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Exam time and I am having a hard time finding any inspiring questions about fractals for our "contemporary math" course.

We found the perimeter and area of various Koch snowflakes and Sierpinski triangles.

Ideally the questions would be straightforward examinations of these two types of fractals at about the same level of difficulty as the perimeter and area calculations.

Surely there is something else interesting about them?

This is for non-STEM (non-METS) students, so things like logarithms and complex numbers would probably be a bit too intense to spring on the final exam.

Is there some simple way to indicate their fractional dimension? (Some easy to describe way in which they are not 1-dimensional, and they are not 2-dimensional).

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up vote 1 down vote accepted

If you make a three-dimensional Sierpinski pyramid (formed of four smaller ones), then you (if not your students) can calculate its fractal dimension as... 2! Such a nice answer... is there any way to see it directly? Yes, if you balance the tetrahedral pyramid on one of its edges, and look straight down, you will see all the tiny pyramids fitting together perfectly to fill the two-dimensional square field of view (the square's diagonals being the top and bottom edge of the balanced tetrahedron).

Not sure whether it's suitable material for your exam, but it is elementary and surprising.

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