Table of Contents
150 relations: Abraham de Moivre, Abu Bakr al-Hassar, Abu Kamil, Adolf Hurwitz, Adrien-Marie Legendre, Al-Mahani, Algebra, Algebraic independence, Algebraic number, Almost all, Annals of Mathematics, Apartness relation, Arithmetic, Bhāskara I, Bhāskara II, Binary number, Brahmagupta, Brahmana, Brjuno number, Cantor's diagonal argument, Cantor's first set theory article, Carl Benjamin Boyer, Catalan's constant, Charles Hermite, Charles Méray, Clifford A. Pickover, Coefficient, Commensurability (mathematics), Complete metric space, Completely metrizable space, Complex number, Computable number, Constructive proof, Constructivism (philosophy of mathematics), Continued fraction, Countable set, Crelle's Journal, Cube root, David Hilbert, Dedekind cut, Diophantine approximation, E (mathematical constant), Eduard Heine, Egypt, Equation, Errett Bishop, Euclid, Euclidean distance, Eudoxus of Cnidus, Euler's constant, ... Expand index (100 more) »
- Irrational numbers
- Sets of real numbers
Abraham de Moivre
Abraham de Moivre FRS (26 May 166727 November 1754) was a French mathematician known for de Moivre's formula, a formula that links complex numbers and trigonometry, and for his work on the normal distribution and probability theory.
See Irrational number and Abraham de Moivre
Abu Bakr al-Hassar
Al-Hassar or Abu Bakr Muhammad ibn Abdallah ibn Ayyash al-Hassar (أبو بكر محمد ابن عياش الحصَار) was a 12th-century Moroccan mathematician.
See Irrational number and Abu Bakr al-Hassar
Abu Kamil
Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ (Latinized as Auoquamel, أبو كامل شجاع بن أسلمبن محمد بن شجاع, also known as Al-ḥāsib al-miṣrī—lit. "The Egyptian Calculator") (c. 850 – c. 930) was a prominent Egyptian mathematician during the Islamic Golden Age.
See Irrational number and Abu Kamil
Adolf Hurwitz
Adolf Hurwitz (26 March 1859 – 18 November 1919) was a German mathematician who worked on algebra, analysis, geometry and number theory.
See Irrational number and Adolf Hurwitz
Adrien-Marie Legendre
Adrien-Marie Legendre (18 September 1752 – 9 January 1833) was a French mathematician who made numerous contributions to mathematics.
See Irrational number and Adrien-Marie Legendre
Al-Mahani
Abu-Abdullah Muhammad ibn Īsa Māhānī (ابوعبدالله محمد بن عیسی ماهانی, flourished c. 860 and died c. 880) was a Persian mathematician and astronomer born in Mahan, (in today Kermān, Iran) and active in Baghdad, Abbasid Caliphate.
See Irrational number and Al-Mahani
Algebra
Algebra is the branch of mathematics that studies algebraic structures and the manipulation of statements within those structures.
See Irrational number and Algebra
Algebraic independence
In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K. In particular, a one element set \ is algebraically independent over K if and only if \alpha is transcendental over K.
See Irrational number and Algebraic independence
Algebraic number
An algebraic number is a number that is a root of a non-zero polynomial (of finite degree) in one variable with integer (or, equivalently, rational) coefficients.
See Irrational number and Algebraic number
Almost all
In mathematics, the term "almost all" means "all but a negligible quantity".
See Irrational number and Almost all
Annals of Mathematics
The Annals of Mathematics is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
See Irrational number and Annals of Mathematics
Apartness relation
In constructive mathematics, an apartness relation is a constructive form of inequality, and is often taken to be more basic than equality.
See Irrational number and Apartness relation
Arithmetic
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division.
See Irrational number and Arithmetic
Bhāskara I
Bhāskara (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work.
See Irrational number and Bhāskara I
Bhāskara II
Bhāskara II (1114–1185), also known as Bhāskarāchārya, was an Indian polymath, mathematician, astronomer and engineer.
See Irrational number and Bhāskara II
Binary number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" (zero) and "1" (one).
