Channel: singingbanana

Category: Education

Tags: calculatorcubicmathematicscurvemathsequationcubic plane curveslide ruleproblempuzzlepolynomialmathnomogram

Description: Turn a cubic curve (with no x^2 term) into a calculator for sums, multiplications and square-roots. Simply draw a line across the curve so that it intersects at three points, a, b and c. We may now label the curve in a way such that a + b = c or ab = c. I used the cubic curve y = x^3 - 3x, print out the curves below: cccalculator for addition: singingbanana.com/cccalculatoraddition.png cccalculator for multiplication: singingbanana.com/cccalculatormultiplication.png (Or, if you prefer the curves with the axes: singingbanana.com/cccalculatoradditionwithaxes.png singingbanana.com/cccalculatormultiplicationwithaxes.png) Here's an alternative scale for multiplication so it's more like a slide rule. Magnitude just requires common sense singingbanana.com/cccalculatormultiplicationaltscale.png This was pointed out to me when my friend Colin Wright shared this blog post cp4space.wordpress.com/2012/08/29/elliptic-curve-calculator But I think the description in this video is simpler, which is based on this post from 1953 by Richard K. Guy singingbanana.com/a%20single%20scale%20nomogram.jpg Thanks to Phil Ramsden for doing the curve in Mathematica for me, and for reminding me how roots work.