Re: waaay off-topic (was: waay off-topic, previously way-off and Re: U2-darn few bugs...)

[Daniel Say say@xxxxxxxx]

> Sure, absolutely correct. The slide rule (Napier's bones) is based on
> logarithmic scales and logarithms are ways of doing arithmetic with
> exponents. I had this gorgeous double-length slide rule entering
> high school in 1962. Then I took a class in high school that involved
> first old-fashioned adding machines (you know, with shifting
> carriages) that we wrote algorithms for. The slide rule got dusty
> once we took on the IBM 1620. I still remember 2600020003 fondly. 
> (Points to those who know.)
>
	No, "Napier's bones" are a mulitplication
	table set of rods, with a multiplication
	table on each of the four faces of the
	long square-cross-section rods.
	One of the many illustrations
	http://nrich.maths.org/content/02/09/penta4/bones2.gif
	and 	
	http://www.maxmon.com/images/hstfig4.gif
	among many others.

	Lots of calculation examples at
	http://en.wikipedia.org/wiki/Napier's_bones
	More serious at http://mathworld.wolfram.com/NapiersBones.html
	
	Slide rules are still sold and there are many
	sites devoted to various models. Purdue University
	created a museum wall of slide rules last year
	with donated and discarded profs' 'rules.
	
	Circular rules could have a longer scale in a
	smaller space, though usually the central circle
	was the same length as normal rule. One advantage
	was that the answer would not go "off-scale" or
	outside the ruler. With CI (C scale inverted)
	and D scales you could keep answers on the scale
	rather than adding the exponents out past the end
	of the rule.

	http://en.wikipedia.org/wiki/Slide_rule
	discusses circular rules among others.

	The obsessive site http://www.sphere.bc.ca/test/build.html
	shows how to download graphics and build your own.
	The venerable site http://solar.physics.montana.edu/kankel/math/csr.html
	has a nicer template.

	I still have my Concise circular, preferring
	its size to the 10 inch slipstick
	http://www.concise.co.jp/eng0731/circle01.html
	I find it useful for establishing a table of
	ratios, or in no power situations.	
>
> On Feb 25, at 1:33 AM, Carl Distefano wrote:
>
> >
> >Reply to note from "Robert Holmgren"  Fri, 24
> >Feb 2006 14:55:12 -0500
> >
> >>What about negative roots? Do they make "sense"?
> >
> >Well -- correct me if I'm wrong, David -- a root is a fractional
> >exponent, as in 2^(1/2) equals the square root of 2, so a negative
> >root must be the reciprocal of the fractional exponent, as in
> >2^(-1/2) equals 1 over the square root of 2, or 1/(2^(1/2)).
> >
> >For me it all hangs together when I think of the slide rule (do kids
> >today even know what that is?), which works on the principle that to
> >multiply two numbers you add the exponents, and to divide them you
> >subtract. So, for example, to multiply 2^(1/2) times 2^(-1/2),
> >you'd add 1/2 plus -1/2, to get zero, and 2^0=1, and indeed if you
> >multiply those two numbers, which are reciprocals of each other, the
> >result is 1, and Bob's your uncle.
> >
> >--
> >Carl Distefano
> >cld@xxxxxxxx
> >
>