See Irrational number and Binary number
Brahmagupta
Brahmagupta (–) was an Indian mathematician and astronomer.
See Irrational number and Brahmagupta
Brahmana
The Brahmanas (Sanskrit: ब्राह्मणम्, IAST: Brāhmaṇam) are Vedic śruti works attached to the Samhitas (hymns and mantras) of the Rig, Sama, Yajur, and Atharva Vedas.
See Irrational number and Brahmana
Brjuno number
In mathematics, a Brjuno number (sometimes spelled Bruno or Bryuno) is a special type of irrational number named for Russian mathematician Alexander Bruno, who introduced them in.
See Irrational number and Brjuno number
Cantor's diagonal argument
Cantor's diagonal argument (among various similar namesthe diagonalisation argument, the diagonal slash argument, the anti-diagonal argument, the diagonal method, and Cantor's diagonalization proof) is a mathematical proof that there are infinite sets which cannot be put into one-to-one correspondence with the infinite set of natural numbersinformally, that there are sets which in some sense contain more elements than there are positive integers.
See Irrational number and Cantor's diagonal argument
Cantor's first set theory article
Cantor's first set theory article contains Georg Cantor's first theorems of transfinite set theory, which studies infinite sets and their properties.
See Irrational number and Cantor's first set theory article
Carl Benjamin Boyer
Carl Benjamin Boyer (November 3, 1906 – April 26, 1976) was an American historian of sciences, and especially mathematics.
See Irrational number and Carl Benjamin Boyer
Catalan's constant
In mathematics, Catalan's constant, is defined by where is the Dirichlet beta function.
See Irrational number and Catalan's constant
Charles Hermite
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.
See Irrational number and Charles Hermite
Charles Méray
Hugues Charles Robert Méray (12 November 1835, in Chalon-sur-Saône, Saône-et-Loire – 2 February 1911, in Dijon) was a French mathematician.
See Irrational number and Charles Méray
Clifford A. Pickover
Clifford Alan Pickover (born August 15, 1957) is an American author, editor, and columnist in the fields of science, mathematics, science fiction, innovation, and creativity.
See Irrational number and Clifford A. Pickover
Coefficient
In mathematics, a coefficient is a multiplicative factor involved in some term of a polynomial, a series, or an expression.
See Irrational number and Coefficient
Commensurability (mathematics)
In mathematics, two non-zero real numbers a and b are said to be commensurable if their ratio is a rational number; otherwise a and b are called incommensurable.
See Irrational number and Commensurability (mathematics)
Complete metric space
In mathematical analysis, a metric space is called complete (or a Cauchy space) if every Cauchy sequence of points in has a limit that is also in.
See Irrational number and Complete metric space
Completely metrizable space
In mathematics, a completely metrizable space (metrically topologically complete space) is a topological space (X, T) for which there exists at least one metric d on X such that (X, d) is a complete metric space and d induces the topology T. The term topologically complete space is employed by some authors as a synonym for completely metrizable space, but sometimes also used for other classes of topological spaces, like completely uniformizable spaces or Čech-complete spaces.
See Irrational number and Completely metrizable space
Complex number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.
See Irrational number and Complex number
Computable number
In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.
See Irrational number and Computable number
Constructive proof
In mathematics, a constructive proof is a method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object.
See Irrational number and Constructive proof
Constructivism (philosophy of mathematics)
In the philosophy of mathematics, constructivism asserts that it is necessary to find (or "construct") a specific example of a mathematical object in order to prove that an example exists.
See Irrational number and Constructivism (philosophy of mathematics)
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.
See Irrational number and Continued fraction
Countable set
In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers.
See Irrational number and Countable set
Crelle's Journal
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
See Irrational number and Crelle's Journal
Cube root
In mathematics, a cube root of a number is a number such that.
See Irrational number and Cube root
David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of his time.
See Irrational number and David Hilbert
Dedekind cut
In mathematics, Dedekind cuts, named after German mathematician Richard Dedekind (but previously considered by Joseph Bertrand), are а method of construction of the real numbers from the rational numbers.
