Koch Snowflake
The resulting Koch snowflake has finite area but infinite perimeter - a shape defying Euclidean geometry's assumptions about smooth boundaries and integer dimensions.
In 1904, Swedish mathematician Helge von Koch constructed this peculiar geometric object: start with an equilateral triangle, subdivide each side into thirds, replace the middle third with two sides of a smaller equilateral triangle, and repeat infinitely. The resulting Koch snowflake has finite area but infinite perimeter - a shape defying Euclidean geometry's assumptions about smooth boundaries and integer dimensions.
Mandelbrot recognized that Koch's abstract construction wasn't merely mathematical curiosity - it described real natural structures like coastlines and biological branching systems.
Notable Traits of Koch Snowflake
- Finite area but infinite perimeter
- Non-integer fractal dimension
- First mathematical fractal (1904)