median
don steward
mathematics teaching 10 ~ 16

Friday, 13 March 2009

sierpinski







how many black triangles at each stage?

 how many black triangles?















Sierpinski triangles are fairly easy to construct on an electronic whiteboard.

draw a shape (or a word)
copy this twice and put the three together as an equilateral (or isosceles) triangle
group these three and maybe shrink them

copy two more of these and again fit them together in a triangle

keep going...

this task presents a way of looking at powers:
  • if you count the number of black triangles at each stage you get powers of 3
  • if you look at the way the base line is divided into equal sections you get powers of 2
  • if you look at the fractions of the whole triangles shaded (black), you get powers of 3/4

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