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How is the natural constant e calculated in mathematics?
Vortex or spiral is a very common form of natural things, such as: a wisp of smoke curling up, ripples swaying gently on the blue lake, several snails slowly climbing the fence and countless stars dancing in the quiet night sky ... The aesthetic significance of spiral, especially logarithmic spiral, can be expressed in exponential form: φkρ=αe, where α and k are constants, φ is the polar angle and ρ is the polar diameter. For the convenience of discussion, we define the form of e or by e as "natural law". Therefore, the core of "natural law" is e.e. As a mathematical constant, it is the basis of natural logarithmic function. Sometimes called Euler number, named after the Swiss mathematician Euler; There is also a relatively rare name, Napier constant, to commemorate the Scottish mathematician John? Napier introduced logarithm. It is one of the most important constants in mathematics, just like pi and imaginary units I and E. Its numerical value is about (decimal point 100): e ≈ 2.7182818284 59045 23536 02874 71352 66249 77572 47093 6995 95749 66966. +0382178 52516 64274 first mentioned the constant e, which is a table in the appendix of John Napier's logarithmic work published in 16 18. But it didn't record this constant, only a list of natural logarithms calculated from it, which is generally believed to be made by William Oughtred. It was Jacob Bernoulli who first thought that E was a constant. The first known use of the constant e was Leibniz's communication with Huygens at 1690 and 169 1, which was denoted by B. 1727. Euler began to express this constant with e; E was first used in publications, and it was Euler Mechanics in 1736. Although some researchers later used the letter C, E was widely used and finally became the standard. The reason why E is used is really unknown, but it may be because E is the first letter of the word "index". Another view is that A, B, C and D have other common usages, and E is the first available letter. However, it is unlikely that Euler chose this letter because it is the initials of his own name, because he is a very modest person and always properly affirms the work of others. Many growth or decay processes can be simulated by exponential function. The important thing about exponential function is that it is the only function whose derivative is equal to (multiplied by a constant). E is irrational number and transcendental number (see Lindemann-Weierstrass theorem).