Euler's formula [SEP] named after
Euler's formula
Euler's formula, named after Leonhard Euler, is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. Euler's formula states that for any real number :
where is the base of the natural logarithm, is the imaginary unit, and and are the trigonometric functions cosine and sine respectively, with the argument given in radians. This complex exponential function is sometimes denoted ("cosine plus i sine"). The formula is still valid
most famous formula in all mathematics". And Benjamin Peirce, a 19th-century American philosopher, mathematician, and professor at Harvard University, after proving Euler's identity during a lecture, stated that the identity "is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth".
A poll of readers conducted by "The Mathematical Intelligencer" in 1990 named Euler's identity as the "most beautiful