What is This?
This website is mainly about Helge Von Koch's snowflake curve. In this website you will find information about Helge Von Koch, his work on the snowflake Curve, and how to find the are and perimeters of the Snowflake and Square Curve. If you need to see different models of the snowflake go to the snowflake curve page, where you will find a video and program (from efg2.com/lab) of the Von Koch snowflake.
Every source used in the making of this website is stated on the reference page.
Snowflake Curve C1-C5
Square Curve C1-C5
Niels Fabian Helge Von Koch
Niels Fabian Helge Von Koch is best remembered for devising geometrical constructs that are now called the Koch curve and the Koch snowflake (or star). He was also an expert on number theory and wrote extensively on the prime number theorem.
Von Koch was born in Stockholm, Sweden on January 25, 1870. He studied at the University of Stockholm. There he had the opportunity to study under Gosta Mittag-Leffler. Von Koch earned his doctorate in mathematics from the University of Stockholm in 1892, writing a thesis that would contribute to the development of functional analysis. In 1893 he accepted a job as assistant professor of mathematics at an unknown school. In 1905 von Koch achieved a promotion when a colleague resigned his professorship at the Royal Technological Institute in Stockholm. The school offered von Koch the chair of pure mathematics, which he promptly accepted.
In 1901, von Koch published On the Distribution of Prime Numbers, which concentrated on the prime number theorem. In 1906, he released his work on curves and snowflakes. The von Koch curve is made by taking an equilateral triangle and attaching another equilateral triangle to each of the three sides. This first iteration produces a Star of David-like shape, but as one repeats the same process over and over, the effect becomes increasingly fractal and jagged, eventually taking on the traditional snowflake shape. The snowflake is actually a continuous curve without a tangent at any point. Von Koch curves and snowflakes are also unusual in that they have infinite perimeters, but finite areas. After writing another book on the prime number theorem in 1910, von Koch succeeded Mittag-Leffler as mathematics professor at the University of Stockholm in 1911. He died in Stockholm on March 11, 1924, having taught for most of the remainder of his life.
