The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: A Rational Mess

Dear Uncle Colin, I’ve got a ratios question, and I don’t understand the solution. The question is: Three numbers, $x$, $y$, and $z$, have a sum of 871. The ratio $x:y$ is 4:5 and the ratio $y:z$ is 3:8. What is the value of $y$? Their solution is to say

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How The Mathematical Pirate Integrates By Parts

The student sighed. “$\int x^3 e^{-2x} \dx$”, he said. “That’s going to be integration by parts. And it’s going to take three steps. What a pain.” “Aharr!” swashbuckled the Mathematical Pirate. “That’s what you think!” “It is what I think,” said the student, slightly bemused. “Would you like to know…”

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Ask Uncle Colin: Should I Interrupt?

Dear Uncle Colin, Sometimes, my professors write wrong things on the board, and I’m never sure whether to correct them. On one hand, I feel like I should respect them and their work; on the other, if I say nothing, I worry that my classmates are getting bad information. What

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Wrong, But Useful: Episode 38

It’s your annual Wrong But Useful Big MathsJam Special! Recorded live, so the audio is a bit shaky in parts. @icecolbeveridge, @reflectivemaths and @peterrowlett discuss Tantrix with some excited background chatter Colin interviews @teakayb (Tom Briggs in real life), who’s at MathsJam with an Enigma machine @pecnut and @mscroggs (Adam

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Ask Uncle Colin: Dividing by decimals

Dear Uncle Colin, A question came up asking me to work out $4.5 + 1.5k = 18-3k$. Obviously, I can rearrange that to get $4.5k = 13.5$ – but how can I divide by 4.5 without a calculator? – Calculating A Number Turning On Ratio Hi CANTOR, and thank for

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On quadratic sequences

This is a guest post from Mark Ritchings, a maths tutor in Bury. A quadratic sequence is a sequence for which the $n$th term is $an^2+bn+c$. The constants $b$ and/or $c$ might be zero but $a$ definitely isn’t. The first term is $a\times 1^2 +b \times 1 + c =

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Ask Uncle Colin: is there a link?

Dear Uncle Colin, I noticed the sum of an arithmetic series and the formula for the area of a trapezium were very similar. How are they related? – Watching Every Interesting Equation, Recognised Something Trapeziumesque Regarding Arithmetic Sequence Sums Hi, WEIERSTRASS, Indeed, they are related, as you can see from

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How do you estimate the normal distribution for large $z$?

In working out a recent blog post, I had cause to find the probability, in a standard normal distribution, of $z < -23$. Beyond "that's a REALLY SMALL NUMBER"1, I was stumped. Could I get anywhere close mentally? A good question. Starting from the definition of the normal distribution, $p(z)

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Ask Uncle Colin: Why don’t you use ‘Dr’ on your books?

Dear Uncle Colin, Is there a reason you don’t use “Dr” in your author name? – Presumably Has Doctorate Hi, PHD! Thanks for your question. Yes, there are several reasons. The one I usually give is that my bank calls me Dr Beveridge and it makes me uneasy. It’s also

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On the trick with 9s

Pick a number, any number1 Let’s say 24,876,028, one of my favourites in the 20-millions. I can tell by looking at it that it’s one more than a multiple of 9. It’s not that clever a trick: I just added up the digits (getting 37), and repeated the trick with

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