Download and printout this complete illustrated guide to Interactive Construction (Word document, 266Kb).
It is likely that tutors will want their students to use the main sections called Foundation, Intermediate and Advanced. These materials cover the requirements of the UK National Curriculum - and much more besides. Foundation level tasks can be used with students at primary and secondary level. These pages are designed to draw the student towards the Foundation, Intermediate and Advanced work, and to make other topics less prominent. The MathsNet icon at the top left of every page always takes you back to the main introductory Construction page, from where all topics are accessible.

Other materials, accessible both from this page and the introductory page, include Euclid's Elements, sacred geometry, Circle-only (or Mascheroni) constructions, Transformations and the Hidden World of triangles and circles. They are intended as follow-up work or project work. Some ideas are quite advanced and may be appropriate for students following post-16 or undergraduate courses. There are also pages describing the background thinking to these materials, a brief history of geometry and technical comments concerning suitable browsers.

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.

• 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! All tasks will give the students a code number which can be used by the tutor for verification of task completed. For the tutor to check these codes they must have password access to the codes page. Contact MathsNet for this password. 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 Ö2, Ö3, Ö5, golden ratio
• extra: various more difficult constructions

Euclid's elements
The Thirteen Books of The Elements forms the basis of any work on geometric construction. In Book I Euclid made 48 Propositions. Many of the propositions appear in these tasks at Intermediate and Advanced level and a link is then included.

sacred geometry
In his book Robert Lawlor looks at the history of geometry and its links with art, architecture, philosophy and religion. The book includes 9 workbooks, which are listed here and illustrated with interactive geometry challenges.

Circle-only constructions
What constructions are possible using only compasses?

Transformation geometry
Constructions of transformations, based on work by Max Jeger

The Hidden World of... triangles (and circles)
Based on parts of the book "You are a mathematician" by David Wells.

• Thinking: inspiration and background to the materials
• A brief history: some key figures and developments over 2500 years
• Sources: books and other recommended websites
• Tech: what you need to make these materials run
• Buttons: description of the interactive buttons used in each task