Koch’s snowflake

Definition

Koch's snowflake is a fractal curve, one of the earliest described. It is constructed by recursively adding smaller equilateral triangles to each side of an initial equilateral triangle.

5 Must Know Facts For Your Next Test

1. The perimeter of Koch's snowflake grows infinitely while its area remains finite.
2. Koch's snowflake is created through an iterative process using infinite geometric series.
3. Each iteration involves dividing each side of the existing shape into three parts and adding a new equilateral triangle in the middle segment.
4. The fractal dimension of Koch’s snowflake is approximately 1.2619, which indicates it has a more complex structure than a simple one-dimensional line.
5. The sum of the lengths of all the segments added at each stage forms an infinite geometric series.

Related terms

Fractal: A complex geometric shape made up of patterns that repeat at every scale and can be split into parts, each of which is a reduced-scale copy of the whole.

Geometric Series:

A series with a constant ratio between successive terms; it converges if the absolute value of the common ratio is less than one.

Iterative Process: A procedure that repeatedly applies a set of rules or operations until a desired level of accuracy or completion is achieved.