Draw a square and an arc of a circle and construct the Golden rectangle. Find the value of the Golden Ratio.
Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.
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,. . . .
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?
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
Construct this design using only compasses
Explain how to construct a regular pentagon accurately using a straight edge and compass.
Construct a line parallel to one side of a triangle so that the triangle is divided into two equal 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.
Describe how to construct three circles which have areas in the ratio 1:2:3.
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.
What fractions can you divide the diagonal of a square into by simple folding?
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.
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
How can you represent the curvature of a cylinder on a flat piece of paper?
Investigate constructible images which contain rational areas.
Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
Drawing a triangle is not always as easy as you might think!
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.