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# E (mathematical constant)

The number is an important mathematical constant that is the base of the natural logarithm. [1]

102 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 scientist, Continued fraction, Cyberculture, Daniel Shanks, De Moivre's formula, Decimal, Derangement, Derivative, Desktop computer, Donald Knuth, Encyclopedic Dictionary of Mathematics, ENIAC, Euler's formula, Euler's identity, Euler–Mascheroni constant, Expected value, Exponential function, Factorial, Gaussian integral, GNU Free Documentation License, Google, Google Labs, Gottfried Wilhelm Leibniz, Gresham College, Imaginary unit, Infinite product, Inflection point, Initial public offering, Integer, Integral, Inverse function, Irrational number, Jacob Bernoulli, John Napier, John von Neumann, ... Expand index (52 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 (styled as apple.

## Asymptotic analysis

In mathematical analysis, asymptotic analysis is a method of describing limiting behavior.

## Austin, Texas

Austin is the capital of the US state of Texas and the seat of Travis County.

## 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 yes/no experiments, each of which yields success with probability p. A success/failure experiment is also called a Bernoulli experiment or Bernoulli trial; when n.

## Binomial theorem

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

## Calculus

Calculus is the mathematical study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

## Cambridge, Massachusetts

Cambridge is a city in Middlesex County, Massachusetts, United States, in the Boston metropolitan area, situated directly north of the city of Boston proper, across the Charles River.

## Charles Hermite

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

## Christiaan Huygens

Christiaan Huygens, FRS (Hugenius) (14 April 1629 – 8 July 1695) was a prominent Dutch mathematician and scientist.

## 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 the imaginary unit, that satisfies the equation.

## Compound interest

Compound interest is interest added to the principal of a deposit or loan so that the added interest also earns interest from then on.

## Computer scientist

A computer scientist is a scientist who has acquired 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.

## Cyberculture

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

## 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) x and integer n it holds that where i is the imaginary unit (i2.

## Decimal

The decimal numeral system (also called base 10 or occasionally denary) has ten as its base.

## 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 a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable).

## Desktop computer

A desktop computer is a personal computer in a form intended for regular use at a single location desk/table due to its size and power requirements, as opposed to a laptop whose rechargeable battery and compact dimensions allow it to be regularly carried and used in different locations.

## Donald Knuth

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

## Encyclopedic Dictionary of Mathematics

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

## ENIAC

ENIAC (or; Electronic Numerical Integrator And Computer) was the first electronic general-purpose computer.

## 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 (\gamma).

## Expected value

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

## Exponential function

In mathematics, an exponential function is a function of the form The input variable x occurs as an exponent – hence the name.

## 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 Inc. is an American multinational technology company specializing in Internet-related services and products.

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

## Gottfried Wilhelm Leibniz

Gottfried Wilhelm von Leibniz (also Godefroi Guillaume Leibnitz,; or; July 1, 1646 – November 14, 1716) was a German polymath and philosopher, and to this day he 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 term imaginary unit or unit imaginary number refers to a solution to the equation.

## Infinite product

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

## Inflection point

In differential calculus, an inflection point, point of inflection, flex, or inflection (inflexion) is a point on a curve at which 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 stock in a company usually are sold to institutional investors that in turn, sell to the general public, on a securities exchange, for the first time.

## 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

The integral is an important concept in mathematics.

## Inverse function

In mathematics, an inverse function is a function that "reverses" another function.

## Irrational number

In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers.

## 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.

## John von Neumann

John von Neumann (Hungarian: Neumann János,; December 28, 1903 – February 8, 1957) was a Hungarian-American pure and applied mathematician, physicist, inventor, polymath, and polyglot.

## 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 (17071783) was a pioneering Swiss mathematician and physicist.

## 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 sin(1/n) 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 an irrational 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 operation to exponentiation.

## Mathematical constant

A mathematical constant is a special number, usually a real 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 plural 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 vector fonts.

## Natural logarithm

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

## Normal distribution

In probability theory, the normal (or Gaussian) distribution is a very common continuous probability distribution.

## Normal number

In mathematics, a normal number is a real number whose infinite sequence of digits in every 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), published by the Oxford University Press, is a descriptive (as opposed to prescriptive) dictionary of the English language.

## Pi

The number is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159.

## 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 (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

## 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, c is a constant, and x varies around c (for this reason one sometimes speaks of the series as being centered at c).

## 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 likeliness 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 that describes the relative likelihood for this random variable to take on a given value.

## Probability theory

Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena.

## 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 that represents a quantity along a continuous 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 coastal seaport city and the seat of King County.

## Series (mathematics)

A series is, informally speaking, the sum of the terms of a sequence.

## Silicon Valley

Silicon Valley is a nickname for the southern portion of the San Francisco Bay Area, which is located in the part of the U.S. state of California known as Northern California.

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

## Steiner's problem

Steiner's problem is the problem of finding the maximum of the function | url.

## Steve Wozniak

Stephen (or Stephan) Gary "Steve" Wozniak (born August 11, 1950), known as "Woz", is an American pioneer of the personal computer revolution of the 1970s (along with Apple Computer co-founder, Steve Jobs).

## Stirling's approximation

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

## Switzerland

Switzerland (Schweiz;Swiss Standard German spelling and pronunciation. The Swiss German name is sometimes spelled as Schwyz or Schwiiz. Schwyz is also the standard German (and international) name of one of the Swiss cantons. Suisse; Svizzera; Svizra or),The latter is the common Sursilvan pronunciation.

## 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 hyperoperator after exponentiation, and is defined as iterated exponentiation.

## TeX

TeX ((with the final consonant sounding like Ancient Greek's or English's) but often pronounced in English) is a typesetting system designed and mostly written by Donald Knuth and released in 1978.

## 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.

## 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 non-zero polynomial equation with rational coefficients.

## Trigonometric functions

In mathematics, the trigonometric functions (also called the circular 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, US dollar or American dollar) is the official currency of the United States and its overseas territories.

## William Oughtred

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

## William Shanks

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

## Wolfram Research

Wolfram Research is a private company that makes computation software.

## 0 (number)

0 (zero; BrE: or AmE) is both a number and the numerical digit used to represent that number in numerals.

## 1 (number)

1 (one; or, also called "unit", "unity", and "(multiplicative) identity", is a number, a numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of "unit length" is a line segment of length 1.

## References

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