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Daily Lesson Plan
Lesson goal: students use measurement and calculation to explore the mathematical principles behind the M.C. Escher lithograph "Print Gallery."
Inspired by the article "Mathematician Fills in a Blank for a Fresh Insight on Art".
The real investigation by Lenstra and several other people took 2 years and involved tools like elliptic curves. So now students from grades 6-8 are expected:

--attempting to determine if these measurements can be represented by common equations (linear, logarithmic/exponential, trigonometric, etc.)
--determining how equations function to produce the unique form of the image (e.g. a spiral, a staircase that always goes upward, a repeating image with slight variations, etc.)
Groups should determine the mathematical principles (or forms) at work in the image (such as the "cyclic bulge," distortion, and elliptical curves employed to define the principles at work in "Print Gallery"). Using these principles as a guideline, groups create an extrapolation of the image from the original work.

* Log and trig functions in grade 6 (or even in 8 with sufficient understanding)?
* Equations producing ever rising staircases?
* Determine elliptical curves?

Extension Activities:
2. Research Fermat's Last Theorem, or another unsolved mathematical problem. Write a short paper describing the history of the problem, the solutions suggested, why these solutions failed, and the prospects for a real solution in the future.



posted by TB reader at 11:00 PM