From Pascal to Sierpinski

This week we will recall the graph-paper drawings of the triangle and explore the geometric properties we discovered, in particular the line-drawing scheme that traces out the pattern of "Pascal's triangle mod 2". This pattern is called the "Sierpinski triangle" or Sierpinski Gasket"

• "0 dimensional" algorithms to create the gasket: Random midpoint-drawing algorithm, biased probabilities modification
• symbolic encodings of the dots, the Sierpinski triangles embedded number system, algebra on the Sierpinski triangle.

• "1 and 2 dimensional" algorithms to create the gasket: Midpoint-Connectors algorithm. (This is the original one that modeled Pascal's Triangle mod 2.) Vanishing Middles algorithm, Multiple Reduction Copy Machine algorithm.

• 3 dimensional: Building the Sierpinski pyramid. 2-day mathematical background and construction project. (May 1999 issue of Mathematics Teacher magazine has project instructions.

Transition into a fractal geometry unit, a whole new world to explore...