See Irrational number and Dedekind cut
Diophantine approximation
In number theory, the study of Diophantine approximation deals with the approximation of real numbers by rational numbers. Irrational number and Diophantine approximation are irrational numbers.
See Irrational number and Diophantine approximation
E (mathematical constant)
The number is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways.
See Irrational number and E (mathematical constant)
Eduard Heine
Heinrich Eduard Heine (16 March 1821 – 21 October 1881) was a German mathematician.
See Irrational number and Eduard Heine
Egypt
Egypt (مصر), officially the Arab Republic of Egypt, is a transcontinental country spanning the northeast corner of Africa and the Sinai Peninsula in the southwest corner of Asia.
See Irrational number and Egypt
Equation
In mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign.
See Irrational number and Equation
Errett Bishop
Errett Albert Bishop (July 14, 1928 – April 14, 1983) was an American mathematician known for his work on analysis.
See Irrational number and Errett Bishop
Euclid
Euclid (Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician.
See Irrational number and Euclid
Euclidean distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them.
See Irrational number and Euclidean distance
Eudoxus of Cnidus
Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, doctor, and lawmaker.
See Irrational number and Eudoxus of Cnidus
Euler's constant
Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma, defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by: \begin \gamma &.
See Irrational number and Euler's constant
Exact trigonometric values
In mathematics, the values of the trigonometric functions can be expressed approximately, as in \cos (\pi/4) \approx 0.707, or exactly, as in \cos (\pi/ 4). Irrational number and exact trigonometric values are irrational numbers.
See Irrational number and Exact trigonometric values
Ferdinand von Lindemann
Carl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German mathematician, noted for his proof, published in 1882, that pi (pi) is a transcendental number, meaning it is not a root of any polynomial with rational coefficients.
See Irrational number and Ferdinand von Lindemann
Fez, Morocco
Fez or Fes (fās) is a city in northern inland Morocco and the capital of the Fès-Meknès administrative region.
See Irrational number and Fez, Morocco
Fibonacci
Fibonacci (also,; –) was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages".
See Irrational number and Fibonacci
Field (mathematics)
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.
See Irrational number and Field (mathematics)
Fraction
A fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.
See Irrational number and Fraction
Fundamental theorem of arithmetic
In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors.
See Irrational number and Fundamental theorem of arithmetic
Gelfond–Schneider theorem
In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers.
See Irrational number and Gelfond–Schneider theorem
Georg Cantor
Georg Ferdinand Ludwig Philipp Cantor (– 6 January 1918) was a mathematician who played a pivotal role in the creation of set theory, which has become a fundamental theory in mathematics.
See Irrational number and Georg Cantor
Gδ set
In the mathematical field of topology, a Gδ set is a subset of a topological space that is a countable intersection of open sets.
See Irrational number and Gδ set
Golden ratio
In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.
See Irrational number and Golden ratio
Greek mathematics
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century BC to the 6th century AD, around the shores of the Mediterranean.
See Irrational number and Greek mathematics
Hexadecimal
In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of sixteen.
See Irrational number and Hexadecimal
Hippasus
Hippasus of Metapontum (Ἵππασος ὁ Μεταποντῖνος, Híppasos; c. 530 – c. 450 BC) was a Greek philosopher and early follower of Pythagoras. Irrational number and Hippasus are irrational numbers.
See Irrational number and Hippasus
Hypotenuse
In geometry, a hypotenuse is the side of a right triangle opposite the right angle.
See Irrational number and Hypotenuse
Imaginary number
An imaginary number is the product of a real number and the imaginary unit, is usually used in engineering contexts where has other meanings (such as electrical current) which is defined by its property.
See Irrational number and Imaginary number
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century.
See Irrational number and Indian mathematics
Infinity
Infinity is something which is boundless, endless, or larger than any natural number.
See Irrational number and Infinity
Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. Irrational number and integer are sets of real numbers.
See Irrational number and Integer
Iraq
Iraq, officially the Republic of Iraq, is a country in West Asia and a core country in the geopolitical region known as the Middle East.
See Irrational number and Iraq
Irrational number
In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers. Irrational number and irrational number are irrational numbers and sets of real numbers.
