Monthly Archives: October 2019

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

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!

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

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

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Post without words #27

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Order of operations considered harmful

[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