Unlike the adventures of Meg Murry, our exploration of dimensions will max out at three. Any past that and we're in physics and/or sci-fi territory.
We'll start with the first dimension: points and lines. There isn't that much to say about the first dimension, since all we can do is find locations and lengths. We have no widths or depths to work with, and number lines are interesting only up until a certain point.
Don't worry. We'll speed past the first dimension pretty quick and jump right into the second, filled with lengths and widths, angles, lines, polygons, and circles. The majority of our time in Geometryland will be spent in the second dimension, exploring the relationships between shapes, angles, perimeters, and even areas.
If everything is in 3D nowadays, why even bother with 2D? What's so special about it? Well, there are many reasons to investigate the second dimension.
- It's cool.
- Even though the real world exists in 3D, our sense of vision is limited to two dimensions only.
- The second dimension is the basis for the third one, so it's important to understand the ins and outs of the 2D world before we add depth to the mix.
Once we've gotten a firm grip on what the second dimension can offer us, we can feel free to put on those 3D glasses and venture into the realm of nets, surface area, and volume.
These are the only dimensions we need to capture the essence of geometry. Who says math isn't as easy as 1, 2, 3?