Monthly Archives: February 2012

Combinatorial proofs

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

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

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

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 , ,