A simple introduction to construction, concentrating on the buttons for constructing:

• points;
• lines;
• circles.

Vocabulary: point, vertex, vertices, line, intersection, parallel, perpendicular, circle, centre, circumference, square, rectangle, rhombus, parallelogram, quadrilateral, triangle, isosceles, equilateral.

Essential constructions including:

• perpendicular lines;
• parallel lines;
• bisectors of lines and angles;
• triangles: isosceles, equilateral, right-angled;
• angles: 90°, 45°, 60°, 30°, 15°, 75°, 120°, 105°;
• quadrilaterals: trapezium, parallelogram, rhombus, kite, square, rectangle.

Test your skills with a wide range of challenges, some very difficult indeed! Advanced constructions include:

• polygons: equilateral and isosceles triangle, square, rectangle, pentagon, hexagon, octagon;
• rules: various locus definitions, circle, straight line, bisector;
• circles and their properties;
• changes: reflection, rotation, enlargement, translation;
• numbers: square roots, other roots, golden ratio;
• extra: various more difficult constructions

The Thirteen Books of The Elements forms the basis of any work on geometric construction. In Book I Euclid made 48 Propositions, and many appear in these tasks at Intermediate and Advanced level.

In his book Sacred Geometry Robert Lawlor looks at the history of geometry and its links with art, architecture, philosophy and religion. The book includes nine workbooks, which are listed here and illustrated with dynamic geometry challenges.

What constructions are possible using only compasses?

Constructions of transformations, based on work by Max Jeger.

Based on parts of the book You are a Mathematician by David Wells.

...from Greek geometry.

Background information

• Thinking: inspiration and background to the materials;
• A brief history: some key figures and developments over 2500 years;
• Sources: books and other recommended websites;
• Buttons: description of the interactive buttons used in each task.