Are you an EPFL student looking for a semester project?
Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.
Concept
E (mathematical constant)
Summary
The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of natural logarithms. It is the limit of (1 + 1/n)n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series
It is also the unique positive number a such that the graph of the function y = ax has a slope of 1 at x = 0.
The (natural) exponential function f(x) = ex is the unique function f that equals its own derivative and satisfies the equation f(0) = 1; hence one can also define e as f(1). The natural logarithm, or logarithm to base e, is the inverse function to the natural exponential function. The natural logarithm of a number k > 1 can be defined directly as the area under the curve y = 1/x between x = 1 and x = k, in which case e is the value of k for which this area equals 1 (see image). There are various other characterizations.
The number e is sometimes called Euler's number (not to be confused with Euler's constant )after the Swiss mathematician Leonhard Euleror Napier's constantafter John Napier. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest.
The number e is of great importance in mathematics, alongside 0, 1, pi, and i. All five appear in one formulation of Euler's identity and play important and recurring roles across mathematics. Like the constant pi, e is irrational (it cannot be represented as a ratio of integers) and transcendental (it is not a root of any non-zero polynomial with rational coefficients). To 50 decimal places, the value of e is:
The first references to the constant were published in 1618 in the table of an appendix of a work on logarithms by John Napier. However, this did not contain the constant itself, but simply a list of logarithms to the base . It is assumed that the table was written by William Oughtred.
The constant itself was introduced by Jacob Bernoulli in 1683, for solving the problem of continuous compounding of interest.
Official source
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.