Mathematical headaches? Problem solved!
Hi, I'm Colin, and I'm here to help you make sense of maths
Mathematical headaches? Problem solved!
Hi, I'm Colin, and I'm here to help you make sense of maths
It’s time for the @BigMathsJam Wrong, But Useful! @stecks (Katie Steckles): Brouwer’s Fixed Point Theorem: “they said it’s a theorem, so I’ve got to believe it.” Mentions @jamesgrime. @christianp (Christian Lawson-Perfect): ordering cards to generate a fractal sequence. @peterrowlett (Peter Rowlett): transforming numbers problems into graphs. Mentions @alexcorner and @wtgowers.
Read More →Dear Uncle Colin, I have to prove that, if $a > b \ge 2$, then $ab > a + b$. I can see it must be true, but I can’t prove it! Any ideas? Questioning Everything Done Hi, QED, and thanks for your message! There are several ways to go
Read More →One of the reasons I’m writing the Dictionary of Mathematical Eponymy is to introduce myself to new ideas, and to mathematicians I didn’t know about. To things I wish I knew more about. Elliptic curves are pretty high on that list. What is the Lutz-Nagell theorem? It’s sometimes - reasonably,
Read More →Dear Uncle Colin, I have to find the greatest common divisor of $x^4 - 5x^3 + 8x^2 - 10x + 12$ and $x^4 + x^2 - 2$. How do I go about that? - Extremely Unhappy, Clueless Learner In Distress Hi, EUCLID, and thanks for your message! Before we try
Read More →In a currently-recent (but by the time you read this, long in the past) Chalkdust1, @cshearer42 gave a puzzle that caught my eye. One of the things I love about Catriona’s puzzles is that you usually get two-for-the-price-of-one: there’s “getting the right answer”, which is not usually hard, and there’s
Read More →Dear Uncle Colin, I’m told that $f(x) = \frac{5x-7}{(x-1)(x-2)}, x\ne 1, x\ne 2$, and need to express it in partial fractions. My usual method would be to write it as $\frac{A}{x-1} + \frac{B}{x-2}$, multiply by $(x-1)(x-2)$ and substitute $x=1$ and $x=2$ to find $A$ and $B$ - but the definition
Read More →On Twitter, @RuedigerSimpson pointed me at an episode of My Favourite Theorem in which @FawnPNguyen mentioned a method for constructing $\sqrt{7}$: draw a circle of radius 4 construct a perpendicular to the radius at a distance of 3 from the centre the distance between the base of the perpendicular and
Read More →Dear Uncle Colin, I need to work out the limit of $\frac{2^{3x} - 1}{3^{2x}-1}$ as $x \to 0$, and I don’t have any ideas at all. Do you? - Fractions Rotten, Exponents Generally Excellent Hi, FREGE, and thanks for your message! There are a couple of ways to approach this:
Read More →This one came from user_1312 on reddit with a heading “This is a bit tricky… Enjoy!”. What else can we do but solve it? Let $m$ and $n$ be positive numbers such that $\frac{m}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{101}$. Prove that $m-n$ is a multiple
Read More →In this month's episode of Wrong, But Useful, we talk to @AJMagicMessage, who is Andrew Jeffrey in real life, and one of the driving forces behind Maths Week England, which in 2019 is November 11th to 15th. Apologies for a few issues with feedback in this episode. Dave takes full
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