6.A[U+0080][U+0099]C[U+0080][U+0099]= 36 ,B[U+0080][U+0099]C[U+0080][U+0099]= 15 ,A[U+0080][U+0099]B[U+0080][U+0099]=
39
7. 90
8. 270
- The ratios of the side lengths and the perimeter are 3 : 1 the same as the scale factor. The ratio of the areas is 9 : 1,
the square of the scale factor.
Self-Similarity (Fractals)
More Complex Fractals –Students need to begin learning about fractals with the simple examples given in the text.
Once they have taken some time to work with, and understand the self-similar relationship, it is amazing to see how
complex and beautiful fractal can become. Numerous examples of exquisite fractals can be found on-line. If you
are lucky enough to have access to computers and a projector, have the students search for fractals and choose their
favorite to share with the class. Student will begin to realize the importance of what there are learning when they see
what a huge ocean they are dipping their toe into.
Applications –Many students need to know how a subject is useful before they are motivated to spend time and
energy learning about it. Throughout the text there have been references to modeling and how mathematical concepts
often need to be adjusted to fit the world around us. Fractals are used to model many aspects of nature including tree
branches, shells, and the coast line. Knowing of the applications of fractals motivates students. If time permits give
a more in-depth explanation, or use this topic to assign research projects.
Video Time –Self-similarity and fractals make up an extremely complex visual topic. There are many videos in
common use that can give a much more exciting and attention grabbing explanation than most teachers can deliver
while standing in front of the classroom. These videos are not hard to come by, and they give an excellent explanation
of the material. It is a nice change of pace for the students, and it gives the instructor some precious time to catch-up
on paperwork. It is the best approach for all.
Create Your Own Fractal –Having the students create their own fractal outside of class is a fun, creative project.
This gives the more artistically minded students an opportunity to shine in the class, and the products make beautiful
wall decorations. Here are some guidelines for the assignment.
a. The fractal should fill the top half of a piece of 8^12 ×11 inch plain white paper turned vertically. To give them
more space, provide them with legal size paper. Be aware that each student will probably require more than
one piece before they create their final product.
b. The fractal should be boldly colored to accentuate the self-similarity.
c. The students should be encouraged to be creative and original in their design.
d. The bottom half of the paper will have a paragraph explaining the self-similarity in the fractal. They should
explain why their design is a fractal.
e. Create a rubric to give to the students at the time the project is assigned so that they will feel like they are
being graded fairly. It is hard to evaluate artwork in a way that everyone feels is objective.2.7. Similarity