# The Flying Colours Maths Blog: Latest posts

## Ask Uncle Colin: Why is $e$ not 1?

Dear Uncle Colin, If $e = \left( 1+ \frac{1}{n} \right)^n$ when $n = \infty$, how come it isn’t 1? Surely $1 + \frac{1}{\infty}$ is just 1? - I’m Not Finding It Natural, It’s Terribly Yucky Hi, INFINITY, and thanks for your message. You have fallen into one of maths’s classic

## Dictionary of Mathematical Eponymy: Hoberman Sphere

What are they? I thought, until I looked closely, that we had a Hoberman sphere in the children’s toybox. We don’t: we have something closely related to it, though. The Hoberman mechanism comprises a series of pairs of pivoted struts arranged end to end. Each pair looks a little like

## Ask Uncle Colin: Curved Surface Areas

Dear Uncle Colin, I’ve been struggling with this: “If the surface area of a sphere to cylinder is in the ratio 4:3 and the sphere has a radius of 3a, calculate the radius of the cylinder if the radius if the cylinder is equal to its height.” Can you help?

## Futility Closet, Fibonacci and Quadratic Residues

I love Futility Closet -- it's an incredible collection of interesting bits and pieces, but it has a special place in my heart because they love and appreciate maths. Not only that, they appreciate maths that I find interesting. The internet has many interesting miscellanies, and many excellent sites specialising

## Ask Uncle Colin: A problem of squares and powers

Dear Uncle Colin, I have to solve $615 + x^2 = 2^y$ for integers $x$ and $y$. I’ve solved it by inspection using Desmos ($x=59$ and $y=12$ is the only solution), but I’d prefer a more analytical solution! Getting Exponent Right Makes An Interesting Noise Hi, GERMAIN, and thanks for

## A logs puzzle

Via @markritchings, an excellent logs problem: If $a = \log_{14}(7)$ and $b = \log_{14}(5)$, find $\log_{35}(28)$ in terms of $a$ and $b$. One of the reasons I like this puzzle is that I did it a somewhat brutal way, and once I had the answer, a much neater way jumped

## Wrong, But Useful: Episode 69

In this episode, we're joined by @christianp, who is Christian Lawson-Perfect in real life, our first returning special guest co-host1. We discuss: The Big Internet Math Off and associated stickerbook 99 variations on a proof by Philip Ording The Art of Statistics - Learning from Data by David Spiegelhalter Maths

## Ask Uncle Colin: A Binary Fraction

Dear Uncle Colin, How would you write $\frac{1}{10}$ in binary? Binary Is Totally Stupid Hi, BITS, and thanks for your message! I have two ways to deal with this: the standard, long-division sort of method, and a much nicer geometric series approach. Long division-esque While I can do the long

## A folding puzzle

Here’s a tweet from @colinthemathmo: Here's another one. Take a square, crease in the halfway mark, fold up a corner - where does the corner go to? What are its coordinates? pic.twitter.com/Bfr0X8ACur — Colin Wright (@ColinTheMathmo) February 12, 2018 I’m not big on origami, but if Colin thinks it’s an

## Ask Uncle Colin: Round-Robin Progress

Dear Uncle Colin, I lost the first game of my Big Internet Math-Off tournament - can I still win the group and qualify for the semi-finals? - Surely Combinations Of Talent, Luck And Nous Deliver? Hi, SCOTLAND, and thanks for your message! Because the tie-break rules aren’t currently clear, I