Type of equations, separated by degree:

Equation of first degree, linear equation:

kx + d = 0

Equation of second degree, quadratic equation:

ax2 + bx + c = 0

Equation of 3rd degree, cubic equation:

ax3 + bx2 + cx + d = 0

When applied it gives a scheme to correctly calculate a figure in a coordinate system.

As correctly pointed out by BrianShader, the list goes on forever. After the cubic equation there is the quartic equation, then there comes the quintic...

# This is elegant silly.

The solutions of the equation x2 - x - 1 = 0 are (1 + √5)/2 and (1 - √5)/2, the long side and the short side of the Golden Mean respectively. That is (1 + √5) : 1 and 1 : (1 - √5) are both the Golden Mean.

The Corresponding Difference Equation:

sn - sn-1 - sn-2 = 0 when rearanged means the next element of the sequence equals the sum of the previous two - the famous Fibonacci sequence.

The Fibonacci sequence is: 0, 1, 1, 2, 3, 5, 8, 13, 21 etc....

# Form the corresponding sequence of quotients:

1, 2, 1.5, 5/3, 8/5, 13/8, 21/13 etc....

The sequence of quotients converges to one of the roots of the polynomial equation.

But every polynomial equation has an analogous difference equation. We may extract a root from any polynomial equation therefore, as long as the sequence of quotients converges.

The QD algorithm is a modern version of this which extracts ?all the roots and ?always converges (Help me Mother!)

Isn't life grand.

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