# Dimension 3

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Lesson Summary:

In this lesson, M.C. Escher takes us on an adventure with two-dimensional creatures attempting to visualize three-dimensional objects. The creatures struggle to understand the concept of depth and must rely on their geometric intuition to understand the shapes crossing through their plane. Escher introduces a second method of explaining polyhedra by inflating them and projecting them onto the plane of the creatures. The lesson concludes with a discussion of the platonic solids and a challenge to visualize the fourth dimension.

Lesson Description:

M. C. Escher tells the adventures of two-dimensional creatures who are trying to imagine three-dimensional objects.

• Who is M.C. Escher?
• Who is Edwin A. Abbott?
• What is Flatland?
• Where can I find 2-dimensional projections of 3-dimensional objects and shapes?
• What are cross-sections of 3-dimensional polyhedron?
• What are platonic solids?
• How can you recognize and identify polyhedron from their projections?
• #### Staff Review

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This lesson is a prelude to a look at the fourth dimension. It is a consideration of the third dimension by 2-dimensional beings, similar to the book Flatland by Edwin A. Abbott. M. C. Escher and his works are also discussed. 3-dimensional polyhedron such as a tetrahedron, cube, octahedron, icosahedron, and dodecahedron are analyzed as they pass through a 2-dimensional plane. Also shown are stereographic projections of the polyhedron on a 2-dimensional plane, and they are identified by their projections.
• #### squeaky78

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it helps me alot