Posted in ask uncle colin, vectors.

Dear Uncle Colin, I’ve got three points: $A$, with a position vector of $(2\bi + 4\bj)$, $B$, with a position vector of $(6\bi + 8\bj)$ and $C$, with a position vector of $(k\bi + 25\bj)$, and they all lie on the same straight line. I have to find $k$, and

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Posted in pi, trigonometry.

A lovely curiosity came my way via @mikeandallie and @divbyzero: In 1992 Daniel Shanks observed that if p~pi to n digits, then p+sin(p)~pi to 3n digits. For instance, 3.14+sin(3.14)=3.1415926529… — Dave Richeson (@divbyzero) July 15, 2016 Isn’t that neat? If I use an estimate $p = 3.142$, then this method

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Posted in ask uncle colin, statistics.

Dear Uncle Colin, My research has determined that female adults have a mean overhead reach of 208.5cm, with a standard deviation of 8.6cm, and follows a normal distribution. I wanted to know the probability that the mean overhead reach of 50 female adults would lie between 180cm and 200cm and

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Posted in statistics.

Don’t get me wrong, The Dorset Echo is one of my favourite local newspapers. They have been kind enough to feed my ego on several occasions, and even if their headlines sometimes don’t quite reflect the gist of the story, I appreciate that. This time, though, they’ve gone too far.1

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Posted in algebra, ask uncle colin.

Dear Uncle Colin, I have a system of equations I can’t solve! $x + y + z = 100$; $.08x +.1y +.2z = 12$; $y – z = 25$ I keep tripping up on the decimals and negative signs! — We’re Extremely Stressed Solving Equations Linear Hello, WESSEL! My best

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Posted in trigonometry.

I have a tendency to write about interesting questions from a ‘here’s how you do it’ point of view, which must give the impression that I never get confused1. To try to dispel that, I wanted to share something that came up in an Oxford entrance paper (the MAT from

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Posted in ask uncle colin, graphs.

Dear Uncle Colin, I’m looking for the equation of a curve that goes through the points $\left(10, \frac{1}{64}\right)$ and $\left(100, \frac{1}{32} \right)$, as — as $x$ gets large — approaches 1. How do I go about it? Always Silence Your Mobile Phone Typing Out Tricky Equations Good advice, ASYMPTOTE! And

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Posted in ranting.

A good friend, a brilliant maths teacher, was recently dissed on Twitter. And if there’s one thing I don’t stand for, it’s good friends and brilliant maths teachers being dissed on Twitter. There was an implication — perhaps inadvertent; I know I’ve fired off short messages too quickly and implied

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