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Exploring Pascal - Introduction || Student Center || Teachers' Place
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1. Patterns, Relations, Functions, Algebra
2. Antonio's Pizza Palace
3. Student Worksheets

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Exploring Pascal's Triangle:

Patterns, Relations, Functions, and Algebra

Working with a partner, study the following array of numbers. What patterns do you see in the arrangement of the numbers? Describe each pattern using words and symbols.

 

As you look for patterns, try to answer the following questions:

Share your discoveries with the group.

See if you can find:

    natural numbers
         1, 2, 3, 4, ...
  pentatope numbers
       1, 5, 15, 35, 70, ...
    powers of 2
         2, 4, 8, 16, ...
  Catalan numbers
       1, 2, 5, 14, 42, ...
    powers of 11
        11, 121, 1331, 14641, ...
  Fibonacci numbers
       1, 1, 2, 3, 5, 8, ...
    triangular numbers
         1, 3, 6, 10, ...
   
  binomial coefficients
    tetrahedral numbers
         1, 4, 10, 20, ...
  probability & combinations
    hexagonal numbers
         1, 6, 15, 28, ...
  Sierpinski triangle
   


Interactive Number Sets: The Geometer's Sketchpad

If you have The Geometer's Sketchpad, you can download and experiment with an interactive version of Pascal's Triangle that will show some of the patterns (401K). You can also download sketches that illustrate Sierpinski's Triangle and Multiples of Threes (385K) and Hexagonal, Tetrahedral, and Pentatope Numbers (389K). If you don't have the Geometer's Sketchpad, you can download a demo version.

If you are using Netscape 3.0, Internet Explorer 3.0 or a later version of these browsers you can view an interactive version of Pascal's Triangle that uses java script. Please be patient; this page takes a few moments to load.

 
Questions? Write to the workshop facilitators.

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Math Forum * * * * 19 April 1998