Where Circles are Square

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 … Continue reading Where Circles are Square →

The Root of Infinity: It’s Surreal!

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. Part 1: Brunswick Schnitzel The number system has been built up … Continue reading The Root of Infinity: It’s Surreal! →

Where in the World?

Here's a conundrum: You buy a watch in Anchorage, Alaska (61°N). It keeps excellent time. Then you move to Singapore, on the Equator. Does the watch go fast or slow? For the answer to this puzzle, read on. The Global Positioning System In the Irish Times column this week ( TM009 ), we look at … Continue reading Where in the World? →

Shackleton’s spectacular boat-trip

A little mathematics goes a long, long way; in the adventure recounted below, elementary geometry brought an intrepid band of six men 800 sea miles across the treacherous Southern Ocean, and led to the saving of 28 lives. Endurance For eight months, Ernest Shackleton's expedition ship Endurance was carried along, ice-bound, until it was finally … Continue reading Shackleton’s spectacular boat-trip →

A Mersennery Quest

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. The search for the … Continue reading A Mersennery Quest →