# December, 2014

## The pull of the planets

This piece was entirely rewritten 2017-06-20 in response to a correction by Adam Atkinson. A friend of a friend stated: "… the planets exert an enormous influence on the tides…" … and that set my oh-no-they-don't-o-meter. Let's have a look, shall we? You might think – as I did when

A student asks: Why do you multiply by 1.07 if you’re adding 7%? I thought 7% was 0.07. You’re quite right – 0.07 is exactly the same thing as 7% (and, if you like, $\frac{7}{100}$). However, if you’re adding on 7%, you need to multiply by 1.07, and here’s why.

## A student asks: upper bounds

A student asks: When you’ve got a value to the nearest whole number, why is the upper bound something $.5$ rather than $.4$? Doesn’t $.5$ round up? So I don’t have to keep writing something$.5$, let’s pick a number, and say we’ve got 12 to the nearest whole number. $12.5$

## A “Proof” that 1 = 2

It’s usually quite simple to spot the error in ‘proofs’ that $1=2$: either someone’s divided by 0 or glossed over inverting a multi-valued function (conveniently forgetting the second square root, for example). You sometimes (as with the sum of natural numbers being $-\frac{1}{12}$, if you throw out all good sense)

## Equation of a circle: the Mathematical Ninja

“Four points,” said the student. “On a circle.” The Mathematical Ninja nodded, impatiently. “$A(-5,5)$, $B(1,5)$, $C(-3,3)$ and $D(3,3)$,” he read from the book, for the third time. A slight crack of a smile. It may have been a snarl. You can never tell with the Mathematical Ninja. “I’m terribly sorry,

## Wrong, But Useful – Episode 21

This month on Wrong, But Useful, @reflectivemaths and I (@icecolbeveridge) talk about… How close is it to Christmas? Who the hell are we and why the hell do we do this? Other maths podcasts: Taking Maths Further and Relatively Prime Colin offers a bounty for pictures of members of the

## A multiplication pattern

Long ago on Wrong, But Useful, my co-host @reflectivemaths pointed out the ‘coincidence’ that $7\times8 = 56$ and $12 \times 13 = 156$ – a hundred more. In fact, it works for any pair of numbers that add up to 15: $x(15-x) = 15x – x^2$, and \$(x+5)(20-x) = 100

## Why you can’t get unlimited chocolate (at least like this)

December! That means it’s time for CHOCOLATE! My dear friend Essbee showed me this: Free chocolate ahoy (and white chocolate, my favourite)! But surely there’s got to be a catch? Of course there’s a catch. You can’t just rearrange an area to end up with a bigger area – moving