Posted in ask uncle colin

Dear Uncle Colin, I work in a call centre, which is run by the numbers. Every employee has to stay above a certain conversion rate, calculated as the number of successful deals resulting from their calls, divided by the number of times they have a call that doesn't go to

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Posted in ninja maths

The Mathematical Ninja glanced at the Rubik Cube and paused. "And $45^3$ is..." A reach for the calculator. A flurry of colour. "Ow!" "91,125," said the Mathematical Ninja, catching the cube on the rebound and swizzling it solved. "Only needed 12 that time." The student sighed. "Go on, then. I

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Posted in ask uncle colin, logarithms, powers

Dear Uncle Colin, I've been asked to find $2^{64}$ without a calculator, to four significant figures. How would you go about this? -- Large Exponent, Horrific Multiplication, Extremely Repetitive Hi, LEHMER! To get a rough answer, I'd usually start with the rule of thumb that $2^{10} \approx 10^3$. I'd conclude

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Posted in podcasts

In the October episode of Wrong, But Useful, @icecolbeveridge and @reflectivemaths have their habitual chat. Dave insults mechanics, then gets stroppy about Colin insulting stats The number of the podcast is 16, 40 and 64, because one number isn't enough for Dave Dave visits a fete and gets ripped off

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Posted in ask uncle colin, matrices

Dear Uncle Colin, I've got a matrix, and I'm not afraid to use it. It's $\begin{pmatrix} 3 & -5 \\ -4 & 2\end{pmatrix}$ Apparently, it has invariant lines. Those, I'm afraid of. How do I find them? -- Terrors About Rank, Safely Knowing Inverses Hi, TARSKI! An invariant line of

Read More →Via @DrTrapezio, an interesting question: Year 13 curve sketching challenge: y = | | | |x| - 1| - 1| - 1| — Luciano Rila (@DrTrapezio) July 14, 2016 Where do you even start with that mess? The answer to that, my friend, is you start in the middle and

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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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