Have been working with my student on the complex plane and Euler's invention of complex exponentiation. I remember having offered a fairly lame disquisition on the nature of Euler's e on this blog at some time in the past, and have had considerable opportunity to revisit my thoughts during the past year of teaching the material. There are a couple of numbers that are considered 'transcendental', two of them are 'e' and 'pi' and Mr. Euler, of the 10-Franc note (unless I am mistaken) connected the two of them in the majesty of his mind in what is known as Euler's formula (one of many)
e^(pi*i) +1 = 0.
Which may be the most elegant masterpiece of all of human history. I really like it.
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