Minicourse Descriptions 2000


Session A: (August 14 - 15)

Archimedean Activities: Tessellations and Polyhedra

Instructors: Will Webber with Ronda Webber

The Archimedean solids and the semi-regular tilings of the plane are very closely related. Using geometric software and building polyhedral models and kaleidoscopes we will investigate these relationships. The participants should leave with a comprehensive understanding of the Archimedean solids as well as a full set of kaleidoscopes, the inserts for those kaleidoscopes, computer sketches, and the instructional materials to use their new understanding in the classroom.


In the Footsteps of Escher: 3-D Puzzles that Tessellate Space

Instructors: Joyce Frost with Karen Hall

Who can resist the allure of 3-D puzzles? Examine the mathematics of polyhedra that pack space: cube, triangular prism, hexagonal prism, rhombic dodecahedron, stellated rhombic dodecahedron, and truncated octahedron. Learn how to make 3-dimensional geometry come alive for your students by involving them in the entire process: discovering puzzles, designing nets, building puzzles, and creating new puzzles. From card stock and contact paper, you will make a variety of puzzles, some old, some obscure, and some recent discoveries. You will leave with numerous high quality puzzles to display, share, or amuse others.


Session B: (August 16 - 17)

Origametry: Geometric Origami

Instructors: Will Webber with Ronda Webber

What would geometry be like if Euclid had neither compass nor straight edge? In this mini course we start with that question and find an equivalent construction system in the world of origami. The topics include the basic Euclidean constructions, folding regular polygons, tying knots in strips of paper, analyzing folds to understand the geometry, and building 3-dimensional models from folded paper. The activities are all hands-on, and the participant should leave with a large assortment of folded models as well as the materials needed to use the ideas in a classroom.


Hands-on Spherical Geometry

Instructors: Philip Mallinson with Carol Hattan

You know very well what an angle is, what a straight line is, and how to measure angles and segments and areas in the plane. But suppose your universe is not a plane but a cone or a cylinder or a cube or a sphere? This minicourse invites you to extend the these basic notions to surfaces that don't look like a flat sheet of paper. You will build your own models and also use commercial products like the Lenart sphere. As well as opening a new world of geometry, geometry on the sphere is also very practical. After all, map makers need to flatten out the world for the pages of an atlas and navigators need to sail in straight lines. How do they do it?


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