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Newton's Polynomial Solver

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This Demonstration shows Newton's method of finding approximate roots of an equation by using three slide rules, called primary, secondary, and tertiary. We can read directly with an auxiliary primary rule. We calculate the value of polynomial for , , and . If its value for is near , is approximately a root of the equation.

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The essence of the original construction was to use slide rules to perform multiplication, while addition was left to a person. We automated addition as well by recording values of polynomial terms and the value of the polynomial in a grid.

The current construction works for coefficients and arguments with absolute value at least 1. Suppose we want to solve the equation . We enter and move sliders to get polynomial value 6 for different positions of . On the auxiliary rule we read , , .

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Contributed by: Izidor Hafner (October 2012)
Based on a note by: C. J. Sangwin
Open content licensed under CC BY-NC-SA

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The slide rules are called primary, secondary, and tertiary. On the primary rule we read according identity . On the secondary rule we read according . The tertiary rule gives us , . The actual value of the polynomial at is , the signs being determined appropriately.

Reference

[1] C. J. Sangwin, "Newton's Polynomial Solver," Journal of the Oughtred Society, 11(1), 2002. pp. 3–7. web.mat.bham.ac.uk/C.J.Sangwin/Sliderules/newtonpoly.pdf.

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