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Recent Comments
 tomtom2357 on The inadequacy of SCLT
 apgoucher on The neural network of the Stockfish chess engine
 El número TREE(3) no es infinito, pero es tan grande que ni siquiera cabe en el universo  La Fragua on TREE(3) and impartial games
 El número TREE(3) no es infinito, pero es tan grande que ni siquiera cabe en el universo – Radio Región on TREE(3) and impartial games
 El número TREE(3) no es infinito, pero es tan grande que ni siquiera cabe en el universo – Radio Centro F.M. 97.1 Pcia. De Buenos Aires on TREE(3) and impartial games
Monthly Archives: September 2012
Hiatus interruptus
I shall be rather busy during the next couple of months, so there may be a noticeable drop in the frequency of posts on Complex Projective 4Space. Nevertheless, I shall endeavour to maintain a steady stream of interesting articles, assuming I … Continue reading
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Good fibrations
We’ll begin by considering Hamiltonian quaternions, a fourdimensional extension to the complex numbers. A particularly interesting bunch of quaternions is the multiplicative group of 120 ‘icosians’. These can be thought of as the vertices of a 600cell or, by duality, the … Continue reading
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Cipher 2: Labyrinth
The Labyrinth usually refers to a particular maze in Knossos on the Greek island of Crete, designed by Daedalus to contain the Minotaur: a ravenous bullhuman hybrid, which found human sacrifices particularly appetising. Theseus navigated these tortuous underground passageways by means of … Continue reading
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MODA: Inequalities
I imagine you’re all eagerly anticipating Cipher Tuesday, which is only a couple of days away now! Meanwhile, the sixth chapter of MODA, namely ‘Inequalities’, is available for download. Preface Combinatorics I (enumerative and geometrical combinatorics) Linear algebra Combinatorics II (graph theory) Polynomials Sequences Inequalities Projective geometry … Continue reading
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163
There is a reasonably popular card game entitled 24, where players attempt to derive 24 by applying basic arithmetic operations to a set of four positive integers. For example, the provided integers may be {3, 3, 8, 8}. A solution must … Continue reading
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Antikythera mechanism
Near the beginning of the 20th century, a shipwreck was discovered. It contained a horde of treasure en route from Greece to Rome, including a lifesize bronze head of a philosopher. The most valuable treasure, however, was a 2000yearold analogue … Continue reading
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MODA: Sequences and Polynomials
It’s reached this time of week again, so I’ve uploaded the fourth and fifth chapters of Mathematical Olympiad Dark Arts. Enjoy! Preface Combinatorics I (enumerative and geometrical combinatorics) Linear algebra Combinatorics II (graph theory) Polynomials Sequences Inequalities Projective geometry Complex numbers Triangle … Continue reading
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Lizard and Spock dice
Continuing the theme of magic squares, we begin with the unique simplest nontrivial magic square. It contains the integers {1, 2, …, 9}, one in each square, such that the rows, columns and diagonals all sum to 15. Remarkably, the converse is … Continue reading
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Linearbounded automata
If we provide a bogstandard computer with an infinite data store, it suddenly becomes a Turing machine: capable of answering any question answerable by any digital computer. Even quantum computers are no more powerful; they are merely faster. For example, a quantum … Continue reading
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Lunisolar calendars
Here’s the post I promised you a while ago. I wrote the first part of this in an email on Burns’ Night of 2011, and the main idea (which Alex Bellos termed the ‘Goucherian calendar’) was mentioned in the Guardian. … Continue reading
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