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# Square root of 2

The square root of 2, or the (1/2)th power of 2, written in mathematics as or, is the positive algebraic number that, when multiplied by itself, gives the number 2. 

91 relations: Algebraic number, American Mathematical Monthly, American Scientist, Aperture, Area, Aristotle, Arithmetic, Aspect ratio, Babylonia, Bailey–Borwein–Plouffe formula, Berlin, Binary number, Binomial transform, Brady Haran, Compass-and-straightedge construction, Congruence (geometry), Continued fraction, Coprime integers, Decimal, Double factorial, Egyptian fraction, Equal temperament, Errett Bishop, Euclid, Euclid's Elements, Euclidean algorithm, F-number, Fibonacci, Fraction (mathematics), Fundamental theorem of arithmetic, Gelfond–Schneider constant, Hexadecimal, Hippasus, History of India, Imaginary unit, Integer, Intellectica, Interpolation (manuscripts), Irrational number, Irreducible fraction, ISO 216, Johan Ludvig Heiberg (historian), John Horton Conway, Law of excluded middle, Mathematical induction, Methods of computing square roots, Monic polynomial, Multiplicative inverse, Natural number, Normal number, ... Expand index (41 more) »

## Algebraic number

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

## American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

## American Scientist

American Scientist (informally abbreviated AmSci) is an American bimonthly science and technology magazine published since 1913 by Sigma Xi, The Scientific Research Society.

## Aperture

In optics, an aperture is a hole or an opening through which light travels.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

## Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.

## Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

## Aspect ratio

The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions.

## Babylonia

Babylonia was an ancient Akkadian-speaking state and cultural area based in central-southern Mesopotamia (present-day Iraq).

## Bailey–Borwein–Plouffe formula

The Bailey–Borwein–Plouffe formula (BBP formula) is a spigot algorithm for computing the nth binary digit of the mathematical constant pi using base-16 representation.

## Berlin

Berlin is the capital and the largest city of Germany, as well as one of its 16 constituent states.

## Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

## Binomial transform

In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences.

## Brady Haran

Brady John Haran (born 18 June 1976) is an Australian-born British independent filmmaker and video journalist who is known for his educational videos and documentary films produced for BBC News and his YouTube channels, the most notable being Periodic Videos and Numberphile.

## Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

## Congruence (geometry)

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

## 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.

## Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

## 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.

## Double factorial

In mathematics, the double factorial or semifactorial of a number (denoted by) is the product of all the integers from 1 up to that have the same parity (odd or even) as.

## Egyptian fraction

An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.

## Equal temperament

An equal temperament is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio.

## Errett Bishop

Errett Albert Bishop (July 14, 1928 – April 14, 1983) was an American mathematician known for his work on analysis.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

## Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

## Euclidean algorithm

. EXAMPLES CAN BE FOUND BELOW, E.G., IN THE "Matrix method" SECTION.

## F-number

The f-number of an optical system (such as a camera lens) is the ratio of the system's focal length to the diameter of the entrance pupil.

## Fibonacci

Fibonacci (c. 1175 – c. 1250) was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".

## Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

## Fundamental theorem of arithmetic

In number theory, the fundamental theorem of arithmetic, also called the unique factorization theorem or the unique-prime-factorization theorem, states that every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.

## Gelfond–Schneider constant

The Gelfond–Schneider constant or Hilbert number is two to the power of the square root of two: which was proved to be a transcendental number by Rodion Kuzmin in 1930.

## Hexadecimal

In mathematics and computing, hexadecimal (also base, or hex) is a positional numeral system with a radix, or base, of 16.

## Hippasus

Hippasus of Metapontum (Ἵππασος ὁ Μεταποντῖνος, Híppasos; fl. 5th century BC), was a Pythagorean philosopher.

## History of India

The history of India includes the prehistoric settlements and societies in the Indian subcontinent; the advancement of civilisation from the Indus Valley Civilisation to the eventual blending of the Indo-Aryan culture to form the Vedic Civilisation; the rise of Hinduism, Jainism and Buddhism;Sanderson, Alexis (2009), "The Śaiva Age: The Rise and Dominance of Śaivism during the Early Medieval Period." In: Genesis and Development of Tantrism, edited by Shingo Einoo, Tokyo: Institute of Oriental Culture, University of Tokyo, 2009.

## Imaginary unit

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

## 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").

## Intellectica

Intellectica is a biannual peer-reviewed academic journal of cognitive psychology that was established in 1985 and covers research in a broad range of subjects such as perception, motricity, language, and reasoning.

