Constructions

What fractions can you divide the diagonal of a square into by simple folding?

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

Drawing a triangle is not always as easy as you might think!

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

How can you represent the curvature of a cylinder on a flat piece of paper?

The challenge is to produce elegant solutions. Elegance here implies simplicity. The focus is on rhombi, in particular those formed by jointing two equilateral triangles along an edge.

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

Describe how to construct three circles which have areas in the ratio 1:2:3.

Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.

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.