Leonhard Euler is regarded as one of the very greatest and most productive mathematicians of all time, despite dying over 2 centuries ago. Many believe his so-called “Euler’s Identity” to be the “most beautiful” or simply “greatest” mathematical formula of all time:
e^πi + 1 = 0
It combines 5 of the most basic, yet diverse (...and seemingly unrelated) elements within the field of math: the numbers 0 and 1, the value pi (3.141....), the value e (2.718....), and the basic imaginary number i (square root of -1), into a single simple true equation (the proof of which is beyond this blog, but easily findable on the Web).
Paul Nahin has written a recent book devoted to explication of this wonderful formula:
"Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills"
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