Cynthia Lanius

Sierpinski Triangle Math Questions On Sierpinski's Triangle

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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

 
     
  1. Look at the triangle you made [Opens new window] in Step One. What fraction of the triangle did you NOT cut out?

  2. What fraction of the triangle in Step Two is NOT cut out?

  3. What fraction did you NOT cut out in the Step Three triangle?

  4. Do you see a pattern here? Use the pattern to predict the fraction of the triangle you would NOT cut out in the Step Four Triangle. Confirm your prediction and explain.

  5. CHALLENGE: Develop a formula so that you could calculate the fraction of the area which is NOT cut out for any step.

  6. Write the fractions in the above questions in order from least to greatest. Write a statement about how their order connects to the cutting out process.

  7. Find another interesting pattern in the fractal called the Sierpinski Triangle. Write a paragraph descibing this pattern.
lanius@math.rice.edu

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Copyright 1996-2009 Cynthia Lanius
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URL http://math.rice.edu/~lanius/fractals/Sier_Ques/