Posted in ask uncle colin.

Dear Uncle Colin, Can two polynomials be equal everywhere in some non-trivial interval $[a,b]$ but not equal elsewhere? - Lacking A Good Reasonable Answer, No Good Explanation Hi, LAGRANGE, and thanks for your message! The answer is “no”, but to explain why, I need to give you a few pieces

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Posted in puzzles.

A puzzle that came to me via @sheena2907: Choose two numbers, $x$ and $y$, uniformly from $[0,1]^2$. What’s the probability that $\frac{x}{y}$ rounds to an even number? What’s the probability that it rounds down to an even number? As always, spoilers below the line. Rounding One of my best approaches

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Posted in ask uncle colin.

Dear Uncle Colin, Is there a rigorous explanation of why the direction of the inequality changes when you flip the sign? - Fuzzy Logic, Inequality Puzzle Hi, FLIP, and thanks for your message! Here are my best efforts at a rigorous explanation; I’d be interested to read anyone else’s go

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Posted in puzzles.

A nice thinker from Futility Closet: A rail one mile long is lying on the ground. If you push its ends closer together by a single foot, so that the distance between them is 5279 feet rather than 5280, how high an arc will the rail make? Feel free to

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Posted in podcasts.

In this, the penultimate episode of Wrong, But Useful, we’re joined by @karenshancock (who is Karen Hancock in real life). We discuss: A scoring system for an online quiz round. The Big Mathoff What is a surd? Currently reading Ratio by Michael Ruhlman - a cookery book that starts from

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Posted in ask uncle colin.

Dear Uncle Colin, I’m trying to solve $\frac{x}{x-1} = \frac{1}{x-1}$. I think the answer should be 1, but my teacher disagrees. What do you think? - First Results Are Contradicting Teachers’ - Is One Nonsense? Hi, FRACTION, and thanks for your message! It’s tempting, here, to multiply both sides by

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Posted in arithmetic, haskell.

This is an extended version of my entry in the Lockdown Mathoff at the Aperiodical Binet’s formula1 is a lovely way to generate the $n$th Fibonacci number, $F_n$. If $\phi = \frac{1}{2}\left(\sqrt{5} + 1\right)$, then $$F_n = \frac{ \phi^n - (-\phi)^{-n} }{\sqrt{5}}$$ Haskell and computation The main reason I’m writing

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Posted in ask uncle colin.

Dear Uncle Colin, Why does $0! = 1$ and not 0? - Nothing Is Logical Hi, NIL, and thanks for your message! My best explanation for this - by which I mean, the one I can get some people to accept, goes like this: $4! = 4 \times 3 \times

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Posted in dome.

There was a Fields Medallist named Dan Quillen, after whom are named several things in topics I’ve never head of. Other than Quillen, so far as I can tell, the only mathematical eponyms beginning with Q relate to Willard Van Ormine Quine. I know him from Godel, Escher, Bach, where

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