Find the vertices of a pentagon given the midpoints of its sides.
What fractions can you divide the diagonal of a square into by
Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
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?
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
Drawing a triangle is not always as easy as you might think!
A first trail through the mysterious world of the Golden Section.
You are given a circle with centre O. Describe how to construct with a straight edge and a pair of compasses, two other circles centre O so that the three circles have areas in the ratio 1:2:3.
How can you represent the curvature of a cylinder on a flat piece of paper?
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.
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.
You are only given the three midpoints of the sides of a triangle.
How can you construct the original triangle?
Jenny Murray describes the mathematical processes behind making patchwork in this article for students.
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,. . . .
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