# June, 2019

## Ask Uncle Colin: A Cosine Proof

Dear Uncle Colin How would you prove that $\cos(2x) > 1 - 2x^2$ for $x > 0$? - Can’t Obviously See It, Need Explanation Hi, COSINE, and thanks for your message! I’d start by noting that as soon as $x > 1$, the right hand side is smaller than -1,

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## The Fundamental Theorem of Countdown

I grew up with Countdown as part of my diet. I had a crush on Carol Vorderman (before she went all advertisey and weird). I loved the numbers game, obviously – although I still have some slight resentment that Ian Scarrott was class champion rather than me. A few years

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## Ask Uncle Colin: A Modest Inheritance

Dear Uncle Colin, My six siblings and I have inherited a fortune of £$10^{10} + 10^{(10^2)} + \dots 10^{(10^{10})}$, to be divided evenly between us. However, we’re a very squabbly family, so we want to know how much money will be left over once it’s divided up. Can you help?

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## A Challenge to the Mathematical Ninja

“I beg your pardon?!” yelled the Mathematical Ninja. The terribly well-dressed gentleman stood his ground. “I said, sensei, I would work $0.8^{10}$ out differently.” A sarcastic laugh. “This, I have to see!” “Well, $8^{10} = 2^{30}$, which is about $10^{9}$.” “About.” “Obviously, we can do better with the binomial: $2^{10}$

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## Wrong, But Useful: Episode 68

In this month’s thrilling installment of Wrong, But Useful, we’re joined by @c_j_smith, who is Calvin Smith in real life. We discuss… Number of the Podcast: 5 Are Fish and Chip shop owners good at maths? Two maths puns and a maths joke Are there ‘popular’ books that ‘lead you

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## Ask Uncle Colin: Consecutiveness

Dear Uncle Colin, Can there be two or more consecutive irrational numbers? - Between A Number And Consecutive… Huh? Hi, BANACH, and thanks for your message! We… have a problem here. When you’re dealing with integers, consecutive is really neatly defined: every number has a single successor, a number that’s

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## Google’s Keypad

One of the many lovely things about Big MathsJam is that I’ve found My People - I’ve made several very dear friends there, introduced others to the circle, and get to stay in touch with other maths fans through the year. It’s golden. Adam Atkinson is one of those dear

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## Ask Uncle Colin: A Trigonometric Puzzle

Dear Uncle Colin, I’m given that $0 \le x \lt 180^o$, and that $\cos(x) + \sin(x) = \frac{1}{2}$. I have to find $p$ and $q$ such that $\tan(x) = -\frac{p + \sqrt{q}}{3}$. Where do I even start? - Some Identity Needing Evaluation Hi, SINE, and thanks for your message! There

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## The Dictionary of Mathematical Eponymy: The Fermat Cubic

So far in the Dictionary of Mathematical Eponymy, I’ve not picked anyone properly famous. I mean, if you’re a keen recreational mathematician, you’ll have heard of Collatz or Banach; a serious mathematician might know about Daubechies, and a chess enthusiast would conceivably have come across Elo. But everyone has heard

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##### Where do you teach?

I teach in my home in Abbotsbury Road, Weymouth.

It's a 15-minute walk from Weymouth station, and it's on bus routes 3, 8 and X53. On-road parking is available nearby.