What is eulers formulae
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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 x:
{\displaystyle e^{ix}=\cos x+i\sin x,} {\displaystyle e^{ix}=\cos x+i\sin x,}
where e is the base of the natural logarithm, i is the imaginary unit, and cos and sin are the trigonometric functions cosine and sine respectively, with the argument x given in radians. This complex exponential function is sometimes denoted cis x ("cosine plus i sine"). The formula is still valid if x is a complex number, and so some authors refer to the more general complex version as Euler's formula.[1]
Euler's formula is ubiquitous in mathematics, physics, and engineering. The physicist Richard Feynman called the equation "our jewel" and "the most remarkable formula in mathematics".[2]
When {\displaystyle x=\pi } {\displaystyle x=\pi }, Euler's formula evaluates to {\displaystyle e^{i\pi }+1=0} e^{i\pi }+1=0, which is known as Euler's identity.
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the geometrical formula V − E + F = 2, where V, E, and F are the numbers of vertices, edges, and faces of any simple convex polyhedron or of an equivalent topological graph.