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# E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics. 

111 relations: Antiderivative, Apple II, Asymptotic analysis, Austin, Texas, Base (exponentiation), Bernoulli trial, Binomial distribution, Binomial theorem, Calculus, Cambridge, Massachusetts, Charles Hermite, Christiaan Huygens, Christian Goldbach, Complex number, Compound interest, Computer hardware, Computer scientist, Continued fraction, Daniel Shanks, De Moivre's formula, Decimal, Derangement, Derivative, Desktop computer, Differential equation, Donald Knuth, Early Modern Switzerland, Encyclopedic Dictionary of Mathematics, ENIAC, Entropy (information theory), Euler's formula, Euler's identity, Euler–Mascheroni constant, Expected value, Exponential decay, Exponential function, Exponential growth, Factorial, Gaussian integral, GNU Free Documentation License, Google, Google Labs, Gottfried Wilhelm Leibniz, Gresham College, Imaginary unit, Infinite product, Infinity, Inflection point, Initial public offering, Integer, ... Expand index (61 more) »

## Antiderivative

In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.

## Apple II

The Apple II (stylized as Apple.

## Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

## Austin, Texas

Austin is the capital of the U.S. state of Texas and the seat of Travis County, with portions extending into Hays and Williamson counties.

## Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

## Bernoulli trial

In the theory of probability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted.

## Binomial distribution

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q.

## Binomial theorem

In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.

## Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

## Cambridge, Massachusetts

Cambridge is a city in Middlesex County, Massachusetts, and part of the Boston metropolitan area.

## Charles Hermite

Prof Charles Hermite FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.

## Christiaan Huygens

Christiaan Huygens (Hugenius; 14 April 1629 – 8 July 1695) was a Dutch physicist, mathematician, astronomer and inventor, who is widely regarded as one of the greatest scientists of all time and a major figure in the scientific revolution.

## Christian Goldbach

Christian Goldbach (March 18, 1690 &ndash; November 20, 1764) was a German mathematician who also studied law.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

## Compound interest

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.

## Computer hardware

Computer hardware includes the physical parts or components of a computer, such as the central processing unit, monitor, keyboard, computer data storage, graphic card, sound card and motherboard.

## Computer scientist

A computer scientist is a person who has acquired the knowledge of computer science, the study of the theoretical foundations of information and computation and their application.

## Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

## Daniel Shanks

Daniel Shanks (January 17, 1917 – September 6, 1996) was an American mathematician who worked primarily in numerical analysis and number theory.

## De Moivre's formula

In mathematics, de Moivre's formula (also known as de Moivre's theorem and de Moivre's identity), named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) and integer it holds that where is the imaginary unit.

## Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

## Derangement

In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position.

## Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

## Desktop computer

A desktop computer is a personal computer designed for regular use at a single location on or near a desk or table due to its size and power requirements.

## Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

## Donald Knuth

Donald Ervin Knuth (born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University.

## Early Modern Switzerland

The early modern history of the Old Swiss Confederacy (Eidgenossenschaft, also known as the "Swiss Republic" or Republica Helvetiorum) and its constituent Thirteen Cantons encompasses the time of the Thirty Years' War (1618&ndash;1648) until the French invasion of 1798.

## Encyclopedic Dictionary of Mathematics

The Encyclopedic Dictionary of Mathematics is a translation of the Japanese.

## ENIAC

ENIAC (Electronic Numerical Integrator and Computer) was amongst the earliest electronic general-purpose computers made.

## Entropy (information theory)

Information entropy is the average rate at which information is produced by a stochastic source of data.

## 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 identity

In mathematics, Euler's identity (also known as Euler's equation) is the equality where Euler's identity is named after the Swiss mathematician Leonhard Euler.

## Euler–Mascheroni constant

The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.

## Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

## Exponential decay

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.

## Exponential function

In mathematics, an exponential function is a function of the form in which the argument occurs as an exponent.

## Exponential growth

Exponential growth is exhibited when the rate of change—the change per instant or unit of time—of the value of a mathematical function is proportional to the function's current value, resulting in its value at any time being an exponential function of time, i.e., a function in which the time value is the exponent.

## Factorial

In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.

## Gaussian integral

The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function e−x2 over the entire real line.

The GNU Free Documentation License (GNU FDL or simply GFDL) is a copyleft license for free documentation, designed by the Free Software Foundation (FSF) for the GNU Project.

Google LLC is an American multinational technology company that specializes in Internet-related services and products, which include online advertising technologies, search engine, cloud computing, software, and hardware.

Google Labs was a page created by Google to demonstrate and test new projects.

## Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

## Gresham College

Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England.

## Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation.

## Infinite product

In mathematics, for a sequence of complex numbers a1, a2, a3,...

## Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

## Inflection point

In differential calculus, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.

