DMC with Walter Stromquist: The Cubic Formula and Other Strange Algebra

Walter Stromquist's topic is the cubic formula, and how to remember it or reconstruct it if you forget. It isn't complicated: If you want to solve 𝑥3+3𝑝𝑥=2𝑞, find any number 𝑡 whose square is 𝑝3+𝑞2, and any number 𝑢 whose cube is 𝑞+𝑡. Then 𝑥=𝑢+𝑝/𝑢 satisfies the equation. We will see why this formula is so much less satisfying than the quadratic formula, and how people really find roots of cubics.

But I might not get very far with that, because first I want to tell a story about a second-grader who learns about pixies and fairies, and wonders whether the fairies know how to add fractions.

In case the equations are hard to read, they are:

x cubed + 3px = 2q
t
p cubed + q squared
u
q + t
x = u + p/u

Please contact anation@brynmawr.edu with comments, questions, or concerns.