The Flying Colours Maths Blog: Latest posts

Ask Uncle Colin: An Exponential Limit

Dear Uncle Colin, I need to work out the limit of $\frac{2^{3x} - 1}{3^{2x}-1}$ as $x \to 0$, and I don’t have any ideas at all. Do you? - Fractions Rotten, Exponents Generally Excellent Hi, FREGE, and thanks for your message! There are a couple of ways to approach this:

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A Harmonic Conundrum

This one came from user_1312 on reddit with a heading “This is a bit tricky… Enjoy!”. What else can we do but solve it? Let $m$ and $n$ be positive numbers such that $\frac{m}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{101}$. Prove that $m-n$ is a multiple

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Wrong, But Useful, Episode 73

In this month's episode of Wrong, But Useful, we talk to @AJMagicMessage, who is Andrew Jeffrey in real life, and one of the driving forces behind Maths Week England, which in 2019 is November 11th to 15th. Apologies for a few issues with feedback in this episode. Dave takes full

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Ask Uncle Colin: How many draws?

Dear Uncle Colin, I’m trying to figure out how many possible draws there are for the Champions’ League quarter-finals. There are eight teams involved, and let’s assume first leg home advantage doesn’t matter (so A vs B is the same as B vs A) and there’s no restriction on which

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Dictionary of Mathematical Eponymy: The Kovalevskaya Top

When I was about eight, my parents bought, as a Christmas gift for my brother and me, a “Jungle Gym”, plastic tubes and connectors that fit together to make whatever the imagination came up with, a sort of large-scale Meccano. My brother went out into the garden to build castles

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Ask Uncle Colin: Missing Planes

Dear Uncle Colin, I’m told that 70% of the aircraft that go missing in a certain country are subsequently rediscovered. Of those that are recovered, 60% have an emergency locator, and 90% of those that aren’t recovered, don’t have a locator. Supposing an aircraft has disappeared, what’s the probability it

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Summing Products

Some days your mind wanders into an interesting puzzle: not necessarily because it’s a difficult puzzle, but because it has familiar result. Then the puzzle becomes, how are the two things linked? For example, I had cause to add up all of the numbers in the times tables - let’s

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Wrong, But Useful: Episode 72

In this month's podcast, we're joined by @CoreMathsCat, who is Catherine van Sarloos in real life. We discuss: Number of the Podcast: 179 (balloons) Maths Week England is mid-November (11-16th). Catherine is involved in running a contest for it! Via Peter Rowlett: Women’s names Via Adam Atkinson: rounding up or

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Ask Uncle Colin: A Curve

Dear Uncle Colin, I’m given that a curve has equation $y = ax^3 + bx^2 + cx + 1$. It has a turning point at $\left( -1, \frac{11}{3} \right)$ and an inflexion point when $x=2$. How do I find the missing constants? - I’m Not Feeling Like Evaluating Constants, Thanks

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Hotplates

“Do the hotplates heat the food through properly?” “Oh yes, they come out of the oven at 200 degrees and the temperature drops by a degree every minute.” To @dragondodo’s credit, she did not launch into a lecture on Newton cooling. But she did grumble about it to me -

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