Topological Turmoil

Objectives

• Develop mathematical reasoning.

• Make connections and solve problems.

• Communicate and express their understanding.

• Explain the importance of observation when doing math.

Materials

• see individual activities for materials.

Background

Topology is the mathematical study of shapes and spaces.

Topology involves looking at the shapes that result through stretching, transforming, deforming, folding and twisting. Tearing, on the other hand, is not allowed!

Some of the shapes involved include polygons and circles which can be manipulated in space to create different shapes.

These puzzles are a great way for students to explore 2-dimensional shapes in 3-dimensional space.

Vocabulary

Topology: the mathematical study of shapes and spaces.

Flexagon: Folded paper polygons that have the fascinating property of changing their faces when they are flexed.  Flexagons can be made from a pattern of squares or equilateral triangles.

Mobius strip/band: A strip of paper which has been given a half twist, and connected end-to-end. It only has one side and one edge.

Tetra-tetra-flexagon: A flexagon made from a folded paper rectangle that is 4 squares long and 3 squares wide.

Other Resources

Flexagon Portal | Flexagons

Questacon – The National Science and Technology Centre | Galleries: Science Garden | Möbius

Wolfram | Math World | Topology