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# Author Archives: Brent

## do go no to

dodo do go on do no harm do to others go do likewise go-go music go no further goto considered harmful no can do it’s a no go a big no-no say no to drugs what to do here or … Continue reading

## Book review: Tales of Impossibility

[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.] Tales of Impossibility: The 2000-Year Quest to Solve … Continue reading

Posted in books, review
Tagged algebra, antiquity, circle, constructible, construction, cube, geometry, impossibility, polygon, problems, square, tales, trisect
4 Comments

## A new counting system

0 = t__ough 1 = t_rough 2 = th_ough 3 = through So, for example, trough through tough though though. English is so strange.

## A simple proof of the quadratic formula

If you’re reading this blog you have probably memorized (or used to have memorized) the quadratic formula, which can be used to solve quadratic equations of the form But do you know how to derive the formula? Usually the derivation … Continue reading

## 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!