Exploring Hexaflexagons
A Grade 12 mathematics worksheet focused on the construction, properties, and mathematical principles behind hexaflexagons.
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Exploring Hexaflexagons
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This worksheet explores hexaflexagons, fascinating paper models with hidden faces. Answer the questions to demonstrate your understanding of their construction and mathematical properties.
1. A hexaflexagon is a flat model, usually made of paper, that can be to expose different faces.
2. The most common type of hexaflexagon is the trihexaflexagon, which has faces.
3. Hexaflexagons are typically constructed from a strip of paper divided into a series of triangles.
4. Describe the basic steps involved in constructing a trihexaflexagon from a strip of equilateral triangles. You may use a diagram if it aids your explanation.
5. Which mathematical concept is most closely related to the way hexaflexagons reveal different faces?
Topology
Calculus
Probability
Algebra
6. Explain what is meant by 'flexing' a hexaflexagon and why it allows different faces to be seen.
7. A hexahexaflexagon has six faces that can be flexed.
True
False
8. All hexaflexagons must be made from equilateral triangles.
True
False
Match each term with its correct definition.
9. Patting
a. The process of revealing hidden faces on a hexaflexagon.
10. Flexing
b. A method of flattening a hexaflexagon to prepare for flexing.
11. Tuckerman Traverse
c. A systematic method for finding all faces of a hexaflexagon.