Constructions

problem
Curvy areas

Age

14 to 16

Challenge level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Jomista mat

Age

7 to 11

Challenge level

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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
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
Three tears

Age

14 to 16

Challenge level

Construct this design using only compasses
problem
Yin yang

Age

7 to 11

Challenge level

Can you reproduce the Yin Yang symbol using a pair of compasses?
problem
Pentabuild

Age

16 to 18

Challenge level

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

Age

16 to 18

Challenge level

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

Age

14 to 16

Challenge level

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.