Helge von Koch

Koch Snowflake Investigation Angus Dally Background: In 1904, Helge von Koch identified a fractal that appeared to model the snowflake. The fractal was built by starting with an equilateral triangle and removing the inner third of each side, building another equilateral triangle where the side was removed, and then repeating the process indefinitely. The process is pictured below, showing the original triangle at stage zero, and the resulting figures after one, two and three iterations.

Mathematical Investigation: VON KOCH’S SNOWFLAKE CURVE Ha Yeon Lee 11B Mathematics HL • Introduction: ➢ History of Von Koch’s Snowflake Curve The Koch snowflake is a mathematical curve, which is believed to be one of the earliest fractal curves with description. In 1904, a Swedish mathematician, Helge von Koch introduced the construction of the Koch curve on his paper called, “On a continuous curve without tangents, constructible from elementary geometry”

but the mathematical roots of itt date back to the 17th century. Recursion was studied in the 17th century, and in the 19th century continuous but not differentiable functions were studied. In the early 1900’s, Helge von Koch gave a more geometric definition of fractals called the Koch snowflake. Later in 1915, Wacław Sierpiński constructed his famous triangle. In a nonmathematical sense fractals are never ending self similar patterns, in Brave New World there are plenty examples