# Zome Geometry

## Hands-on Learning with Zome Models

### George W. Hart   and  Henri Picciotto

Key Curriculum Press, 2001

This book is full of fun and beautiful things you can make with the wonderful Zome System geometry construction set.  It is a hands-on guide to the geometry of three-dimensional space.

#### Target:

• School programs looking for geometry enrichment
• Primarily high school students and teachers
• Also middle school  (much of the text uses no trigonometry)
• College math enrichment and courses for future math teachers
• Math / geometry / geodesic dome aficionados
• Science museums and educational toy stores which sell Zome sets

1. Angles, Polygons, Polyhedra
2. Icosahedron and Dodecahedron
3. Platonic Solids
4. Counting
5. Symmetry
6. Euler's Theorem
7. Lengths and Golden Ratio
8. Tessellations
9. Duality
10. Descartes' Theorem
11. Cubes in a Dodecahedron
12. Archimedean Solids
13. Strut Lengths and Angles
14. Zonohedra
15. Area
16. Space Structures
17. Volume
18. Big domes
19. Coordinates
20. Self-intersecting polyhedra
21. The Fourth Dimension
22. Stellations
23. Fractal Structures
24. Proof of Euler's Theorem and Descartes' Theorem
25. Further Explorations

#### Approach:

Using a series of hands-on construction activities, the book presents geometric ideas in the context of the Zome set.  Many of the topics are closely related to standard geometry curricula, e.g., similarity and proportion, symmetry, relations between lengths and angles, (x,y,z) coordinates, and polyhedra.  These might be used in the  classroom as manipulative reinforcement activities.  Other topics go beyond most curricula and are suitable for enrichment or project ideas, e.g., fractals, duality, space structures, geodesic domes, and the fourth dimension.

Topics are introduced with engaging challenges to invite exploration.  Three-dimensional constructions alternate with careful analysis and discussion of the models.  Each chapter ends with a list of ideas for further exploration, suitable for projects.

The reader looking simply to construct interesting models and gain insight from them may jump into the sections in any order, perhaps thumbing through and being enticed by a section's pictures.  However, the mathematical discussion which accompanies the constructions follow a careful development, each section building on previous material.

Green struts: The original Zome sets contained only blue, red, and yellow struts.  Now they make the long-awaited green struts as well, and the book includes many constructions for them.  However, it is designed so the material which requires green struts is optional, so the book can be used by people with either new or old Zome kits.  The book uses three lengths of green struts which are found in Zome's Advaned Mathematics Creator Kit.  They also sell a Green Lines Starter Kit which contains those three lengths plus green struts in six other lengths not used in the book.

### Ordering:

It is available directly from the publisher; also Zome Geometry and Zome kits can be ordered directly from Zometool Corporation.