φ, π, e, and i by David PerkinsMy rating: 5 of 5 stars
It's been a couple of decades since I did any real math study. φ, π, e, and i caught my eye because I know the author through an online forum, plus I was looking for a book with a non-alphanumeric character in the title for a book club.
Fortunately, φ, π, e, and i is written for undergraduates so it required only that I unearth some things that are buried in my brain under 20 years of other stuff. For someone who is actively learning college-level mathematics, most of the stuff that I'd forgotten would be fresh in mind. Of course, when I got confused I could always ask the author for clarification! But that wasn't often necessary, since the book is clearly written and uses endnotes to provide extra detail where a conclusion may not be obvious.
φ, π, e, and i isn't just about the math itself, but also some of the history behind the numbers. The Sanskrit poet and the Italian mathematician who both discovered the Fibonnaci sequence, for instance, which comes up as one learns about φ. Or the parallel conception of complex numbers in Norway and Germany around 1800. I found the history to be just as interesting as the math itself, particularly when more than one historical figure had approached a problem from different directions but came to the same conclusion. That kind of convergence really puts the universal nature of mathematics in focus.
The four chapters of the book (one for each constant, naturally) build on one another nicely. Techniques used in the earlier chapters make appearances later on, and the book ends with the well-known e^(iπ)=-1 and less well-known φ = e^(iπ/5) + e^(-iπ/5), tying all four together in one statement. A fitting way to wrap up an interesting trip through the definition and history of some of math's most important numbers!
