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Koch Snowflake
FRACTALS
Introduction
 Koch snowflake is also known as Koch star or Koch island
 Is a fractal curve.
 Introduced by Sweedish Mathematician Helge von Koch.
 First appeared in a research paper in 1904 as “On a continuous
curve without tangents, constructible from elementary geometry”.
Construction
 Koch curve can be created by starting with a equilateral triangle.
 Each side of the equilateral triangle is divided into three parts, then
the middle part of the divided side is taken as a base and a triangle
is constructed. And this iteration is continued. This will create an
infinite curve. An animated image looks like this(To be seen in
slideshow)
Properties
 It is continuous everywhere but differentiable nowhere
 Perimeter: Pn=3.s.(4/3) 𝑛
Where: s is the length of the side of original triangle
n is the iteration
 Area: An = (ao/5)(8-3(
4
9
) 𝑛)
Where: ao is the area of the original triangle
 References:
 http://en.wikipedia.org/wiki/Koch_snowflake
 http://mathworld.wolfram.com/KochSnowflake.html
 http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm

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Koch snowflake

  • 2. Introduction  Koch snowflake is also known as Koch star or Koch island  Is a fractal curve.  Introduced by Sweedish Mathematician Helge von Koch.  First appeared in a research paper in 1904 as “On a continuous curve without tangents, constructible from elementary geometry”.
  • 3. Construction  Koch curve can be created by starting with a equilateral triangle.  Each side of the equilateral triangle is divided into three parts, then the middle part of the divided side is taken as a base and a triangle is constructed. And this iteration is continued. This will create an infinite curve. An animated image looks like this(To be seen in slideshow)
  • 4. Properties  It is continuous everywhere but differentiable nowhere  Perimeter: Pn=3.s.(4/3) 𝑛 Where: s is the length of the side of original triangle n is the iteration  Area: An = (ao/5)(8-3( 4 9 ) 𝑛) Where: ao is the area of the original triangle
  • 5.  References:  http://en.wikipedia.org/wiki/Koch_snowflake  http://mathworld.wolfram.com/KochSnowflake.html  http://ecademy.agnesscott.edu/~lriddle/ifs/ksnow/ksnow.htm