On 8/29/2012 2:15 PM, Mike Stay wrote:
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.
What is the base of the logarithms on a slide rule. :-) Brent Meeker