### There are 21 results

Broad Topics >

Transformations and constructions > Constructions

##### 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.

##### Age 16 to 18 Challenge Level:

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

##### Age 16 to 18 Challenge Level:

Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72.

##### Age 14 to 16 Challenge Level:

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

##### 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,. . . .

##### Age 16 to 18 Challenge Level:

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?

##### 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.

##### Age 14 to 16 Challenge Level:

Construct this design using only compasses

##### 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.

##### Age 14 to 16 Challenge Level:

What fractions can you divide the diagonal of a square into by simple folding?

##### Age 14 to 16 Challenge Level:

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?

##### Age 14 to 16 Challenge Level:

Prove that, given any three parallel lines, an equilateral triangle
always exists with one vertex on each of the three lines.

##### Age 14 to 16 Challenge Level:

Describe how to construct three circles which have areas in the ratio 1:2:3.

##### Age 14 to 16 Challenge Level:

Drawing a triangle is not always as easy as you might think!

##### Age 14 to 16 Challenge Level:

How can you represent the curvature of a cylinder on a flat piece of paper?

##### 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?

##### Age 7 to 16 Challenge Level:

Explore patterns based on a rhombus. How can you enlarge the
pattern - or explode it?

##### Age 7 to 16 Challenge Level:

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.

##### Age 14 to 16 Challenge Level:

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.

##### Age 14 to 18 Challenge Level:

Investigate constructible images which contain rational areas.

##### Age 11 to 16 Challenge Level:

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.