The figure below shows an outermost 1 × 1 square, within which appears an inscribed circle, within which appears an inscribed square, within which appears another inscribed circle, within which appears another inscribed square. Although the figure does not show it, this process can be continued indefinitely. Let L_{1}= 1 be the length of the first (largest) square, L_{2} be the length of a side of the second square, L_{3} be the length of a side of the third square, and so on. Calculate L_{20.}

“A good problem is one that you do not know how to start.” –Lockhart, Mathematician’s Lament

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I am happy to meet outside of class, but it is best to schedule an appointment with me, otherwise I might go biking or hiking or take my dog for a walk. You can do this by talking with me in class or by sending me an e-mail at maria.moses@northwestschool.org at least one day in advance. ** **

(By the way, this me at the summit of Mt. Baker. I'm proud of this moment not so much for getting to the top, but more so for the hours of training I completed that got me there and for never giving up when I was challenged.)

Video on The*Key to Success:*

*http://www.ted.com/talks/angela_lee_duckworth_the_key_to_success_grit*

Association of Women in Math: *https://sites.google.com/site/awmmath/home*