# Browsing category geometry

## A MathsJam Masterclass

At the East Dorset MathsJam Christmas party, @jussumchick (Jo Sibley in real life) posed the following question: There are two ways to draw a 16-gon with rotational symmetry of order 8 inside a unit circle, as shown. What's the ratio of their areas? Typically, I look at this sort of

## How I approximated $\pi$ for “Pi Day”

There was a post here, but it's not here any more! Instead, it's over at the Aperiodical, as part of their $\pi$ Day approximation challenge.

## Equation of a circle: the Mathematical Ninja

"Four points," said the student. "On a circle." The Mathematical Ninja nodded, impatiently. "$A(-5,5)$, $B(1,5)$, $C(-3,3)$ and $D(3,3)$," he read from the book, for the third time. A slight crack of a smile. It may have been a snarl. You can never tell with the Mathematical Ninja. "I'm terribly sorry,

## Why you can’t get unlimited chocolate (at least like this)

December! That means it's time for CHOCOLATE! My dear friend Essbee showed me this: Free chocolate ahoy (and white chocolate, my favourite)! But surely there’s got to be a catch? Of course there’s a catch. You can’t just rearrange an area to end up with a bigger area - moving

In a class recently, I came across a circle theorem problem I’m certain I’ve seen before, but that I didn’t know off the top of my head how to solve. Here it is; have a go at it if you’d like to. ￼ The examiners’ expectation was clearly that the

## Euclid the Game: level 20

Note: since I wrote this post, level 20 has moved to level 23. It may move again in the future, I suppose. Rather than keep updating, it's the one with the tangent to two circles. I LOVE Euclid, the game - it's a brilliant, interactive way to get students (and

## A proof of the sine rule

Here's a nice use of circle theorems: ever wondered why the sine rule works?

## The semicircle puzzle

In a recent episode of Wrong, But Useful, I asked: A square is inscribed within a circle of radius $r$. A second square is inscribed within a semicircle of the same radius. What is the ratio of the areas of the squares? It's easy enough to find the side length

## A riposte to the Mathematical Ninja!

@srcav wasn't going to take that argument lying down! The Ninja looked smug. He thought that was it, game over. I thought it had been a sneaky trick he’d pulled with the Ninja Bread, but I couldn’t change it now. I finally pulled my mouth apart and took a big

## Two mysteries cleared up in one

Since the dawn of time, two mysteries have plagued mathematicians: a) How do you find a centre of a 90º rotation? and b) What's the 45º set square for? Imagine my surprise when I discovered that each is the answer to the other! Some facts about the centre of rotation