# Browsing category core 2

## How to think about co-ordinate geometry (Part III: Circles, tangents and so on)

This is the third and final part of the how to think about co-ordinate geometry series. Due to a failure of calendar-reading, I appreciate this is going out a few days after the C1 and C2 exams, but hey-ho. If you're relying on this blog for your revision tips, you

## Would an infinite number of monkeys eventually write Shakespeare?

“If you had an infinite number of monkeys, there’d be no room for typewriters.” — Jason Arnopp Yes, an infinite number of monkeys would eventually — in fact, before very long at all — write Shakespeare. The problem, then, is finding which of the monkey-poo-smeared manuscripts is actually the whole

## Secrets of the Mathematical Ninja: Pascal’s Triangle

You've seen Pascal's triangle before: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 You get the number in each row by adding its two 'parents' - for instance, each 10 in the row that starts with 1

## What is a circle? (and how do you answer C2 questions about it?)

A conjecture both deep and profound Needs a proof that the circle is round. In a paper by Erdős Written in Kurdish A counter-example is found. One of my favourite questions to ask students is "what's a circle?" because I get to play "so that means this is a circle!"

## A tricky C2 question…

I was sent this by my friend and colleague TeaKay from Blogstronomy, and I've adapted the puzzle slightly to make the sums a little bit nicer. A curve has the equation $y = (x-2)^2 - n^2$. The area bounded by the co-ordinate axes and the curve in the first quadrant

## The smart way to do the binomial expansion (Part 1)

Ah, the binomial expansion. The scourge of my A-level: the sum that was always wider than the paper, and always had one more minus sign than I'd allowed for. A crazy, pointless exercise in arithmetic, if you ask me, only really useful for finding square roots in your head (of

## Why radians rock (and degrees don’t)

If I could wave a magic wand and overhaul just one thing to make the world a better place, I'd have a tough choice. Would I get rid of the QWERTY keyboard in favour of a more sensible layout? Would I make the English language fonetik? Would I take maths