Drawing a 4-D Cube |

- Start with a point.
- Drag the point to create a line segment.
- Drag the end points of the line segment a direction "perpendicular" to the line segment to make a square.
- Drag the corner points of the square a direction "perpendicular" to the square to make a cube.
- Drag the corner points of the cube a direction "perpendicular" to the cube to make a 4-D Cube.

- How many "points" does a 4-D hypercube have?

[Note how at each iteration we grab all the points and drag them into a new dimension, doubling the number of points.] - How many "lines" (edges) does a 4-D hypercube have?
- How many "planes" (faces) does a 4-D hypercube have?

[Concept: Instead of dragging all the "points" at each iteration, think about grabbing all the "lines" at each iteration and dragging all the "lines" into a new dimension. As you drag each line it creates a new plane (or face). For example, to create a 2-D square we grab the 1-D line and drag it into a new dimension to make a square.] - How many "cubes" does a 4-D hypercube have?

[Concept: Instead of dragging all the "points" or "lines," think about grabbing all the "planes" (faces) and dragging them into a new direction. For example, to create a 3-D cube we grab the 2-D plane (face) and drag it into a new dimension creating a cube.]

- Search Google for "hypercube"
- The concept of
**fractional dimensions**is covered under the topic of fractals.

This would also be a good time to recommend the classic book

Flatland by Edwin A. Abbott

There are many different editions of this book.

There's also a sequel titled Sphereland.

You can also find both books together in one.

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