Maths – the best use for golf balls

May 5th, 2010

Reluctant golfer that he is, the God of Whizz has finally stumbled across the best use for all those silly little balls – maths. Fractals, in fact.

Rather than serve only to be hooked, sliced, or shanked into the near distance, chased by a volley of insults, hundreds of red and blue golf balls have been put towards a magnificent three-dimensional Sierpinski Triangle (or tetrahedron, in this instance).

A use for golf balls - maths fractal pyramid

A use for golf balls - maths fractal pyramid

To those otherwise unversed in Sierpinski’s Triangle (also known as a ‘gasket’), it’s a beautifully elegant fractal.

See how successively small triangular ’subtractions’ from the main triangle produce a lovely, almost threadlike, fractal pattern. The rules for creating this are simple, and can be repeated ad infinitum.

Sierpinski Triangle (Wikimedia)

Sierpinski Triangle (Wikimedia)

  • Start with any triangle in a plane (any closed, bounded region in the plane will actually work).
  • Shrink the triangle to ½ height and ½ width, make three copies, and position the three shrunken triangles so that each triangle touches the two other triangles at a corner.
  • Repeat second step with each of the smaller triangles.
  • (Wikipedia)

    You don’t even have to start with a triangle to end up with a triangular-shaped Sierpinski fractal. Try it!

    Or, better, try the ‘Chaos Game‘, an exotic-sounding name for something you can play with just pencil, paper, ruler, and die:

  • Take 3 points in a plane to form a triangle, you need not draw it.
  • Randomly select any point inside the triangle and consider that your current position.
  • Randomly select any one of the 3 vertex points.
  • Move half the distance from your current position to the selected vertex.
  • Plot the current position.
  • Repeat from third step
  • (Wikipedia)

    [Via Make Blog]


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