Monthly Archives: October 2019

Book review: The Mathematics of Various Entertaining Subjects, Volume 3

Posted on October 31, 2019 by Brent

I have a bunch of books in the queue to review—I hope to begin writing these more regularly again! [Disclosure of Material Connection: Princeton Press kindly provided me with a free review copy of this book. I was not required … Continue reading →

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A combinatorial proof: PIE a la mode!

Posted on October 25, 2019 by Brent

Continuing from my last post in this series, we’re trying to show that , where is defined as which is what we get when we start with a sequence of consecutive th powers and repeatedly take successive differences. Recall that … Continue reading →

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A few words about PWW #27

Posted on October 24, 2019 by Brent

The images in my last post were particular realizations of the famous Sieve of Eratosthenes. The basic idea of the sieve is to repeatedly do the following: Circle the next number bigger than that is not yet crossed out, call … Continue reading →

Posted in pattern, pictures, posts without words, primes | Tagged , , | 4 Comments

Post without words #27

Posted on October 21, 2019 by Brent
Posted in pattern, pictures, posts without words, primes | Tagged , , | 7 Comments

Order of operations considered harmful

Posted on October 7, 2019 by Brent

[The title is a half-joking reference to Edsger Dijkstra’s classic paper, Go To Statement Considered Harmful; see here for more context.] Everyone is probably familiar with the so-called “order of operations”, which is a collection of rules that reflect conventions … Continue reading →

Posted in arithmetic, teaching | Tagged , , , , , , | 9 Comments