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 Uncategorized

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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Posted in ask uncle colin, revision

Dear Uncle Colin, I have to revise for an upcoming test — and my teacher is demanding proof! What’s the best way to convince my teacher I’ve revised? — Totally Evidence-based Study Time Hello, TEST – great question! Depending on the kind of test, you have several options that leave

Read More →An interesting tweet, some time ago, from @RJS2212: Two unit fractions where denominators differ by 2Add fractionsNumerator & denominator of the sum are two smaller numbers of Pythag triple — Robert J Smith (@RJS2212) May 30, 2016 And of course, you wonder two things: a) why does it work, and

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Posted in ask uncle colin, mechanics 3

Dear Uncle Colin, I clumsily dropped a particle of mass $m$! Luckily, it’s attached to a light elastic string with a modulus of elasticity of $3mg$ and natural length $a$. The other end of the string is attached to the point where I dropped the weight from. When I say

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