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Fibonacci multiples

Posted on May 15, 2012

I haven’t written anything here in a while, but hope to write more regularly now that the semester is over—I have a series on combinatorial proofs to finish up, some books to review, and a few other things planned. But … Continue reading →

Posted in arithmetic, challenges, fibonacci, number theory, pattern | Tagged , | 9 Comments

Carnival of Mathematics 86

Posted on May 8, 2012

Welcome to the 86th Carnival of Mathematics! is semiprime, nontotient, and noncototient. It is also happy since and . In fact, it is the smallest happy, nontotient semiprime (the only smaller happy nontotient is 68—which is, of course, 86 in … Continue reading →

Posted in links | Tagged | 1 Comment

I’ll be hosting the Carnival of Mathematics, and the submission deadline is coming up soon—Tuesday, May 1. Please submit something! It could be something you wrote, or something someone else wrote that you enjoyed. All mathematics ranging from elementary to … Continue reading →

Posted on April 23, 2012 | Leave a comment

Book review: In Pursuit of the Traveling Salesman

Posted on April 7, 2012

As mathematical problems go, the “traveling salesman problem” (TSP) is a rare gem: it is simultaneously of great theoretical, historical, and practical interest. On the theoretical front, it is a well-known example of the class of “NP-complete” problems, which lie … Continue reading →

Posted in books, computation, geometry, open problems, review | Tagged , , | 6 Comments

New Carnival of Mathematics

Posted on April 5, 2012

The Carnival of Mathematics has been revived! A big thanks to Mike Croucher of Walking Randomly for organizing it for the past few years, and to Katie Steckles, Christian Perfect, and Peter Rowlett for taking over. The latest edition, carnival … Continue reading →

Posted in links, meta | Tagged | Leave a comment

Making our equation count

Posted on March 3, 2012

[This is post #4 in a series; previous posts can be found here: Differences of powers of consecutive integers, Differences of powers of consecutive integers, part II, Combinatorial proofs.] We’re still trying to find a proof of the equation which … Continue reading →

Posted in combinatorics, pictures | Tagged , , , , | 2 Comments

Combinatorial proofs

Posted on February 17, 2012

Continuing from a previous post, we found that if we begin with th powers of consecutive integers and then repeatedly take successive differences, it seems like we always end up with the factorial of , that is, . We then … Continue reading →

Posted in combinatorics, pictures, proof | Tagged , , | 12 Comments

Differences of powers of consecutive integers, part II

Posted on February 16, 2012

If you spent some time playing around with the procedure from Differences of powers of consecutive integers (namely, raise consecutive integers to the th power, and repeatedly take pairwise differences until reaching a single number) you probably noticed the curious … Continue reading →

Posted in arithmetic, iteration, pascal's triangle | Tagged , , , , | 3 Comments

17×17 4-coloring with no monochromatic rectangles

Posted on February 9, 2012

Quick, what’s special about the following picture? As just announced by Bill Gasarch, this is a grid which has been four-colored (that is, each point in the grid has been assigned one of four colors) in such a way that … Continue reading →

Posted in open problems, pattern, people, pictures | Tagged , , , , , | 5 Comments

Book review: Nine Algorithms that Changed the Future

Posted on February 4, 2012

Nine Algorithms that Changed the Future: the Ingenious Ideas that Drive Today’s Computers, by John MacCormick. Princeton University Press, 2012. I’m often wary of books written for general audiences on technical topics. It’s quite difficult to write in a way … Continue reading →

Posted in books, computation, review | Tagged , ,