Following that business with roots and mixed numbers, I wondered whether there were any other aesthetically pleasing identities to be found. After a fair amount of scribbling, I eventually arrived at the following equation:

As you can see, it is a shambling mish-mash of floor and ceiling functions, factorials, the imaginary unit and the modulus function for complex numbers. However, it also has a very beautiful property, which you may already have identified.

Here is a quick video to explain:

Thomas Oléron Evans, 2015

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