# The 4-D Cube

 Drawing a 4-D Cube
2. Drag the point to create a line segment.
3. Drag the end points of the line segment a direction "perpendicular" to the line segment to make a square.
4. Drag the corner points of the square a direction "perpendicular" to the square to make a cube.
5. Drag the corner points of the cube a direction "perpendicular" to the cube to make a 4-D Cube.
Of course the secret to performing these steps is figuring out what "perpendicular" means. You'll learn that when you study Linear Algebra (what I call Matrix Algebra) in college and study the concept of "orthogonal."

QUESTIONS
1. 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.]
2. How many "lines" (edges) does a 4-D hypercube have?
3. 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.]
4. 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.]

FURTHER RESEARCH