## Archive for January, 2013

### Chess Harmony

Long ago in the Gupta Empire, a great-but-greedy mathematician, Grababundel, presented to the Maharaja a new game that he had devised, called Chaturanga.

Thirty-two of the Maharaja’s subjects, sixteen dressed in white and sixteen in black, were assembled on a field divided into 64 squares. There were rajas and ranis, mahouts and magi, fortiers and foot-soldiers. Continue reading ‘Chess Harmony’

### The Lambert W-Function

In a recent post ( The Power Tower ) we described a function defined by iterated exponentiation:

$\displaystyle y(x) = {x^{x^{x^{.^{.^{.}}}}}}$

It would seem that when ${x>1}$ this must blow up. Surprisingly, it has finite values for a range of x>1. Continue reading ‘The Lambert W-Function’

### Topology Underground

That’s Maths in this week’s Irish Times ( TM013 ) is about the branch of mathematics called topology, and treats the map of the London Underground network as a topological map.

Topology is the area of mathematics dealing with basic properties of space, such as continuity and connectivity. It is a powerful unifying framework for mathematics. Topology is concerned with properties that remain unchanged under continuous deformations, such as stretching or bending but not cutting or gluing. Continue reading ‘Topology Underground’

### The Power Tower

Look at the function defined by an `infinite tower’ of exponents:

$\displaystyle y(x) = {x^{x^{x^{.^{.^{.}}}}}}$

It would seem that for x>1 this must blow up. But, amazingly, this is not so.

In fact, the function has finite values for positive x up to ${x=\exp(1/e)\approx 1.445}$. We call this function the power tower function. Continue reading ‘The Power Tower’

### Archimedes uncovered

The That’s Maths column in this week’s Irish Times ( TM012 ) describes the analysis of the ancient codex known as the Archimedes Palimpsest.

Archimedes of Syracuse

Archimedes (Ἀρχιμήδης, 287-212 BC) was a brilliant physicist, engineer and astronomer, and the greatest mathematician of antiquity. He is famed for founding hydrostatics, for formulating the law of the lever, for designing the helical pump that bears his name, for devising engines of war, and for much more. Continue reading ‘Archimedes uncovered’