[Math Lair] Koch Curve

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animation of Koch curve

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:

[Koch snowflake]
A Koch snowflake.

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.