Constructions

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
LOGO challenge 8 - rhombi

Age

7 to 16

Challenge level

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
problem
LOGO challenge 2 - diamonds are forever

Age

7 to 16

Challenge level

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.
problem
Folding squares

Age

14 to 16

Challenge level

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
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
Pareq exists

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
problem
Gold again

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
page
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?