The Flying Colours Maths Blog: Latest posts

The Mathematical Ninja finds the value of $\pi$

This article has also been published as part of the Relatively Prime zine. The student yelped, and found his wrists and ankles strapped to the wheel before the lesson had even started. "Good morning," said the Mathematical Ninja. "I think you and I need to have a little... talk." The

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Ask Uncle Colin: Changing the variable (FP2 Differential equations)

Dear Uncle Colin, I'm supposed to use the change of variable $z = \sin(x)$ to turn $\cos(x) \diffn{2}{y}{x} + \sin(x) \dydx - 2y \cos^3(x)= 2\cos^5(x)$ into $\diffn{2}{y}{z} - 2y = 2\left(1-z^2\right)$. Yeah but no but. No idea. Lacking, Obviously, Something Trivial Hello, LOST, Right, yes. Nasty one, this. The main

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Second derivatives, reciprocals, and the chain rule

Once in a while, a student puts me on the spot; it's not always deliberate. In this case, changing a variable in a second-order differential equation, he blithely said "Well, $\diffn 2yx = \frac{1}{\diffn 2xy}$..." "Whoa whoa whoa..." "... isn't it?" Now, had I not had a series of discussions

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Wrong, But Useful: Episode 33

In Episode $n$ of Wrong, But Useful (where $n$ is a semiprime followed by two semiprimes and a square), @reflectivemaths and I discuss: Colin's trip to Center Parcs and whether it is sufficiently central The number of the podcast, which is the tetrahedral angle, $\arccos\left(\frac{1}{3}\right)$ The Other Half podcast Our

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Ask Uncle Colin: Why does the finger trick work?

Dear Uncle Colin, In Basic Maths For Dummies, you mention a method for multiplying numbers from 6 × 6 to 10 × 10 on your fingers. It's almost magical! Why does it work? -- Does It Guarantee Interesting Times Sums? Hello, DIGITS, I'm glad you're finding the book helpful! The

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Maths and mental health: dealing with panic

Big disclaimer here: I'm not a mental health professional. I'm someone who has suffered from anxiety and depression. If you are experiencing regular panic attacks, or struggling with depression, please seek medical help. I endured many years of misery because I was too stubborn to go to a doctor or

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Ask Uncle Colin: How do we know the digits of $\pi$ don’t recur?

Dear Uncle Colin1, Supposing $\pi$ were to start repeating -- how long would it take to confirm that it actually was? - Recurring Over Uncanny Numbers of Decimals Dear ROUND2 , Great question! $\pi$, as I'm sure you know, is a number close to 3.1416 that represents the ratio between

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The Mathematical Ninja and the First Rule of $\phi$ club

The Mathematical Ninja placed his quadruple espresso on the table; @dragon_dodo looked up from her laptop and smiled. "You're taking it easy on the caffeine this morning, I see?" The Mathematical Ninja nodded. "Yeah, this is only my third cup. What are you working on?" "Computing assignment." The Mathematical Ninja,

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Ask Uncle Colin: a light matrix product

Dear Uncle Colin, I'm working on a (3D) computer graphics course, and my notes have some equations in that I don't understand. I have a point light at (4D) position $\vec L$, an object translated by a 4D matrix $\bb M$ and a (4D) point on the surface at $\vec

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The Maths Police Investigate: The Beans Of Wrath

This is a guest post, courtesy of @Dragon_Dodo and @FennekLyra. Thanks, Dominika and Eva! It was an unusually quiet morning at the Maths Police HQ. ‘If a mathematician is a device for turning coffee into theorems, what do you reckon the conversion rate is?’ mused agent Dodo over her morning cup

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