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The most beautiful equation in mathematics is:

It is often attributed to Swiss Mathematician Leonhard Euler. Interestingly enough, this is nothing but a statement about rotation!
23 is a shorthand way of writing 2 × 2 × 2. But this is very very different from what means. Mathematicians use this trick over and over again. They overload notations. In fact is a shorthand way of writing an infinite series.
How can we connect infinite series with rotation? Basically, 1 is not 1! 1 is (1, 0). A point in fact. Then what is i? i is a shorthand for writing (0, 1). So when you add 1 + 2 π i , you are in fact ‘adding’ (1, 0) + 2 π (0, 1) = (1, 2 π ).
Food for thought
How do you add many many many points (in fact infinitely many) to get rotation?
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