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Author Archives: Brent
Post without words #29
(This variant was requested by Mark Dominus.)
Book review: Opt Art
[Disclosure of Material Connection: Princeton Press kindly provided me with a free review copy of this book. I was not required to write a positive review. The opinions expressed are my own.] Opt Art: From Mathematical Optimization to Visual Design … Continue reading
More on Human Randomness
In a post a few months ago I asked whether there is a way for a human to reliably generate truly random numbers. I got a lot of great responses and I think it’s worth summarizing them here! Randomness in … Continue reading
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
Posted in books, review
Tagged book, entertaining, magic, mathematics, MOVES
Comments Off on Book review: The Mathematics of Various Entertaining Subjects, Volume 3
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
Posted in arithmetic, combinatorics, proof
Tagged consecutive, difference, function, integers, matching, powers
Comments Off on A combinatorial proof: PIE a la mode!
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
Posted in pattern, pictures, posts without words, primes
Tagged Eratosthenes, prime, sieve
4 Comments
Post without words #27
Posted in pattern, pictures, posts without words, primes
Tagged Eratosthenes, prime, sieve
7 Comments
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 harmful, operations, order, parentheses, parsing, perform, trees
9 Comments
A combinatorial proof: counting bad functions
In a previous post we derived the following expression: . We are trying to show that , in order to show that starting with a sequence of consecutive th powers and repeatedly taking successive differences will always result in . … Continue reading
Posted in arithmetic, combinatorics, proof
Tagged consecutive, difference, function, integers, matching, powers
1 Comment
The Math Less Traveled 