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
Tags: Education, Geometry
Tags: 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.
Tags: 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) = 2n−1. They are called Mersenne primes. The Great Internet Mersenne Prime Search (GIMPS) is aimed at finding ever more prime numbers of this form. Continue reading ‘A Mersennery Quest’