Constructions

problem

Pareq Exists

Age

14 to 16

Challenge level

2 out of 3

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
problem

Folding Squares

Age

14 to 16

Challenge level

2 out of 3

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?
problem

Folding Fractions

Age

14 to 16

Challenge level

2 out of 3

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

Moving Squares

Age

14 to 16

Challenge level

2 out of 3

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

Close to Triangular

Age

14 to 16

Challenge level

3 out of 3

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

Gold Again

Age

16 to 18

Challenge level

2 out of 3

Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
problem

Pentabuild

Age

16 to 18

Challenge level

2 out of 3

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

A Rational Search

Age

16 to 18

Challenge level

3 out of 3

Investigate constructible images which contain rational areas.
article
Mathematical Patchwork

Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
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Making Maths: Stars

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?