Growing a cube – an introduction to 3D coordinates

I built this on Geogebra.  It’s pretty simple but might be a good way in to 3D coordinates and more generally explaining the concept of dimensions.

growing a 3d cube.gif

You can download and open the original Geogebra file here which gives more control than just playing the gif.

  1. Start with all sliders at zero.
  2. As you increase slider a, talk about the first dimension.  Any point in the 1D world can be described by a single number which shows how far along the line you are. Every object in a 1D world is just a line. Long or short. It can be described by a single number which we can call length.
  3. Once a has reached 1, talk about the second dimension. This is now like a floor, or the surface of the earth. We call this a plane.
  4. Increase the slider b.
  5. The world in 2D contains two dimensions, which we can call length and width. There are other words: e.g. breadth, depth.
  6. Every point in a 2D world can be described by 2 coordinates. These are the x and y coordinates.  It’s important to notice that the x-direction (i.e. the x-axis) and the y-directions (the y-axis) are a right-angles to each other or orthogonal. Why is this?
  7. Once b has reached 1, what shape to we have? How many vertices does this shape have? How many edges? What are the coordinates of its vertices? Do we need 3 figure or 2 figure coordinates for a 2D shape?
  8. Now we can bring things into the real world in which we live, the 3D world where shapes also have height.
  9. Increase the slider c to grow the cube upwards.
  10. When c has reached 1, what shape do we have? How many edges, vertices, faces does it have? What are the coordinates of the vertices of this shape?

From there, you could always say:

Why stop at 3 Dimensions?

 

 

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