Monthly Archives: May 2013

Cipher 29: Permutation

This particular ciphertext is 257 characters in length: I ih2 deetnnto nslaitmtm rtxoda r  .deeisixtu    olfiipfye mno i pa)otruuc ur e sisrsi ifaow  auosmsiaas ep loofheltpqbnpu( ttlph imlazafldens he-Teeit5elFmr ecrrurntpmfcth7dcseadtcpeant htlcocs eirhcaine  tr uhsriiirbeoiaao ,e  o  dn reopu enefa r … Continue reading

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FRACTRAN

Some of my favourite books were written by Douglas Adams. (Indeed, my forename was actually named after his surname, rather than my Biblical namesake or the Greek word for ‘indestructible’.) Although I personally prefer the Dirk Gently books, I have … Continue reading

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Things that shouldn’t work, but do

There are several mathematical heuristics (it’s difficult to call them proofs), which are non-rigorous in the best of cases and sometimes seemingly insane. For example, Euler’s ‘proof’ that the sum of the reciprocals of the primes diverges at an asymptotic … Continue reading

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Cipher 28: Irrationality II

This one is essentially a sequel to the fourth cp4space cipher. I imagine that solving this one should be strictly harder for the vast majority of people. JYTFZJOHU. UKJG FJGHGTU GXQN JIV CSIFKIZTUQX ED VTOVH AIG FVOVJOGFE GUBDBJPP PL QJ, FU QSQQWIT … Continue reading

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Words in summation convention

In Einstein summation convention, repeated indices are summed over. For example, . If a Kronecker delta has two different suffices, we can ‘contract’ them as follows: , whereas . Vishal Patil considered contracting English words in this manner. For example, … Continue reading

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Background Problem I

Sam Cappleman-Lynes noticed the seemingly remarkable fact that at least one of the interior angles of a triangle being equal to π/3 is equivalent to the linear relation between the semiperimeter, circumradius and inradius. He provided a clever synthetic solution, and I … Continue reading

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