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Monthly Archives: June 2013
Competitions
There are several items of news worth mentioning. Firstly, I have been informed that the current status of the ‘bounded gaps between primes’ effort has now reached H = 6966, which is impressively low for these sieve methods. According to … Continue reading
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Partition numbers
The partition numbers (sequence A000041) count the number of distinct ways to partition n identical objects. For example, p(5) = 7, as there are seven distinct ways to partition 5 objects: This visualisation, where partitions are graphs whose connected components are … Continue reading
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Cipher 33: Puzzling II
I’ve based this particular cipher on a sliding block puzzle, the initial and final positions of which are displayed below: Here is the ciphertext: 145, 8, 21, 85, 24, 80, 130, 97, 136, 79, 91, 61, 199, 93, 19, 30, … Continue reading
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Assorted news
Firstly, the bounded gaps between primes project has made a considerable amount of progress since the value of H = 285278. The latest result has the following parameters: Tables of admissible ktuples had already been precomputed, so Terence Tao was … Continue reading
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Iterated Aut revisited
In an earlier post, I briefly mentioned the idea of repeatedly iterating the Aut operator (a function which takes an abstract group as its input and outputs the automorphism group) and observing the behaviour. There have been papers on the transfinite version … Continue reading
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Cipher 32: Untitled
This was not the cipher I originally intended to make, but rather a compromise due to time constraints. Also, my complete lack of imagination is manifested in the fact that this cipher lacks a title. The only elegant property is that the … Continue reading
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How to score 1729 in the IA Tripos
Part IA of the Mathematical Tripos is marked in a rather interesting way. A naïve computation of the maximum score is 1120, although it is (in principle) possible to achieve absolutely any score (it need not even be a real … Continue reading
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Quasifractals
One of the more familiar examples of fractal curves is the Koch snowflake. It is a closed curve of infinite length and Hausdorff dimension log(4)/log(3), homeomorphic to the unit circle. It bounds a region which, when combined in two different sizes, … Continue reading
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Plateau
Given two identical circles lying in parallel planes with a common axis of symmetry, what is the minimal surface that connects them? Initially, one might suppose that it is a cylinder (blue in the diagram below). However, we can quickly … Continue reading
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Cipher 31: Polyphasic
Firstly, I’ve been assigned the task of advertising the final episode of Magpie and Stump, which takes place at 21:30 in the Winstanley Lecture Theatre of Trinity College this Thursday (13th June 2013). It will be absolutely epic, and even … Continue reading
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