## Initial public offering

Initial public offering (IPO) or stock market launch is a type of public offering in which shares of a company are sold to institutional investors and usually also retail (individual) investors; an IPO is underwritten by one or more investment banks, who also arrange for the shares to be listed on one or more stock exchanges.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

## Internet culture

Internet culture, or cyberculture, is the culture that has emerged, or is emerging, from the use of computer networks for communication, entertainment, and business.

## Inverse function

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function applied to an input gives a result of, then applying its inverse function to gives the result, and vice versa.

## Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

## ISO 80000-2

ISO 80000-2:2009 is a standard describing mathematical signs and symbols developed by the International Organization for Standardization (ISO), superseding ISO 31-11.

## Jacob Bernoulli

Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.

## John Napier

John Napier of Merchiston (1550 – 4 April 1617); also signed as Neper, Nepair; nicknamed Marvellous Merchiston) was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioannes Neper. John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University. Napier died from the effects of gout at home at Merchiston Castle and his remains were buried in the kirkyard of St Giles. Following the loss of the kirkyard there to build Parliament House, he was memorialised at St Cuthbert's at the west side of Edinburgh.

## John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

## John Wrench

John William Wrench, Jr. (October 13, 1911 – February 27, 2009) was an American mathematician who worked primarily in numerical analysis.

## Joseph Fourier

Jean-Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations.

## Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

## Limit of a function

Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.

## Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

## Lindemann–Weierstrass theorem

In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers.

## Liouville number

In number theory, a Liouville number is a real number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that A Liouville number can thus be approximated "quite closely" by a sequence of rational numbers.

## Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

## Mathematical constant

A mathematical constant is a special number that is "significantly interesting in some way".

## Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

## MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

## Maxima and minima

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).

## Mechanica

Mechanica (Mechanica sive motus scientia analytice exposita; 1736) is a two-volume work published by mathematician Leonhard Euler, which describes analytically the mathematics governing movement.

## Metafont

Metafont is a description language used to define raster fonts.

## Natural logarithm

The natural logarithm of a number is its logarithm to the base of the mathematical constant ''e'', where e is an irrational and transcendental number approximately equal to.

## Normal number

In mathematics, a normal number is a real number whose infinite sequence of digits in every positive integer base b is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b2 pairs of digits are equally likely with density b−2, all b3 triplets of digits equally likely with density b−3, etc.

## Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

## Pi

The number is a mathematical constant.

## Pierre Raymond de Montmort

Pierre Rémond de Montmort, a French mathematician, was born in Paris on 27 October 1678, and died there on 7 October 1719.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

## Prime Obsession

Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (2003) is a historical book on mathematics by John Derbyshire, detailing the history of the Riemann hypothesis, named for Bernhard Riemann, and some of its applications.

## Principal branch

In mathematics, a principal branch is a function which selects one branch ("slice") of a multi-valued function.

## Probability

Probability is the measure of the likelihood that an event will occur.

## Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

## Probability theory

Probability theory is the branch of mathematics concerned with probability.

## Proof that e is irrational

The number ''e'' was introduced by Jacob Bernoulli in 1683.

In mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Roger Cotes

Roger Cotes FRS (10 July 1682 – 5 June 1716) was an English mathematician, known for working closely with Isaac Newton by proofreading the second edition of his famous book, the Principia, before publication.

## Seattle

Seattle is a seaport city on the west coast of the United States.

## Secretary problem

The secretary problem is a famous problem that demonstrates a scenario involving the optimal stopping theory.

## Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

## Silicon Valley

Silicon Valley (abbreviated as SV) is a region in the southern San Francisco Bay Area of Northern California, referring to the Santa Clara Valley, which serves as the global center for high technology, venture capital, innovation, and social media.

## Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

## Steiner's calculus problem

Steiner's problem, asked and answered by, is the problem of finding the maximum of the function | url.

## Steve Wozniak

Stephen Gary Wozniak (born on August 11, 1950), often referred to by the nickname Woz, is an American inventor, electronics engineer, programmer, philanthropist, and technology entrepreneur who co-founded Apple Computer, Inc.

## Stirling's approximation

In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials.

## Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

## Tetration

In mathematics, tetration (or hyper-4) is the next hyperoperation after exponentiation, and is defined as iterated exponentiation.

## The Art of Computer Programming

The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.

## Time constant

In physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.

## Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.

## Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

## Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

## United States dollar

The United States dollar (sign: $; code: USD; also abbreviated US$ and referred to as the dollar, U.S. dollar, or American dollar) is the official currency of the United States and its insular territories per the United States Constitution since 1792.

## William Oughtred

William Oughtred (5 March 1574 – 30 June 1660) was an English mathematician and Anglican clergyman.

## William Shanks

William Shanks (25 January 1812 – June 1882) was a British amateur mathematician.

## Wolfram Research

Wolfram Research is a private company that creates computational technology.

## Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

## 0

0 (zero) is both a number and the numerical digit used to represent that number in numerals.

## 1

1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.

## References

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