Cubic plane curve

A cubic plane curve is a fancy way of talking about a special kind of shape that you can draw on a piece of paper or a computer screen.

Imagine that you have a marker and a blank sheet of paper. First, draw a dot in the middle of the paper. Then, draw some little marks around the dot, like spokes on a wheel. Connect the end of each spoke to its neighbor, so that you have made a six-sided shape that looks like a hexagon.

Now, imagine that you pick up your marker and start drawing a line that touches the hexagon at one point but doesn't cross over any of the edges. You can draw this line any way you like, but it has to start and end at a place where it touches the hexagon.

Congratulations! You have just drawn a cubic plane curve. It's called "cubic" because the curve you drew can be described using a fancy math equation that includes the number three (which is the cube of one, if you've learned about cubing numbers in school).

Scientists and engineers use cubic plane curves to model lots of things, like the shapes of gears and the paths that airplanes take when they fly. They can be really helpful because they help people understand how different objects move and interact with each other.