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 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

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Posted in algebra.

Over on reddit, noncognitivism posted a nice sequence s/he had come across: $4 + 1 = 5 = \sqrt{ (1)(2)(3)(4) + 1 }$ $(4+6) + 1 = 11 = \sqrt{ (2)(3)(4)(5) + 1}$ $(4+6+8) + 1 = 19 = \sqrt{ (3)(4)(5)(6) + 1}$ $…$ $(4+6+ … + (2k+2)) + 1

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Posted in algebra, cav being wrong, ninja maths, pirate maths, ranting.

The Mathematical Pirate took one look at the piece of paper attached to the dock. “They’re BANNING formula triangles?! By order of @srcav?!” He swished his sword around. “Let me figure out where he lives, I’ll show him.” “He lives… inshore, cap’n” said the $n$th mate. “It’s too dangerous.” “Can

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Posted in algebra, big in finland, core 1, core 2, pirate maths.

“Yarr,” said the Mathematical Pirate. “Ye’ll have plundered a decent calculator, of course?” “Er… well, I bought it from Argos, but… aye, cap’n! A Casio fx-83 GT PLUS!” “A fine calculator,” said the Mathematical Pirate. “One that offers you at least three ways to factorise cubics.” “Really!? I thought you

Read More →A student asks: How could I simplify a sum like $(\sqrt 3+\sqrt 2)(\sqrt 3-\sqrt 2)$? Great question! The trick is to treat it like it's an algebraic bracket, like this: $(x + y)(x - y) = x^2 + yx - xy - y^2$ But then you've got $+yx -xy$ in

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Posted in algebra, binomial, further pure 2.

The Mathematical Ninja, some time ago, pointed out a curiosity about Pascal's Triangle and the Maclaurin1 (or Taylor2 ) series of a product: $\diffn{n}{(uv)}{x} = uv^{(n)} + n u'v^{(n-1)} + \frac{n(n-1)}{2} u'' v^{(n-2)} + ...$, where $v^{(n)}$ means the $n$th derivative of $v$ - which looks a lot like Pascal's

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Posted in algebra, ninja maths.

"But I don't liiiiike fractions," said the student. He also didn't like the look of the poker in the Mathematical Ninja's hand, which was beginning to glow red. "Sure you do," said the Mathematical Ninja. "Do I?" "How do you do percentages?" He swished the poker around a bit, as

Read More →You've got the formulas in the book, of course. $u_n = a + (n-1)d$ $S_n = \frac n2 \left(a + L\right) = \frac n2 \left(2a + (n-1)d\right)$ This is somewhere the book and I have a serious disagreement: as a mathematical document, it ought to define its terms. $a$ is

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Posted in algebra, pirate maths.

"Don't tell the Mathematical Ninja," said the Mathematical Pirate. The student shook his head enthusiastically. "Narr!" "You've got $ \frac {7}{x} = 14$. Ask yourself: what would the Mathematical Ninja do?" "The Mathematical Ninja would do something that looked extremely dangerous and terrifying, but was completely under control." "Correct!" said

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