## Interpolation (manuscripts)

An interpolation, in relation to literature and especially ancient manuscripts, is an entry or passage in a text that was not written by the original author.

## 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.

## Irreducible fraction

An irreducible fraction (or fraction in lowest terms or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and -1, when negative numbers are considered).

## ISO 216

ISO 216 specifies international standard (ISO) paper sizes used in most countries in the world today, although not in Canada, the United States, Mexico, or the Dominican Republic.

## Johan Ludvig Heiberg (historian)

Johan Ludvig Heiberg (27 November 1854 – 4 January 1928) was a Danish philologist and historian.

## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

## Law of excluded middle

In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true.

## Mathematical induction

Mathematical induction is a mathematical proof technique.

## Methods of computing square roots

In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a non-negative real number.

## Monic polynomial

In algebra, a monic polynomial is a single-variable polynomial (that is, a univariate polynomial) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x&minus;1, is a number which when multiplied by x yields the multiplicative identity, 1.

## Natural number

In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").

## 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.

## Orders of magnitude (numbers)

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities.

## Paper size

Many paper size standards conventions have existed at different times and in different countries.

## Pell number

In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2.

## Pi

The number is a mathematical constant.

## Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

## Prior Analytics

The Prior Analytics (Ἀναλυτικὰ Πρότερα; Analytica Priora) is Aristotle's work on deductive reasoning, which is known as his syllogistic.

## Proof by contradiction

In logic, proof by contradiction is a form of proof, and more specifically a form of indirect proof, that establishes the truth or validity of a proposition.

## Proof by infinite descent

In mathematics, a proof by infinite descent is a particular kind of proof by contradiction that relies on the least integer principle.

## Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

## Pythagoreanism

Pythagoreanism originated in the 6th century BC, based on the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics and mysticism.

## Q.E.D.

Q.E.D. (also written QED and QED) is an initialism of the Latin phrase quod erat demonstrandum meaning "what was to be demonstrated" or "what was to be shown." Some may also use a less direct translation instead: "thus it has been demonstrated." Traditionally, the phrase is placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been restated exactly, as the conclusion of the demonstration or completion of the proof.

## Quadratic irrational number

In mathematics, a quadratic irrational number (also known as a quadratic irrational, a quadratic irrationality or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the set of rational numbers.

## Quadrilateral

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners.

## Ratio

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.

## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

## Rational root theorem

In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational solutions of a polynomial equation with integer coefficients.

## Recursion

Recursion occurs when a thing is defined in terms of itself or of its type.

## Reductio ad absurdum

In logic, reductio ad absurdum ("reduction to absurdity"; also argumentum ad absurdum, "argument to absurdity") is a form of argument which attempts either to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion, or to prove one by showing that if it were not true, the result would be absurd or impossible.

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## Sexagesimal

Sexagesimal (base 60) is a numeral system with sixty as its base.

## Shulba Sutras

The Shulba Sutras or Śulbasūtras (Sanskrit: "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction.

## Silver ratio

In mathematics, two quantities are in the silver ratio (also silver mean or silver constant) if the ratio of the sum of the smaller and twice the larger of those quantities, to the larger quantity, is the same as the ratio of the larger one to the smaller one (see below).

## Solution of triangles

Solution of triangles (solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known.

## Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

## Square root of 3

The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3.

## Square root of 5

The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5.

## Stanley Tennenbaum

Stanley Tennenbaum (April 11, 1927 – May 4, 2005) was an American mathematician who contributed to the field of logic.

## 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.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

## Tritone

In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones.

## Unit square

In mathematics, a unit square is a square whose sides have length.

## Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

## University of Georgia

The University of Georgia, also referred to as UGA or simply Georgia, is an American public comprehensive research university.

## Viète's formula

In mathematics, Viète's formula is the following infinite product of nested radicals representing the mathematical constant pi: It is named after François Viète (1540–1603), who published it in 1593 in his work Variorum de rebus mathematicis responsorum, liber VIII.

## Wheel of the Year

The Wheel of the Year is an annual cycle of seasonal festivals, observed by many modern Pagans.

## Yasumasa Kanada

is a Japanese mathematician most known for his numerous world records over the past three decades for calculating digits of pi.

## YBC 7289

YBC 7289 is a Babylonian clay tablet in the Yale Babylonian Collection, notable for containing an accurate sexagesimal approximation to the square root of 2, the length of the diagonal of a unit square.

## 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).

## 2

2 (two) is a number, numeral, and glyph.

## References

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