Problem of the Week

Rodin's "Thinker" contemplates the problem of the week.

WEEK TWELVE: Spiraling Out Of Control!

Solutions due by high noon on Friday, Dec 14, 2012.

I. Consider the spiral created by starting at (0,0) and moving right 1, up 2, left 3, down 4, right 5, etc.  If you do this 100 times, where does the spiral end?  How long is it?  (See top picture below.)

II. Suppose we define a "step" as the distance between (0,0) and (1,1).  Consider the spiral created by starting at (0,0) and moving 1 step to the northeast, 2 steps to the northwest, 3 steps to the southwest, 4 steps to the southeast, etc.  If you do this 100 times, where does the spiral end?  How long is it?  (See middle picture below.)

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III. (For MEGA bonus points.)  Consider the spiral defined by

x(t) = e^t(cos t) ,     y(t) = e^t(sin t).

If the spiral is 300 units long, where does it end?  (See bottom picture below, which is not quite drawn to scale.)

This problem is brought to you by Maegan Bos.

Submit your solutions to Maegan Bos.  You may submit either a hard copy or an electronic file.  Good luck!

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