The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: Is my friend crazy?

Dear Uncle Colin, A friend of mine told me that $1 + 2 + 4 + 8 + ... = -1$. Is he crazy, or is there something going on here? -- Somehow Enumerating Ridiculous Infinitely Extended Sum Dear SERIES, There are a couple of 'proofs' of this non-fact that

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Review: Sumaze

Even as someone who owes at least some of his maths skills to computer games (I played L in the late 80s and would love to see it resurrected, and there's a lot to be said for the mental arithmetic in something like Football Manager), my heart still sinks a

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Rewriting a function without going piecewise

You know the ridiculous kind of pseudo-context question that makes you go 'Why doesn't Lisa get a proper hobby rather than timing her friends doing jigsaw puzzles?'? You could replace pretty much all of them with "A mathematician is trying to be clever by...". In this particular case, a mathematician

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Ask Uncle Colin: A logarithmic coincidence?

Dear Uncle Colin, I noticed that $2^{\frac{1}{1,000,000}} = 1.000 000 693 147 2$ or so, pretty much exactly $\left(1 + \frac{1}{1,000,000} \ln(2)\right)$. Is that a coincidence? Nice Interesting Numbers; Jarring Acronym Dear NINJA, The easiest way to see that it's not a coincidence is to check out $3^{\frac{1}{1,000,000}} $, which

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Review: Things To Make And Do In The Fourth Dimension, by Matt Parker

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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An interesting GCSE triangle

It's not often I have anything nice to say about EdExcel. I've usually found their exams to be the most predictable and least thought-provoking of all the boards (at least until they finally snapped in 2013 and let Kate the Photographer loose on an unsuspecting cohort). At GCSE, their advanced

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Wrong, But Useful: Episode 29

In this episode of Wrong, But Useful, @reflectivemaths and @icecolbeveridge...: Argue about the inferiority of statistics Give a number of the podcast: $e^{\frac{\pi}{2}} = i^i \approx 0.20788...$ Review @standupmaths's excellent Things to Make and Do in the Fourth Dimension Investigate equable shapes in several dimensions, with reference to @tombutton's MathsJam

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Ask Uncle Colin: an integral that’s giving me a headache

Dear Uncle Colin, I've been trying to work out $I = \int_0^{\frac \pi 4} x \frac{\sin(x)}{\cos^3(x)} \d x$ for hours. It's the fifth time this week I've been up until the small hours working on integration and it's affecting my work and home life. I'm worried I'm becoming a calcoholic.

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The Maths Police (Financial Unit) Investigate

A guest post from @FennekLyra, who is Eva in real life. Thanks, Eva! “Want to see something awful?” asked Agent Lyra1 suddenly, turning to her fellow maths agent and friend Dodo at the £16,000 question of Who Wants To Be A Millionaire? that both of them watched daily. “Oh come

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Ask Uncle Colin: two almost-matching sequences

Dear Uncle Colin Somebody told me that the sequences $\left \lfloor \frac {2n}{\ln(2)} \right \rfloor$ and $\left \lceil \frac{2}{2^{\frac 1n}-1} \right \rceil$ were equal up to the 777,451,915,729,368th term, and I shivered in ecstasy. Is there something wrong with me? -- Sequences Considered Harmful When Agreeing Really Zealously Hi, SCHWARZ

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