Koch Snowflake: Perimeter

Fractal Playlist: • Fractals
This video continues with the Koch Snowflake, named after the Swedish mathematician Helge Von Koch. The shape has an infinite perimeter but a finite area.
This video focuses on finding the perimeter of the snowflake by looking at the perimeter after each step of the iteration process and noticing a pattern. Once the pattern is noticed, the question can be asked of what happens to the formula for the perimeter as the number of steps carried out in the iteration approaches infinity.
This fractal is formed by starting with an equilateral triangle and carrying out a simple process known as iteration infinitely many times. Each step of the process cuts the sides of the triangle into three equal pieces and replaces the middle piece with an equilateral triangle (without the inner side).
Fractals appear in many different areas of nature, including lightning, river systems, the nervous and circulatory systems, trees, clouds, coastlines, and so on. Natural fractals have demonstrate self similarity throughout many orders of magnitude but only purely mathematical objects, like the Koch Snowflake or the Sierpinski triangle, show infinite self similarity.
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[@sobejennifer]

I just got a question what if the initial side of the triangle is 9 cm what will be the side for P1 and P2 P3

[@EulersAcademy]

Thanks for watching. That's a great question to think about. In P1, each side length is 4/3 the length of the original side. 9 cm multiplied by 4/3 is 12 cm. For P2, it is 4/3 the length of the side in P1. Try to calculate this one on your own and then just remember that P3 is 4/3 the length of P2. If you get stuck, let me know and I can help walk you through this.

[@sobejennifer]

Does the side change or remains the same ??

[@EulersAcademy]

Thanks for watching and good question. At each step of the iteration, the side will become something different (longer) which is why the perimeter increases as the number of steps increase.