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Recent Comments
- NooneAtAll on Graph minors
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Author Archives: apgoucher
∂ eclipse
There was a solar eclipse today. Certain regions (including the Faroe Islands, familiar to anyone who has listened to the Shipping Forecast) landed in the umbra, experiencing a total eclipse. I was slightly less fortunate, landing in the penumbra (thereby … Continue reading
Posted in Uncategorized
2 Comments
Proto-Penrose tilings
A while ago, Roger Penrose famously filed a lawsuit against Kimberly Clark when his wife discovered that a roll of quilted lavatory paper was adorned with his aperiodic tiling. Although the tiling occurs naturally in quasicrystals, Penrose was probably the … Continue reading
Posted in Uncategorized
2 Comments
Oligomath 2: When are polylogarithms integers?
Consider the following series, where k and r are positive integers (and r is strictly greater than 1). Here Li_-k is a polylogarithm. We shall pose the following question: For what values of k and r is Q(r, k) an integer? It … Continue reading
Posted in Oligomath
5 Comments
Oligomath 1: Deletion and duplication
Collaborative mathematics tends to be extremely fruitful. This is epitomised by the recent ‘polymath’ projects, culminating in a nice proof of density Hales-Jewett along with the frighteningly impressive results on bounded gaps between primes. On a much smaller scale, several … Continue reading
Posted in Oligomath
4 Comments
Holyhedron update
A while ago, I mentioned the concept of holyhedra: polyhedra, all of whose faces are multiply-connected. The first known example had 78 585 627 faces, and was later superseded by a highly symmetric example with as few as 492 faces. … Continue reading
Posted in Uncategorized
9 Comments
Ménage primes
The Online Encyclopedia of Integer Sequences has recently celebrated its fiftieth anniversary, amassed over 250 000 sequences of varying importance, and heralded the 75th birthday of its creator Neil Sloane. It is somewhat surprising, therefore, that no-one appears to have … Continue reading
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6 Comments
Random circular mazes
In 1995, William Jockush, Peter Shor and James Propp published the statement and proof of the celebrated Arctic Circle Theorem. This roughly states that if you choose a random domino tiling of an Aztec diamond (a particular family of polyominoes), … Continue reading
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1 Comment
Cipher 71: Monoalphabetic II
As promised, the fourth season of cp4space ciphers has now commenced. Here’s a monoalphabetic substitution cipher with a nine-letter plaintext containing a man’s name. The password for the solvers’ area is the person who killed that man, entirely in lowercase: F B’ … Continue reading
Posted in Ciphers
3 Comments
Tweetable architecture
Quite probably the most world-renowned architect of the 21st century, Zaha Hadid, has been recently commissioned to design a new fluid dynamics exhibition in the London Science Museum. It will certainly add much more depth than its current collection of … Continue reading
Posted in Activities
3 Comments
Tributes to cryptanalysts
Earlier on cp4space, I mentioned how there were a couple of planned tributes to Alan Turing and Bill Tutte. Subsequently, both of these projects have since been completed. Firstly, the premiere of A Man From The Future was performed by the … Continue reading
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