Posted in ask uncle colin, calculus.

Dear Uncle Colin, When I differentiate $y=2x^2 + 7x + 2$ and apply the $nx^{n-1}$ rule, why do I only apply it to the $2x^2$ and the $7x$ but not the 2? — Nervous Over Rules, Mathematically A Liability Hi, NORMAL, and thanks for your message! There are several ways

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Posted in logarithms, ninja maths.

"Isn't it somewhere around $\phi$?" asked the student, brightly. "That number sure crops up in a lot of places!" The Mathematical Ninja's eyes narrowed. "Like shells! And body proportions! And arrawk!" Hands dusted. The Mathematical Ninja stood back. "The Vitruvian student!" The student arrawked again as the circular machine he

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Posted in ask uncle colin, calculus.

Dear Uncle Colin, I have an equation $3y, \dydx =x$. When I separate and integrate both sides, I end up with $\frac{3}{2}y^2 = \frac{1}{2}x^2$, which reduces to $y = x\sqrt{\frac{1}{3}}+c$. With the initial condition $y(3) = 11$, I get $y = x\sqrt{\frac{1}{3}}+11-3\sqrt{\frac{1}{3}}$, but apparently this is incorrect. What am I

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Posted in common errors.

I'm a big advocate of error logs: notebooks in which students analyse their mistakes. I recommend a three-column approach: in the first, write the question, in the second, what went wrong, and in the last, how to do it correctly. Oddly, that's the format for this post, too. The question

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Posted in ask uncle colin.

Dear Uncle Colin, There is a famous puzzle where you're asked to form 100 by inserting basic mathematical operations at strategic points in the string of digits 123456789. This can be achieved, for example, by writing $1 + 2 + 3 – 4 + 5 + 6 + 78 +

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Posted in podcasts.

On this month's episode of Wrong, But Useful, @icecolbeveridge and @reflectivemaths are joined by special guest co-host @christianp. This time, we talk about: Christian, who is involved in @mathsjam and the @aperiodical, and has a number of the podcast: 13. He dislikes it because of its times table; I like

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Posted in arithmetic, prime numbers, proof.

Every so often, a puzzle comes along and is just right for its time. Not so hard that you waste hours on it, but not so easy that it pops out straight away. I heard this from Simon at Big MathsJam last year and thought it'd be a good one

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Posted in ask uncle colin.

Dear Uncle Colin, Apparently, you can use L'Hôpital's rule to find the limit of $\left(\tan(x)\right)^x$ as $x$ goes to 0 – but I can't see how! – Fractions Required, Example Given Excepted Hi, FREGE, and thanks for your question! As it stands, you can't use L'Hôpital – but you can

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Posted in geometry.

This is a guest post from @ImMisterAl, who prefers to remain anonymous in real life. It refers to the problem in this post: a semi-circle is inscribed in a 3-4-5 triangle as shown; find $X$. As with any mathematical problem, my first thought was to sort out exactly what I

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Posted in ask uncle colin, graphs.

Dear Uncle Colin, I don't understand why the normal gradient is the negative reciprocal of the tangent gradient. What's the logic there? — Pythagoras Is Blinding You To What's Obvious Hi, PIBYTWO, and thanks for your message! My favourite way to think about perpendicular gradients is to imagine a line

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