Constructions

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?
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

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?
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

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

Cool as Ice

Age

11 to 16

Challenge level

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.