Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
What fractions can you divide the diagonal of a square into by simple folding?
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?
Drawing a triangle is not always as easy as you might think!
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.
Construct this design using only compasses
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
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,. . . .
What shape and size of drinks mat is best for flipping and catching?
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Investigate constructible images which contain rational areas.
How can you represent the curvature of a cylinder on a flat piece of paper?
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.
Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
Describe how to construct three circles which have areas in the ratio 1:2:3.
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.