The Mathematics of Wallpaper

CONTENTS OF CURRICULUM UNIT 10.04.02

  1. Unit Guide
  1. Introduction
  2. Overview
  3. Objectives
  4. Symmetry on a Plane
  5. Finite Figures
  6. Frieze Patterns
  7. Wallpaper Groups
  8. Teaching Strategies
  9. Classroom Activities
  10. Endnotes
  11. Resources
  12. Appendix - Implementing National Standards

Repeat After Me!

Carol P. Boynton

Published September 2010

Tools for this Unit:

Finite Figures

Finite figures, unlike lines, do not go on forever. They are shapes which have no translational symmetry. The shapes discussed in this unit will be regular polygons, defined as a shape with all its sides equal and all its angles equal. Regular polygons have reflections and rotations as symmetries – they have reflectional symmetry, and also rotational symmetry.

Symmetry Classification of quadrilaterals

Square – 8 symmetries – the regular quadrilateral

Rectangle and rhombus – 4 symmetries

Parallelogram, kite and isosceles trapezoid – 2 symmetries

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