# The Flying Colours Maths Blog: Latest posts

## Ask Uncle Colin: A Differential Equation

Dear Uncle Colin, What's the correct method to find the general solution of $y''+4y'+4y=(3+x)e^{-2x}$? I've got the complementary function just fine (it's $y=Ae^{-2x}+Bxe^{-2x}$), but I'm going in circles with the particular integral. - Differential Equation's Solutions Are Really Gruesome; Ugly Exponential Scariness Hi, DESARGUES, and thanks for your message! I

## Review: Hello World, by Hannah Fry

The best science writers (as far as I'm concerned, at least) are the ones who make you feel like you're sitting down for a coffee with a smart friend, excited about a thing they know about, a thing they've found out, or a thing they've just put together. I have

## Ask Uncle Colin: Decimal arithmetic

Dear Uncle Colin, How do people do decimal calculations like $80 \times 0.15$ in their heads? It seems impossible. - Doesn't Everyone Seem Clever, Answering Readily These Evil Sums Hi, DESCARTES, and thank you for your message! There are several possible strategies for a question like this - how I

## The Mathematical Ninja And The Driving Awareness Course

“What are you doing here?” “Never mind that, sensei, how on earth did they catch you?” “... I don’t want to talk about it. In any case, I was only doing 5% more than the speed of light.” “Yeah, that poses more questions than it answers, in honesty.” The Powerpoint

## Ask Uncle Colin: A Log Approximation

Dear Uncle Colin, According to John D Cook, you can estimate the natural logarithm of a number $x$ by working out $\log_2(x)-\log_{10}(x)$. It seems to be pretty accurate - but why? Not A Problem - Interesting Exponential Riddle Hi, Napier, and thanks for your message! That is indeed a conundrum:

## On Customer Survey Forms

In the olden days, I had a proper job1 writing software for customer survey forms. Among other things, our users could ask their customers to rate how likely it was that they would recommend the product to their friends. Typically, this would be on a ten-point scale, from extremely unlikely

## Ask Uncle Colin: Two triangles

Dear Uncle Colin, When I'm 8 metres away from a flagpole, the angle of elevation to its top is exactly 40º, according to this angle-measurey-majigger I have here. What will it be when I'm only five metres away? The Hypotenuse Eludes One; Does One Look Into Trigonometric Expressions? Hi, THEODOLITE,

## Wrong, But Useful: Episode 59

In Episode 59 of Wrong, But Useful, we’re joined by @el_timbre, who is Emma Bell in real life. We discuss: Emma’s Roots column in Chalkdust1 Number of the podcast: 64, because it’s pleasing, and Dave sings the 64 Zoo Lane theme, which is less so. Emma’s hexastix construction and the

## The Maths Behind The Errors In The Maths Behind

I recently had a flurry of correspondence with translators of The Maths Behind (available wherever etc., but also soon in Swedish and Korean): embarrassingly, they had caught several mistakes in the book. These things happen; we try to put them right and move on. However, it got me wondering: can

## Ask Uncle Colin: A Trigonometric Proof

Dear Uncle Colin, I have a trig identity I can't prove! I have to show that $\frac{\cos(x)}{1-\sin(x)} = \tan(x) + \sec(x)$. Strangely Excited Comment About Non-Euclidean Trigonometry. Hi, SECANT, and thanks for your message! This is a slightly sneaky one, but definitely a good one to practice. Let's do it