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# Re: [Phys-l] thermodynamics assessment

John Denker wrote:
Hi --

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.

John is here referring to his previous collection of puzzles,
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
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 =&nbsp8.8235
* 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