The End of Error

11 Powers

Section 10.1 showed a three-dimensional visualization of the saddle-shaped surface for multiplication, z = x × y. A similar saddle-shape occurs in the plot for z = x^y, shown in a different way above, with a contour plot. The red corners are increasing values of the general power function x^y and the blue corners are decreasing values. Computing the function means navigating a minefield of exception cases, as well as facing a previously unsolved math conundrum.

11.1 Square

Compared to the four basic arithmetic operations, finding x^y for general values of x and y is a big jump up in effort. We start this chapter with a really soft toss, ...