Constructions

problem
The medieval octagon

Age

14 to 16

Challenge level

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
problem
Pentabuild

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

Describe how to construct three circles which have areas in the ratio 1:2:3.
problem
Two points plus one line

Age

14 to 16

Challenge level

Draw a line (considered endless in both directions), put a point somewhere on each side of the line. Label these points A and B. Use a geometric construction to locate a point, P, on the line, which is equidistant from A and B.
problem
Half a triangle

Age

14 to 16

Challenge level

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
problem
A patchwork piece

Age

7 to 11

Challenge level

Follow the diagrams to make this patchwork piece, based on an octagon in a square.
problem
Yin yang

Age

7 to 11

Challenge level

Can you reproduce the Yin Yang symbol using a pair of compasses?
project
Flip your mat!

7 to 14

What shape and size of drinks mat is best for flipping and catching?
problem
Attractive rotations

Age

11 to 14

Challenge level

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
problem
Constructing triangles

Age

11 to 14

Challenge level

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?