# Free Essay: Mathematical Investigation: VON KOCH'S SNOWFLAKE CURVE Ha Yeon Lee 11B Mathematics HL • Introduction: ➢ History of Von Koch's

Koch curve. 1. n. [Reservoir Characterization]. A curve used to generate a certain type of fractal geometry. Straight lines are replaced by regular polygons

In his 1904 paper entitled "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire" he used the Koch Snowflake to show that it is possible to have figures that are continuous everywhere but differentiable nowhere. Helge von Koch improved this definition in 1904 and called it the Koch curve (now called a Koch snowflake). In the 1930s, Paul Levy and George Canto both found additional fractal curves. 2018-10-03 · The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described.

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It begins with an equilateral triangle; three new equilateral triangles are constructed on each of its sides using the middle thirds as the bases, which are then removed to form a six-pointed star. The Koch Snowflake was created by the Swedish mathematician Niels Fabian Helge von Koch. In his 1904 paper entitled "Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire" he used the Koch Snowflake to show that it is possible to have figures that are continuous everywhere but differentiable nowhere. The von Koch snowflake is made starting with a triangle as its base.

He also shows in the paper that there are two functions f f f and g g g which are both nowhere differentiable such that the snowflake curve is x = f (t) 2015-01-19 2012-06-25 The Koch snowflake is also known as the Koch island. The Koch snowflake along with six copies scaled by \(1/\sqrt 3\) and rotated by 30° can be used to tile the plane [].The length of the boundary of S(n) at the nth iteration of the construction is \(3{\left( {\frac{4}{3}} \right)^n} s\), where s denotes the length of each side of the original equilateral triangle.

## The most intuitive example of a fractal is the boundary of the Koch snowflake which was constructed by the Swedish mathematician Helge von Koch in. 1904. The

portal Education in Sweden Norra Real Kungsholmens gymnasium Sodra 7, Wikipedia. Nyckelord: Fraktal, Koch snowflake, Mandelbrot, Polygon, Sierpinski.

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Koch curve: The Koch curve or Koch snowflake is a mathematical curve, and it is one of the earliest fractal curves which was described. Its basis came from the Swedish mathematician Helge von Koch.

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Each iteration, each side is divided into thirds and the central third is turned into a triangular bump, therefore the perimeter increases. (The Koch curve is one side of the Koch snowflake; in other words, you can get a Koch snowflake by sticking three Koch curves together.) Von Koch invented the curve as a more intuitive and The Koch curve is named after the Swedish mathematician Niels Fabian Helge von Koch (25 January 1870 – 11 March 1924). An example Koch Snowflake is shown on the right. Niels Fabian Helge von Koch The Koch snowflake is the limit approached as the above steps are followed over and over again.

Helge von Koch improved this definition in 1904 and called it the Koch curve (now called a Koch snowflake). In the 1930s, Paul Levy and George Canto both found additional fractal curves. 2018-10-03 · The Koch snowflake (also known as the Koch curve, Koch star, or Koch island) is a mathematical curve and one of the earliest fractal curves to have been described.

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An example Koch Snowflake is shown on the right. Niels Fabian Helge von Koch 2019-12-11 2020-01-17 Von Koch Snowflake Algorithm. One of the simplest examples of a classic fractal is the von Koch "snowflake curve". Created in 1904 by the Swedish mathematician Helge von Koch, the snowflake curve has a truly remarkable property, as we will see shortly.

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### Experten: Då bör du söka hjälp. Av: Anna von Koch ·. Publicerad: tor 12 mar 2020. Uppdaterad: fre 27 mar 2020. Foto: kieferpix / iStockphoto. Hälsa | Family.

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