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 A curious construction of the Mathieu group M11  Complex Projective 4Space on Stella octangula
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Monthly Archives: January 2013
Cipher 14: Remorse
The previous cipher seems to remain unsolved, even though it is indeed solvable. It was originally created by a hermit living in the Adirondack mountains, and was first deciphered by Dave Greene. He subsequently wrote a message in the cipher and passed it … Continue reading
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Visualising complex functions
Tim Large suggested to me a new idea of how to render meromorphic functions on the complex plane. Basically, we draw the surface of the Earth on the Riemann sphere (the codomain of the function), and colour each point on the complex plane … Continue reading
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Ordinal music
The most popular music video of last year is, arguably, Gangnam Style by the famous Korean artist, Ψ. One of the noteworthy features is the presence of ‘accumulation points’ in the music; these occur at 1:07 and 2:29 in the … Continue reading
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Origami
Firstly, I’ll take this opportunity to wish James Cranch a marvellous 30th birthday. This post was inspired by the conception of a new ‘origami society’ at Trinity. Having never tried it before, it took me a while to decipher the instructions … Continue reading
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Cipher 13: Intercardinal
As rasterised images invariably lose quality, this particular cipher is in the form of a PDF document. Click on the link to Cipher XIII to open it.
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CayleyBacharach applications
The CayleyBacharach theorem in projective geometry states that if two cubics share nine points (in sufficiently general position) and a third cubic passes through eight of those points, then it also passes through the ninth. Here, ‘sufficiently general position’ means … Continue reading
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Nontrivial mutual friends
Suppose we have a set of n people, and we want to encapsulate a particular relation which holds between them. For instance, the people who have featured on the cipher solvers page can be represented by a directed acyclic graph. … Continue reading
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Assorted stuff
This post contains miscellaneous topics which don’t deserve individual articles, but are still worth mentioning nonetheless. Stereographic map projections When you look at a map of the world, the most common projection is the Mercator projection. This is a conformal … Continue reading
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Projective Cranch geometry
The Encyclopedia of Triangle Centres contains a collection of over 5000 different points in the plane of a triangle, represented by the letter X followed by an identifier. The wellknown triangle centres include the circumcentre (X3), centroid (X2), orthocentre (X4) and incentre … Continue reading
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Cipher 12: Knot homophonic
This week’s cipher is a (noninvertible!) matrix of knots, which you can view by clicking on the image below: When mathematicians originally classified knots, they made the mistake of believing that two knots (10_161 and 10_162 in the original table) were different … Continue reading
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