The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: inverses and all sorts

Dear Uncle Colin, I'm stuck on a trigonometry question: find $\cos\br{\frac{1}{2}\arcsin\br{\frac{15}{17}}}$. Any bright ideas? - Any Rules Calculating Some Inverse Notation? Hi, ARCSIN, and thanks for your message! That's a nasty one! Let's start by thinking of a triangle with an angle of $\arcsin\br{\frac{15}{17}}$ - the opposite side is 15

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Wrong, But Useful: Episode 58

In this episode of Wrong, But Useful, we are joined by freelance mathematician @becky_k_warren, formerly of NRICH Becky likes sharing maths with people who "don't like maths" and the #beingmathematical twitter chat Number of the podcast: 157, which is the middle of a sexy prime triplet. Colin goes all Rees-Mogg

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Why the factor and remainder theorem work

So there I was, merrily teaching the factor and remainder theorems, and my student asked me one of my favourite questions: "I accept that the method works, but why does it?" (I like that kind of question because it makes me think on my feet in class, and that makes

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Ask Uncle Colin: Quadratic sequences

Dear Uncle Colin, I had to find the $n$th term of a quadratic sequence (1, 6, 17, 34, 57). I remember my teacher saying something about a table, but I couldn't figure it out. Can you help? Struggles Expressing Quadratics Using Educator's Notation - Concrete Explanation? Hi, SEQUENCE, and thank

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Two coins, one fair, one biased

When the redoubtable @cuttheknotmath (Alexander Bogomolny) poses the following question: Two Coins: One Fair, one Biased #FigureThat #math #probability — Alexander Bogomolny (@CutTheKnotMath) March 5, 2018 ... you know there must be Something Up. Surely (the naive reader thinks) the one with two heads out of three is

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Ask Uncle Colin: A Coin Toss Conundrum

Dear Uncle Colin, Please can you settle an argument? I say, if you toss a coin three times, the probability of getting all heads is one in four, because the only possibilities are HHH, HHT, HTT and TTT. My friend says it's one in eight, being $\frac{1}{2}\times \frac{1}{2} \times \frac{1}{2}$.

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A calculator puzzle

"Your calculator has broken, leaving you with only the buttons for $\sin$, $\cos$, $\tan$ and their inverses, the equals button and the 0 that starts on the screen. Show that you can still produce any positive rational number." When this showed up on Reddit, I knew I was in for

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Ask Uncle Colin: An Unclear Inequality

Dear Uncle Colin, I solved $(x+1)(x-2)(x+3)>0$ by saying there were three possibilities, $x+1>0$, $x-2>0$ or $x+3>0$. The middle one gives $x>2$ and that's the strictest, so that was my answer - but apparently it's wrong. Why is that? - Logical Expressions Seem Silly Hi, LESS, and thank you for your

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A Varignon Vector Masterclass

I recently listened to @mrhonner's episode of @myfavethm, in which he cited Varignon's Theorem as his favourite. What's Varignon's Theorem when it's at home? It states that, if you draw any quadrilateral, then connect the midpoints of adjacent sides, you get a parallelogram. Don't believe it? Try Mark's nifty geometry

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Ask Uncle Colin: Argentina vs Nigeria

Dear Uncle Colin, This is the fifth time in the last six World Cups that Nigeria have been drawn against Argentina in the group stages. What are the odds?! - Coincidences At FIFA? Unlikely! Hi, CAFU, and thanks for your message! I'm going to make some simplifying assumptions for this

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