Koch curve
Curva de Koch
- Date
- 1904 · confidence high
- Place
- Stockholm, Sweden
- Credited to
- Helge von Koch
- Field
- Knowledge & symbols
What was discovered
Von Koch built a continuous curve that, surprisingly, has no tangent anywhere: it is obtained by repeatedly replacing the middle third of each segment with two sides of an equilateral triangle, a process that can be repeated infinitely. The closed snowflake version, with infinite perimeter but finite area, was later popularized as one of the first examples of a fractal.
The closed "snowflake" form does not appear in the original 1904 article, but in later work.
What it led to
- Mandelbrot's fractal geometry
- Canonical examples of pathological curves in analysis
Built on
- Weierstrass's continuous nowhere-differentiable function