# May, 2020

## Ask Uncle Colin: A difference of polynomials

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

## A puzzle from Sheena

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

## Ask Uncle Colin: Flipping Signs

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

## Bending a long bar

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

## Wrong, But Useful: Episode 79

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

## Ask Uncle Colin: A Fractional Equation

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

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

## Ask Uncle Colin: The Empty Product

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

## Dictionary of Mathematical Eponymy: The Quine-McCluskey Algorithm

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