| In mathematical analysis, Euler's identity, named after Leonhard Euler, is the equation e^{i pi} =-1 where e -[link] is Euler's number, the base of the natural logarithm, i-[link] is the imaginary unit, one of the two complex numbers whose square is negative one (the other is -i,!), and pi-[link] is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is considered by many to be remarkable for its mathematical beauty. Three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants: * The number 0. * The number 1. * The number π, which is ubiquitous in trigonometry, geometry of Euclidean space, and mathematical analysis (π ≈ 3.14159). * The number e, the base of natural logarithms, which also occurs widely in mathematical analysis (e ≈ 2.71828). * The number i, imaginary unit of the complex numbers, which contain the roots of all nonconstant polynomials and lead to deeper insight into many operators, such as integration. |





























































































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Ayhan Tomak
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