio and Fibonacci numbers.
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?
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.
What groups of transformations map a regular pentagon to itself?