Here's a snippet from an interview with Guy in which he explains the concept: Guy: ... OK. My first theorem is a very nice one. If you look in an early issue of the Mathematical Gazette, roughly the British equivalent of the Monthly, you’ll find “A Single Scale Nomogram.” I merely made the observation that a cubic equation with no x^2 term has zero for the sum of its roots. If you draw a cubic curve, y = x^3 + ax + b and put a straight line y = mx + c across it, the sum of the x-coordinates of the intersections is zero. If the curve is symmetrical about the origin (b = 0) and you change the sign of x on the negative half, then one coordinate is equal to the sum or difference of the other two. Combine this with the principle of the slide rule, which simply adds one chunk to another. For example, if the chunks are logs, you have multiplication and division. Anything you can do with a slide rule you can do with any single-scale nomogram. That was my first theorem, I suppose. On Wed, Aug 29, 2012 at 1:08 PM, Richard Guy <rkg@cpsc.ucalgary.ca> wrote:
See: A single scale nomogram, Math. Gaz., 33(1949) 43 or 37(1953) 39. R.
On Wed, 29 Aug 2012, Adam P. Goucher wrote:
You may be aware of the Abelian group operation on elliptic curves. We can exploit this to multiply, divide and square-root real numbers just by drawing a straight line on an elliptic curve marked with two logarithmic scales:
http://cp4space.wordpress.com/2012/08/29/elliptic-curve-calculator/
I've tried it on a printed version, and can achieve somewhere between 2 and 3 significant figures of precision, depending on the calculation.
Obviously it is of no practical use today, since we have electronic calculators and so forth. But in theory, this could have been made way back in 1830, when it could have been used for calculations in navigation and ballistics.
Sincerely,
Adam P. Goucher
http://cp4space.wordpress.com/
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