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Puzzle: continued root (Part 1)

May 4, 2010 pm31 11:50 pm

With Spanish AP taking 20% of each class, and with all the juniors worked up over AP US stress, this was a “diminished” teaching day in the midst of a diminished teaching week. I scheduled today for “practice solving trig equations” – but I had a beautiful challenge problem, and let it and its extensions eat up two-thirds of each period:

Find x:  x = \sqrt{2 + \sqrt{2 +\sqrt{2 +\sqrt{2 +\sqrt{2 + ...}}}}}

Divided by missing classmates into clusters, the kids got stuck or made little progress on their own. Five minutes in the buzz changed… I could hear groups considering answers. At least two had decided to evaluate \sqrt{2 + \sqrt{2 +\sqrt{2 +\sqrt{2 +\sqrt{2}}}}} or some similar partial roots, and had decided that either this thing was 2, or it was a little less than two.

They disagreed. Fairly loudly. Was x 2, or was it a little less than 2?

I took a risk. “You guys did well. It’s clearly either 2 or a little less than 2. One of them’s got to be the answer, the other’s close. Let’s go on to some trigonometry practice.”

I read them right. Nothing doing. They wanted to know. And I had them hooked for a half hour or so investigation. That’ll be Part 2.

5 Comments leave one →
  1. May 4, 2010 pm31 11:57 pm 11:57 pm

    I see “formula does not parse”?

    • May 5, 2010 am31 12:43 am 12:43 am

      I scrambled the LaTeX, saw your comment, and fixed it. Thanks. Problem: sqr\ renders nothing. Needs to be sqrt\. Let’s see if I remember.

  2. May 5, 2010 am31 9:15 am 9:15 am

    Great problem! And I am always inspired by the ways you inspire/psychologically manipulate your students. =)


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