Imagine a world where circles are square and π is equal to 4. Strange as it seems, we live in such a world: urban geometry is determined by the pattern of streets in a typical city grid and distance “as the crow flies” is not the distance that we have to travel from place to place. Continue reading ‘Where Circles are Square’

## Archive for November, 2012

### The Root of Infinity: It’s Surreal!

Published November 22, 2012 Occasional 1 CommentTags: Analysis, Number Theory

Can we make any sense of quantities like “the square root of infinity”? Using the framework of *surreal numbers*, we can.

- In Part 1, we develop the background for constructing the surreals.
- In Part 2, the surreals are assembled and their amazing properties described.

### A Mersennery Quest

Published November 1, 2012 Irish Times Leave a CommentTags: History, Number Theory, Primes

**The theme of That’s Maths (TM008) this week is prime numbers. Almost all the largest primes found in recent years are of a particular form **

*M*(

*n*)

*=*2

^{n}

*−*1

**. They are called Mersenne primes. The**Continue reading ‘A Mersennery Quest’

*Great Internet Mersenne Prime Search*(GIMPS) is aimed at finding ever more prime numbers of this form.