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*From*: Brian Whatcott <betwys1@sbcglobal.net>*Date*: Sun, 10 Jan 2010 10:23:52 -0600

John Denker wrote:

Hi --John is here referring to his previous collection of puzzles,

Here is a short, simple quiz: /snip/

This should not be too closely linked to my previous

"amusing" math quiz; this one is amusing in a different

way. It is also much easier to grade.

of which one sticks in mind:

from a unit square, cut four diagonals to produce an equilateral octagon.

What is the length of the diagonal cuts?

The kicker was the stipulation: no calculators.

Like several of his other puzzles, the solutions depended on knowing a way

to work square roots to within 1 percent. Thinking about this skill,

I realised that like everything else, it was open to Googling.

And here is one prescription for kids:

* we'll try for the square root of 75.

* As 8^2 = 64 and 9^2 = 81, you know the answer is somewhere between

the two.

* Guess it's 8.5 then work out 75/8.5 = 8.8235

* Work out the average of 8.5 and 8.8235. It's (8.5 + 8.8235)/2 =

8.66175. /This is a very close answer!/

* To get much closer, work out 75/8.66175 = 8.6588.

* Work out the average of 8.66175 and 8.6588 to get 8.660275.

* Hey - that's well close enough. 8.660275^2 =75.00036308.

from here:

http://www.murderousmaths.co.uk/books/sqroot.htm

Brian W

**References**:**[Phys-l] thermodynamics assessment***From:*John Denker <jsd@av8n.com>

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