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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

372.0. "BIG IDEAS FOR YOUNG MATHER" by SPRITE::HODGES () Wed Nov 06 1985 13:59

I'm looking for ideas that carry a lot of weight.  My favorite is the
story of little Gauss, when his teacher asked the class to add up the numbers
from 1 to 100.  He saw that 1+99=100, 2+98=100, etc., so 50 * 100 (+ 50) is
the total.  It's a great story -- a good idea -- and for a kid (I'm looking on
behalf of a kid) it can carry a lot of weight, leading into the basic idea of
taking the sum of a series, area of triangles, integral of linear functions,
etc.

Are there other stories or ideas like this?  All branches of math considered.

T.R	Title	User	Personal Name	Date	Lines
372.1		METOO::YARBROUGH		`Thu Nov 07 1985 08:41`	6
	You would probably enjoy the writings of George Polya, e.g. 'How to Solve It' or his two-volume set called 'Mathematics and Plausible Reasoning'. He deals with mathematical induction and other problem -solving techniques in a systematic way. Lynn Yarbrough
372.2		MANANA::COLGATE		`Thu Nov 07 1985 17:45`	5
	Re .0: It actually adds up to 5050 - 49 pairs of sums that equal 100, the number 100 itself and then 50. (I remember trying to do this one in my head when I was a little kid! - the 5050 answer will always be with me!) Wim
372.3		REX::MINOW		`Fri Nov 08 1985 10:28`	5
	Also, check out the four volume set called (I think) "The World of Mathematics". It should be in most libraries. It has a lot of good stuff, though nothing about (post 1950) computers. Martin.
372.4		HARE::GILBERT		`Fri Nov 08 1985 12:01`	7
	A couple other 'big ideas': Aristotle's method of determining specific gravity comes to mind (though it is non-mathematical). Pythagoras' geometric proof of the Pythagorean formula (actually, the diagram gave the insight which led to the formula).
372.5		ADVAX::J_ROTH		`Mon Nov 11 1985 07:54`	7
	Courant and Robbins 'What is Mathematics' is another one of the older 'classics', and may be worth looking for. It's available in paperback, I think. It's also pre-computer, but should have some stimulating material... - Jim
372.6		TAV02::NITSAN		`Mon Nov 11 1985 23:03`	5
	What about the story of Archimedes (sp?) and the weight/volume discovery? Eureka!!! Nitsan D. :-)
372.7		HARE::GILBERT		`Tue Nov 12 1985 14:22`	3
	re .-1 Already mentioned in .4 (sort of). I thought Aristotle didn't sound right.
372.8	The Last Problem	COMICS::DEMORGAN	Richard De Morgan, UK CSC/CS	`Mon Nov 16 1987 04:25`	3
	Re .3: the author is James R Newman. See also "The Last Problem" by E T Bell; it is one volume and very funny - it's also relatively old, I think I read it in about 1959.
372.9	do math toys go in this topic?	GUESS::DERAMO	Dan D'Eramo	`Wed Dec 19 1990 14:55`	19
	Being in the holiday season reminded me of a childhood toy. It was a plastic balance scale that came with plastic numerals, 1-9 or 1-10. Larger numbers were represented by larger (and therefore heavier) numerals. You hung the pieces on the two sides of the scale, and when the sums of both sides were the same, the scale would balance. I was fascinated by the idea of coming up with a set of weights for pieces that would work the same way, except multiplicatively instead of additively. I realized that one would have to be weightless, and that the obvious relations between two, four, eight; and three, nine; and two, three, six; etc. would have to hold. I didn't get as far as to independently discover logarithms, but when I eventually did learn about logarithms I realized they were the solution I had been looking for long before. Dan