Posted in algebra, big in finland, probability, puzzles.

Zeke and Monty play a game. They repeatedly toss a coin until either the sequence tail-tail-head (TTH) or the sequence tail-head-head (THH) appears. If TTH shows up first, Zeke wins; if THH shows up first, Monty wins. What is the probability that Zeke wins? My first reaction to this question

Read More →Uncle Colin recently explained how he would prove the identity $\sin(2x) \equiv 2 \sin(x)\cos(x)$. Naturally, that isn’t the only proof. @traumath pointed me at an especially elegant one involving the unit circle. Suppose we have an isosceles triangle set up like this: The vertical ‘base’ of the triangle is $2\sin(\alpha)$

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Posted in big in finland, reviews.

It’s genuinely difficult to write an innovative maths book, something that’ll teach even the most grizzled and cynical of tutors a thing or two, but @standupmaths1 has done exactly that. Most popular maths books, my own included, tread a pretty familiar path through the history of maths, throw out a

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Posted in big in finland, puzzles, sport.

A puzzle that occurred to me watching Wimbledon this week: A tennis match goes to five sets. The number of games one of the players wins in each set forms an arithmetic series. Given that the two players won the same number of games in total, who won the match?

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Posted in ask uncle colin, big in finland.

Dear Uncle Colin, I read somewhere that if you work out $\frac{1}{999,999,999,998,999,999,999,999}$, you get the Fibonacci sequence. Is that really true? Is there witchcraft at work? — Feeling Inspired By Ordinary Numbers; Arithmetic Calculation Can Intimidate! Hi, FIBONACCI! First, to put your mind at rest, there’s no witchcraft at work

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Posted in big in finland, circles, geometry.

A tweet from @GregSchwanbeck some time back asked: Does square or circle have greater perimeter? A surprisingly hard prob for HS: http://t.co/vwLIs26pcC #mathchat #math pic.twitter.com/Vpjop8yU7G — Greg Schwanbeck (@GregSchwanbeck) March 16, 2015 The setup is: one side of a square is tangent to a circle, and two corners of the

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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

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Posted in big in finland, ninja maths, trigonometry.

“$\cos^{-1}(0.93333)$, said the student. A GCSE student, struggling a little; the Mathematical Ninja bit his tongue rather than correct him to $\arccos$ or to $\frac {14}{15}$; he also accepted, grudgingly, the answer was going to be in degrees. “Maybe 21 bad degrees?” “21.04”, said the student. “Not too terrible.” “I

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Posted in big in finland, ninja maths.

“… which works out to be $\frac{13}{49}$,” said the student, carefully avoiding any calculator use. “Which is $0.265306122…$”, said the Mathematical Ninja, with the briefest of pauses after the 5. “I presume you could go on?” “$…448979591…$” “All right, all right, all right. I suppose you’re going to tell me

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