Catching up on new submissions to the arXiv, I came across a paper by Robert Baillie, “Summing the Curious Series of Kempner and Irwin,” which is item 0806.4410 in the mathematics listings. Here’s the abstract, exactly as it appears at http://lanl.arxiv.org/abs/0806.4410v1:
In 1914, Kempner proved that the series 1/1 + 1/2 + … + 1/8 + […]

I have a longstanding friendly feud with my Editor-in-Chief over the use of logarithmic scales in graphs. I tend to go for a log plot if there’s the slightest hint of an exponential trend in the data; she argues that the human sense of numbers is inherently linear, and thus a nonlinear scale should be […]

When I finished writing about the Zeno wagering game recently, I had some trees left over, so I thought I would try planting them here.
In the Zeno article I was trying to understand and explain the structure of this peculiar-looking tree, which I’ll call the tangled tree:

As a warmup exercise, I started out with […]

The latest issue of American Scientist is just out, both on the newsstand and on the web. My “Computing Science” column is titled “Wagering with Zeno”; it returns to a subject mentioned briefly in an earlier column, “Follow the Money.”
Consider a random walk on the interval (0,1), where the walker moves according to these […]

The interesting thread of comments on Wednesday’s post about “electoral hex” led me to look more closely at the graph for the Lower 48 states:

I’ve constructed the graph—and it wasn’t easy, by the way—on the rule that two states are linked by an edge if they share a common boundary of more than one point. […]

The answer to the question in the headline is: Too many. After I wrote about Sudoku a couple a years ago, I thought I had cured my addiction; but I’ve been a shameless backslider.
I return to the subject now, in this public confessional mode, to correct an error in my 2006 column. Citing a […]

Zeno of Elea—the philosopher of footraces that never end and arrows that never reach their target—seems a figure so lost in abstractions and infinities that it’s hard to imagine him living in some particular place and time. But Elea was a real town, a sixth-century B.C.E. Greek settlement on the Tyrrhenian coast of Italy. The […]

Very likely you already know how to count, but let’s review anyway. The usual counting sequence for the natural numbers starts 1, 2, 3, 4, 5, … and goes on for quite some time. Some people prefer to start 0, 1, 2, 3, 4, 5, …, but they wind up in the same place […]

From the listener’s point of view, the utility curve for mathematics talks seems to look something like the plot at right. If you already know everything about a subject before you walk into the room, you’re not likely to learn much. At the opposite extreme, if your prior knowledge is absolutely zero, it’s again all […]

There’s a lot of mathematics going on here in San Diego, and I’m taking notes. But for now, what I have to offer is a bucket of pixels:

It’s hard to get excited about the architecture of convention centers. They’re like airports: You’re pleasantly surprised if they’re merely functional. In many respects the San Diego convention […]