1. Here's proof that Pythagoras' theorem really works.
2. And here's a slightly longer explanation of why a² + b² = c².
3. This is how pi works.
4. This is why the area of a circle is πr².
5. This is how a straight line can draw out a curved shape.
6. Here are two more examples of straight lines tracing hyperboloids.
The one on the right shows the full hyperboloid.