Cynthia Lanius

Sierpinski Meets Pascal

Check it out!

 
Table of Contents

Introduction

  Why study fractals?
    What's so hot about
    fractals, anyway?

  Making fractals
    Sierpinski Triangle
         Using Java
         Math questions
         Sierpinski Meets Pascal
    Jurassic Park Fractal
         Using JAVA
         It grows complex
         Real first iteration
         Encoding the fractal
         World's Largest
    Koch Snowflake
         Using Java
         Infinite perimeter
         Finite area
         Anti-Snowflake
            Using Java

  Fractal Properties
    Self-similarity
    Fractional dimension
    Formation by iteration

  For Teachers
    Teachers' Notes
    Teacher-to-Teacher

  Comments
    My fractals mail
    Send fractals mail

  Fractals on the Web
    The Math Forum

  Other Math Lessons
    by Cynthia Lanius

  Awards
    This Site has received

 
Notice the triangle above is all filled in.

Now, what does this have to do with Sierpinski's Triangle?

Try shading all the little triangles in Pascal's Triangle except the odd numbered ones, and see what happens. (That includes shading the triangles with no numbers and the even numbered ones.)

Now compare it to the triangle below. (Hidden way below so you won't cheat)You can get Sierpinski's Triangle from Pascal's!

To people who like math, that's really cool.
How about you?

 
Do you find any other interesting patterns in Pascal's Triangle? Email me your answer. I'd love to hear from you.

lanius@math.rice.edu


Sierpinski Meets Pascal

Here's more information on building Sierpinski's Triangles from Pascal's.

You may obtain a print version of this page.

Back to Sierpinski's Triangle

Copyright 1996-2007 Cynthia Lanius
URL http://math.rice.edu/~lanius/fractals/pas2.html