Mathematics Today!
Task: You need to create the cover and content of this edition of "Mathematics Today" magazine. The publishers have requested a theme that has to do with fractals. The picture should pertain to the following problem...
Your challenge this month:
You must find the area for each of the colors in the Sierpinski Triangle above. The tricky part is that you must use the triangle formula for area only once!
1) Below shows how to create a fractal called Sierpinski's Triangle. A fractal is a shape that repeats itself in a pattern over and over again. Each level of the pattern is similar to the original. For this fractal, we need to find the midpoints of each side of the triangle and connect them. Look at the example below.
2) You need to do this for each triangle that points up. You have to complete this through four iterations. This will be the cover of the magazine.
3) Now, you have to use at least 4 different colors to decorate. Do not use more than one color in one triangle.
4) Look for a relationship between sizes of the largest triangle to each of the smaller triangles.This will help you find the areas of the colors without measuring repeatedly. Write your work with answers on the final page. Make sure that you check your work by adding the areas for each color together. The areas should add up to the area of the original triangle.
5) Your finished magazine will have the following pages in order:
a) Cover
b) How can I create a fractal? (2 iterations must be completed)
c) What is a fractal?
d) Relationships of triangles in Sierpinski's Triangle
e) What is Pascal's Triangle?
f) How is Pascal's Triangle related to Sierpinski's Triangle?
g) Reflections sheet.
h) Final page with all work and answer for the cover of the magazine
The deadline for the magazine is 10 business days (2 weeks) from today!
Good luck!
Achieving your goal here will set you up for a second edition ...
"Special Edition of Mathematics Today: Yin and Yang"
Note: the preceding task works in conjunction with packet of material.