Explain how to construct a regular pentagon accurately using a
straight edge and compass.
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?
Draw a square and an arc of a circle and construct the Golden
rectangle. Find the value of the Golden Ratio.
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?
Construct a line parallel to one side of a triangle so that the
triangle is divided into two equal areas.
What fractions can you divide the diagonal of a square into by simple folding?
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,. . . .
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
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.
Drawing a triangle is not always as easy as you might think!
How can you represent the curvature of a cylinder on a flat piece of paper?
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Construct this design using only compasses
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
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.
Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.
Design and construct a prototype intercooler which will satisfy agreed quality control constraints.
Investigate constructible images which contain rational areas.