When a math book has an intriguing image on the cover, it’s fun to get to the point in the book where the meaning of the image is explained. I have some ideas for book covers I’d like to write about, but here I’d like to point out three such posts I’ve already written.
Weierstrass elliptic function
The book on the left is Abramowitz and Stegun, affectionately known as A&S. I believe the function plotted on the cover is the Weierstrass elliptic function, as I wrote about here.
As the image suggests, my copy of A&S has seen a bit of wear. At one point the cover fell off and I put it back on with packing tape.
Möbius transformation of circles
The book in the middle is my well-worn copy of my undergraduate complex analysis text. The cover is a bit dirty and pages are falling out, a sort of Velveteen rabbit of math books.
I haven’t written a post about the cover per se, but I did write about the necessary math to recreate the image on the cover here. That post explains how to compute the image of a circle under a Möbius transformation. The image on the left is mapped to the image on the right via the function
f(z) = 1/(z – α).
Here α is the point on the right where all the outer circles are tangent. If you wanted to reconstruct the image on the cover, it would be easier to proceed from right to left: start with the image on the right because it’s easier to describe, and apply the inverse transformation using the instructions in the blog post to produce the image on the left.
I wrote about the book on the right here. I believe the image on the cover is the plot of a Hankel function.
Here’s a post explaining the image on the cover Abstract Algebra by Dummit and Foote.
And here is a post explaining the image on the cover of A Course of Modern Analysis by Whittaker and Watson.