# Newton's Polynomial Solver

Newton's Polynomial Solver

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.

x+bx+ax=d

3

2

x

x+bx+ax

3

2

x

1

x

2

x

3

x

i

d

x

i

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 , , .

x-6x+11x=6

3

2

a=11,b=-6

x

i

x

x=1

1

x=2

2

x=3

3