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