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 … Continue reading Chess Harmony
Month: January 2013
The Lambert W-Function
Follow on twitter: @thatsmaths In a recent post ( The Power Tower ) we described a function defined by iterated exponentiation: $latex \displaystyle y(x) = {x^{x^{x^{.^{.^{.}}}}}} &fg=000000$ It would seem that when $latex {x>1}&fg=000000$ this must blow up. Surprisingly, it has finite values for a range of x>1. Below, we show that the power tower … 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 … Continue reading Topology Underground
The Power Tower
Look at the function defined by an `infinite tower' of exponents: $latex \displaystyle y(x) = {x^{x^{x^{.^{.^{.}}}}}} &fg=000000$ 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 $latex {x=\exp(1/e)\approx 1.445}&fg=000000$. We call this function the power tower … 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 … Continue reading Archimedes uncovered
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