The Koch curve (also known as the von Koch curve) is a type of fractal. It was first described in a 1904 paper by Swedish mathematician Helge von Koch, making it one of the first fractal curves to be described.
It's pretty simple to create:
Repeating the process an infinite amount of times creates the Koch curve. The first seven iterations of this process are illustrated at the top of the page.
A similar curve is the Koch snowflake, which is the same as a Koch curve, except the starting point is a triangle, which results in the shape on the right, one that looks a little bit like a snowflake. Even though the length of the curve is infinite, the area enclosed by the curve is finite; it converges on an area 8/5 of the area of the original triangle.
Here are some activities to try:
Sources used (see bibliography page for titles corresponding to numbers): 17, 56.