Monthly Archives: July 2013

Cipher 38: 60 percent wordsearch

Update: In my blithering ineptitude, I accidentally missed the bottom row off of the cipher. It has now been amended, and should be a 20 × 20 grid: The backdrop is a photograph of the Dumbbell Nebula, which I captured over a year ago by … Continue reading

Further news

As usual, I’ll start this post by mentioning the current state of the bounded gaps between primes project. The current values are , with an unconfirmed result giving a value of H below 5000. It’s surprising how far these sieve methods … Continue reading

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Converting problems into elliptic curves

Several geometric problems and Diophantine equations can be converted into the task of finding rational points on elliptic curves. The canonical example is to determine for which rational numbers n can a right-angled triangle with rational side lengths have an area of … Continue reading

Cipher 37: Honeycomb II

As 37 is a centred hexagonal number, I decided to opt for a vaguely hexagonal arrangement: As usual, there is a password-protected solvers’ area.

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Mathematical Ashes

The competition known as the Mathematical Ashes was created by analogy with the better-known cricketing Ashes, and is an annual competition between Britain and Australia. At the moment, Britain is in the lead, with Australia attempting to reduce the gap. … Continue reading

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Von Neumann universe

The von Neumann universe V is the hierarchy of all set-theoretic sets. It is itself too large to be a set, and therefore is considered to be a proper class. There’s a very simple systematic construction of the von Neumann universe, … Continue reading

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Cipher 36: Concube cum cerebro

Despite currently suffering from hay fever, I was able to combine the following attributes into a cipher: The title is in alliterative Latin. The index of the cipher (36) is a perfect square, as is the length of the cipher … Continue reading

Generalised TFAE

The abbreviation TFAE (the following are equivalent) is often used in the statement of various theorems. Of course, a completely synonymous phrase would be ‘any one of these implies the other n − 1′. This then admits a natural generalisation … Continue reading

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PSL(2,Z)

A particularly important function is Klein’s j-function. It is defined on the upper half-plane of the complex numbers, and is incredibly symmetrical. For example, it is periodic, and thus invariant under translations by integers: It is also invariant under a larger … Continue reading

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Cipher 35: Adjacency mania

You may find this one easier if you’ve attempted Cipher 6.

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