Monthly Archives: September 2013

Cipher 47: Plughole

At the moment, assuming everything has gone according to plan, I should currently be on a northward-bound train, returning from Kevin Buzzard’s talk at the Royal Society. As with some of the earlier ciphers, this is bipartite, consisting of both an image … Continue reading

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Lattice gases and conformal maps

Any fluid dynamicist would be able to tell you that fluids obey partial differential equations such as the Navier-Stokes equations. This macroscopic behaviour should, and indeed can, be derived from applying Newton’s laws of motion to the individual molecules in the … Continue reading

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The Whetstone of Witte

The first instance of the concept of a symbolic mathematical equation is usually attributed to Robert Recorde, a Welsh mathematician, in a 1557 book with the rather verbose title ‘The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the … Continue reading

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Since the conception of the European Girls’ Mathematical Olympiad (henceforth abbreviated to EGMO), the British Mathematical Olympiad Committee has run an annual national olympiad specifically for aspiring female mathematicians. The third edition of the Mathematical Olympiad for Girls (MOG) takes place … Continue reading

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Cipher 46: Hellenic Angler Leviathan

+39256408486145507991522778312122523892525408578736546 Sorry about the cryptic title and lack of hints.

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Rational approximations to Platonic solids

It is straightforward to position a cube such that its vertices are all integer coordinates. For instance, we could choose its eight vertices to be (±1, ±1, ±1). Similarly, the vertices of a regular octahedron can be positioned at cyclic permutations … Continue reading

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Desert Island Theorems

Suppose you were cast away on a desert island. You’re only allowed to take a maximum of eight known theorems with you, along with rudimentary results such as ZFC axioms together with ‘boring stuff’ such as mathematical induction over the naturals, commutativity … Continue reading

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W. T. Tutte

In the not-too-distant future, people are going to be celebrating the 100th birthday of Bill Tutte. He’s not quite as well-known as Alan Turing, which is a shame since they were both equally invaluable in the cryptanalysis at Bletchley Park. You … Continue reading

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Cipher 45: Sisyphean

Occasionally, some of my ciphers have the frustrating property that whilst easy to realise what to do, they can still be incredibly long-winded to solve. I can imagine that this is one such cipher: I apologise for the profusion of Petersen … Continue reading

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Perrin sequence

The Perrin sequence is defined by a recurrence relation, and is qualitatively similar to the Lucas sequence. The initial terms are and subsequent terms are defined by , and summarised in the following spiral of equilateral triangles: As you can … Continue reading

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