Beauty in Mathematics

Sometimes when "doing" mathematics you end up with something that succinctly captures what you mean and presents it in a rather beautiful way. Now while beauty in mathematics has many examples - in particular Euler's Identity and in my opinion the sub-object classifier from category theory (it even has a facebook page) - formal specification is not really one area where this has been seen.

Here's a quick diagram from a paper I've been collaborating on with the Visual Modelling Group in Brighton, I personally think that this very succinctly states the relationship between information entropy and various classifications - at least in the framework we're using...

[0,1] is the 'set' of Reals and the precise definition of infoMeasure not strictly specified but the capturing of the mapping between various IP addresses and their geolocation mapping to various levels of detail of accuracy, and from there to a measurement in terms of entropy is still rather elegant.

Returning back to Euler's Identity...funny how Euler's work has an inherent beauty in it, especially when you consider Euler's Identity was considered the most beautiful mathematical expression and Eulerian circles the basis of the diagrammatic notation used above.