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Recent Comments
Monthly Archives: September 2013
Leech lattice
I’ve been intending to write about the Leech lattice for a while now. I wanted to ensure that I could actually do it justice, and in particular make it strictly more comprehensive than the Wikipedia and Mathworld articles. The authoritative source on … Continue reading
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Category of scones
(This post is completely unrelated to the category of cones. Apologies if you were mistakenly directed here by a fuzzy search engine.) In May 2013, the category theorist Dr Eugenia Cheng (whom you may recognise from her quotations on the Imre Leader Appreciation Society) wrote a … Continue reading
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Cipher 44: Dostin
This is classically used as a rudimentary compression algorithm, although it also makes for a nice cipher challenge. 000011010110111 0100001111000111 1110 11000011100111101101001 001011101010100111 110100101 01001110100111110001010110001110111101111011010, 001001110101101001101010 11100111 1110 01100100000101001010011111101010 0000101100100, 0011001101011010010110 01011001100010101100011110010100000111 1111010000000010001010111 0011010110000110 01001110111111110110100111 110100101 001000111001011011111011000011110100 1111010010101100110000110 111111001100011001010111111001010000 11011010 … Continue reading
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Ten things you (possibly) didn’t know about the Petersen graph
Some mathematical objects are completely boring. Others have a few interesting properties. The Petersen graph, by comparison, has a plethora of quite remarkable features that, taken alone, would each qualify the graph as being interesting. I’ve mentioned this graph a few times … Continue reading
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Exotic continued fractions
Given a real number x, computing its continued fraction can reveal a lot of information. In the simplest case, the continued fraction terminates if and only if the number is rational. One particular example of this is the rational , … Continue reading
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Cipher 43: Palindrome
For this cipher, I have encoded the information in a list of real numbers. Ordinarily, these would be complex, but I managed to circumvent this. Unfortunately, the ciphertext is thus longer than it needs to be. Really, it’s twice as … Continue reading
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Pappian and Desarguesian planes
Breaking news: Patrick Stevens (whom you may recognise from the cp4space cipher-solving leaderboard) has published a collection of poems pertaining to Sylow’s theorems. Anyway, on the real projective plane, there are a couple of geometric theorems worth mentioning. The thing that’s interesting … Continue reading
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