Posted in mechanics 1.

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

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Posted in gcse.

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.

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Posted in gcse.

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. $12.5$

Read More →An occasional series highlighting common errors that refuse to die. “It just… won’t stay dead!” he said, as the Mathematical Zombie moved closer. “$(a+b)^2 = a^2 + b^2$”, it said. “Brains! $(a+b)^2 = a^2 + b^2$.” “But… it doesn’t!” he said. “You have to multiply out the brackets!” “$(a+b)^2 =

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Posted in logarithms, ninja maths.

“Coincidence?” said the Mathematical Ninja. “I think not!” He looked at his whiteboard pen as if wondering how best to fashion a weapon out of it. He wrote: $10^3 = 1,000$ $2^{10} = 1,024 = 1.024 \times 10^3$ So $10 \ln (2) = 3 \ln(10) + \ln(1.024)$ But $\ln(1.024) \simeq

Read More →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)

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Posted in circles, ninja maths.

“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,

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Posted in podcasts.

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

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Posted in algebra.

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

Read More →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

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