# December, 2016

## Ask Uncle Colin: Find me a circle!

Dear Uncle Colin, I have two points and I want to construct a circle of a given radius that passes through them. Is it possible? -- Every Underspecified Circle Lives Its Dream Hi, EUCLID, and thanks for your message! There are three possible answers to this, depending on the size

## Some charitable suggestions

Some charitable suggestions Hello! I'm going to be a bit more personal than usual with this post; it's Boxing Day and in the spirit of goodwill to all, I wanted to highlight some of my favourite charities. As you know, the Flying Colours Maths blog is absolutely free of charge,

## Ask Uncle Colin: Why is it not 4?

Dear Uncle Colin, I have a binomial expansion of $(1+x)^\frac{1}{2}$ and need to approximate $\sqrt{5}$. Apparently you need to substitute in $x=\frac{1}{4}$, but I'd have thought $x=4$ was a more obvious choice. What gives? -- Roots Are Dangerous If Understood Sloppily Hi RADIUS, and thanks for your message! That does

## Some exam technique tips for the new GCSE

Reports are filtering in to Flying Colours Towers about the mock exams recently taken by year 11s. Words like 'bloodbath' and 'disaster' feature prominently (my students, I should add, have acquitted themselves well and are in line to be mentioned in dispatches for bravery.) There's a reason the new-style papers

## Ask Uncle Colin: How do I multiply big numbers together?

Dear Uncle Colin, How do you multiply big numbers like $2158 \times 1812$? I try to do it using the column method or the grid, but I always make mistakes. -- A Desperately Desired Error Reduction Hi, ADDER, and thanks for your message! I've been playing with something midway between

## Quickfire reviews

As I happened to be in London last week, I took an afternoon to visit the Science Museum and, especially, the Winton Gallery exhibit on Mathematics. Maths! In the Science Museum! What a treat! Or so I hoped. The Winton Gallery: Mathematics There's a bit in Surely You're Joking, Mr

## Wrong, But Useful: Episode 39

In this month's Christmassy episode of Wrong, But Useful, @reflectivemaths and I discuss: Number of the podcast: 9 Shout outs to: @aap03102 (Chris Smith) for his maths newsletter @mathistopheles (Thomas Oléron Evans) and @fryrsquared (Hannah Fry) for sending me a copy of their book @chalkdustmag for the lovely card @fryrsquared

## This is what you trained for!

(Based on something that actually happened!)

Dear Uncle Colin, My teacher suggested that if you factorise a quadratic and add the brackets, you get the derivative. I am now too frightened to sleep. -- Quadratic Understanding Is Not Easy Hi, QUINE, and thanks for your message! To take a simple example, \$x^2 + 5x + 6

## A nice bit of nrichment

My dear friend @ajk44 pointed me at a puzzle on the excellent Nrich site1, and I enjoyed it enough to share my solution. (If you don't want it spoiled, don't read beyond the blockquote.) Four jewellers had respectively 8 rubies, 10 sapphires, 100 pearls and 5 diamonds. Each gave one