# The Flying Colours Maths Blog: Latest posts

## Wrong, But Useful: Episode 57

Owing to a spotty connection, the sound quality is a bit patchy on this one. Apologies. In this month's installment, we are joined by Belinda Keir. We discuss: Belinda convenes the Sydney MathsJam and is on the committee for the Celebration of Mind What makes a mathematician? Why Belinda is

## $\cos(72º)$, revisited: a geometric method

Some months ago, I wrote about a method for finding $\cos(72º)$, or $\cos\br{\frac{2\pi}{5}}$ in proper units. Almost immediately, the good people of Twitter and Facebook - notably @ImMisterAl (Al) and @BuryMathsTutor (Mark)- suggested other ways of doing it. Let's start with Mark's method, which he dissects in his book GCSE

## Ask Uncle Colin: Something powerful

Dear Uncle Colin, I'm trying to solve $3^{2x+1} - 28\times 3^x + 9 =0$. I've split up the first term into $3 \times 3^{2x}$ but then I'm stuck! Any suggestions? Likely Overthinking Gettable Sum Hi, LOGS, and thanks for your message! You've made a really good start there. The piece

## Square wheels on a round(ish) floor

The ever-challenging Adam Atkinson, having noticed my attention to the "impossible" New Zealand exams, pointed me at a tricky question from an Italian exam which asked students to verify that, to give a smooth ride on a bike with square wheels (of side length 2), the height of the floor

## Ask Uncle Colin: Sketching in 3D

Dear Uncle Colin Do you have any tips for sketching three-dimensional vectors? Every time we have an A-level question, my teacher says "draw a diagram!" but I don't know how to draw in 3D. - Got A Useless Sketching Situation Hi, GAUSS, and thank you for your message! Three-dimensional vectors

## Back in 1940…

That @solvemymaths is an excellent source of puzzles and whathaveyou: Meanwhile, back in 1940 when everything was basically shit... pic.twitter.com/A5eKXOunFC — Ed Southall (@solvemymaths) October 7, 2017 How would you find $\sqrt[3]{\frac{1-x^2}{x}}$ when $x=0.962$, using log tables or otherwise? I would start by trying to make the numbers nicer: I

Dear Uncle Colin, I'm sitting my GCSE Maths starting tomorrow. What will the grade boundaries be? - First Exams Are Redoubtable Hi, FEAR, I'm writing this, believe it or not, in early February1. I'm not even sure this summer's GCSE papers have been written yet, but I am going to

## A Handshake Problem From the MathsJam Shout

One of the puzzles in the MathsJam Shout looked impossible, so obviously I sat down with Mr Miller and had a go at it. I don't have it in front of me, but it went something like: A couple hosts a party to which five other couples are invited. At

## Ask Uncle Colin: A Complex Roots Problem

Dear Uncle Colin, I had a question in an exam that gave a cubic, $f(x) = x^3 - 8x^2 + cx + d$, with roots $\alpha$, $\beta$ and $\gamma$. When plotted on an Argand diagram, the triangle formed by the three roots has area 8. Given that $\alpha=2$, find $c$

## Wrong, But Useful: Episode 56

In Episode 56 of Wrong, But Useful, we're joined by @zoelgriffiths (Zoe Griffiths), maths communicator from Think Maths. Zoe had her poem e, to thee, x in @chalkdustmagazine recently, and did a set about misleading statistics at @aeoud (An Evening Of Unnecessary Detail) Bad polls and fake stats, including this