dimension : intro page

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Dimension
	•	Introduction

	•	Slicing a Cube
	•	Playground Activity
	•	Cow Contour Levels

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The activities and pages in this chapter ask the question: how do we use 2-dimensions (paper) to illustrate 3-dimensional objects (hills, cows, cubes, etc.)?

These pages don't consider

• what "dimension" means (that's in the fractal chapter);
• how 1-dimensional objects like chains and spirals differ from 3-dimensional objects like crystals (that's in the the pattern formation chapter); or
• how the difference in dimension between area and volume affects the shapes of natural objects (that's in scale and growth).

Instead, we look at how to draw cross-sections and level curves of existing artifacts. The "slicing a cube" activity shows a movie version of the icon for the chapter, and explains why there is a hexagon trapped in the cube. The "playground" activity requires students to reconstruct 3-d objects from their level curves. The "cow contour" activity describes a standard format for including figures and graphs (this is the format required for the course), and it has students sketch their own cross-sections of 3-d toy cows.

An excellent companion book to this section is Flatland (see [A] below). Flatland tells the story of a 2-dimensional creature who dreams about 1-dimensional space, and who then has the bizzare experience of visiting 3-dimensional space. The story is reminiscent of Plato's The Cave; it is also a satire of Victorian restrictions of women's role in society (so much so that students who do not understand British satire will assume that the book is unbearably sexist).