| Curriculum Topics: | Logarithms, dimension, iteration |
| Fractal Topics: | Fractal dimension, introduction to fractals, iteration |
| Number of days: | 5 |
| Grades: | 10, 11 & 12 |
| Authors: |
| Carrie Embleton | Lincoln-Sudbury Regional High School, Sudbury, MA |
| Dennis Riordan | Masuk High School, Monroe, CT |
| Kristen Amon | Stamford High School, Stamford, CT |
| Emeka Dan-Udekare | Bassick High School, Bridgeport, CT |
| Allen Cook | University of Bridgeport, Bridgeport, CT |
| Susan Hart | Southington High School, Southington, CT |
|
| Objective: | To apply logarithms in determining the dimension of geometric and fractal figures |
| Resources: |
| Attached worksheets |
| Model of Sierpinski tetrahedron (or materials to construct one) |
| Calculator |
|
| Optional Lab Resources: |
| Beans |
| Overhead transparenc y plastic |
| Compasses |
| Scissors |
|
| Description of Lesson: |
| 1) After completing lesson on properties of logarithms, assign Introduction Worksheet as homework. |
| 2) Go over worksheet in detail, and develop formula for dimension, N(s) = (1/s)d.
Use logarithms to solve for dimension. |
| Homework: Koch Curve Worksheet |
| 3) Introduce fractals and look at Koch Curve. To draw Koch Curve on board, use yard stick for each
segment and ruler for second iteration. Determine the dimension of Koch Curve. When looking at the dimension
at each iteration, ask how log 4/log 3 gives same answer as log 16/log 9 and
log 64/log 27. Introuduce Cantor Set. Determine the dimension of Cantor Set. |
| Homework: Sierpinski Tetrahedron Preparation Worksheet with 85 envelopes divided amongst students |
| 4) Have students assemble envelopes and make iterations of Sierpinski Tetrahedron. |
| Homework: Fractal Dimension Worksheet |
| 5) Discuss Worksheet. Determine the dimension of the Sierpinski Tetrahedron. |
| Homework: Write a journal entry in the form of a letter to Professor Michael Frame, explaining what a
fractal is, how you get the dimension of the fractal, and explain how a dimsension can be a decimal. He's a very
mean fellow who will smack you for a misspelling, so be careful. |
|
| Optional Lessons: |
| Bean bags and Crumpled Paper Lab from Kitchen Science Fractals |
| Peanuts in a Cone Experiment see attached |
| Read "Fractals in the Classroom" in The Physics Teacher, October 2003, make crystal
fractals as described in article and determine their dimension.
|
|