See Irrational number and Irrational number
Irreducible fraction
An irreducible fraction (or fraction in lowest terms, simplest form 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).
See Irrational number and Irreducible fraction
Islamic inheritance jurisprudence
Islamic Inheritance jurisprudence is a field of Islamic jurisprudence (فقه) that deals with inheritance, a topic that is prominently dealt with in the Qur'an.
See Irrational number and Islamic inheritance jurisprudence
Johann Heinrich Lambert
Johann Heinrich Lambert (Jean-Henri Lambert in French; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally identified as either Swiss or French, who made important contributions to the subjects of mathematics, physics (particularly optics), philosophy, astronomy and map projections.
See Irrational number and Johann Heinrich Lambert
Joseph-Louis Lagrange
Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier; 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange or Lagrangia, was an Italian mathematician, physicist and astronomer, later naturalized French.
See Irrational number and Joseph-Louis Lagrange
Jyeṣṭhadeva
Jyeṣṭhadeva was an astronomer-mathematician of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama.
See Irrational number and Jyeṣṭhadeva
Karl Weierstrass
Karl Theodor Wilhelm Weierstrass (Weierstraß; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern analysis".
See Irrational number and Karl Weierstrass
Kerala school of astronomy and mathematics
The Kerala school of astronomy and mathematics or the Kerala school was a school of mathematics and astronomy founded by Madhava of Sangamagrama in Tirur, Malappuram, Kerala, India, which included among its members: Parameshvara, Neelakanta Somayaji, Jyeshtadeva, Achyuta Pisharati, Melpathur Narayana Bhattathiri and Achyuta Panikkar.
See Irrational number and Kerala school of astronomy and mathematics
Latin translations of the 12th century
Latin translations of the 12th century were spurred by a major search by European scholars for new learning unavailable in western Europe at the time; their search led them to areas of southern Europe, particularly in central Spain and Sicily, which recently had come under Christian rule following their reconquest in the late 11th century.
See Irrational number and Latin translations of the 12th century
Law of excluded middle
In logic, the law of excluded middle or the principle of excluded middle states that for every proposition, either this proposition or its negation is true.
See Irrational number and Law of excluded middle
Leonhard Euler
Leonhard Euler (15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician, and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in many other branches of mathematics such as analytic number theory, complex analysis, and infinitesimal calculus.
See Irrational number and Leonhard Euler
Leopold Kronecker
Leopold Kronecker (7 December 1823 – 29 December 1891) was a German mathematician who worked on number theory, algebra and logic.
See Irrational number and Leopold Kronecker
Logarithm
In mathematics, the logarithm is the inverse function to exponentiation.
See Irrational number and Logarithm
Long division
In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple enough to perform by hand.
See Irrational number and Long division
Madhava of Sangamagrama
Mādhava of Sangamagrāma (Mādhavan) Available was an Indian mathematician and astronomer who is considered to be the founder of the Kerala school of astronomy and mathematics in the Late Middle Ages.
See Irrational number and Madhava of Sangamagrama
Magnitude (mathematics)
In mathematics, the magnitude or size of a mathematical object is a property which determines whether the object is larger or smaller than other objects of the same kind.
See Irrational number and Magnitude (mathematics)
Manava
Manava (750 BC – 690 BC) was an author of the Hindu geometric text of Sulba Sutras. The Manava Sulbasutra is not the oldest (the one by Baudhayana is older), nor is it one of the most important, there being at least three Sulbasutras which are considered more important.
See Irrational number and Manava
Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
See Irrational number and Mathematics
Mathematics in the medieval Islamic world
Mathematics during the Golden Age of Islam, especially during the 9th and 10th centuries, was built upon syntheses of Greek mathematics (Euclid, Archimedes, Apollonius) and Indian mathematics (Aryabhata, Brahmagupta).
See Irrational number and Mathematics in the medieval Islamic world
Mathematics Magazine
Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.
See Irrational number and Mathematics Magazine
Mathematische Annalen
Mathematische Annalen (abbreviated as Math. Ann. or, formerly, Math. Annal.) is a German mathematical research journal founded in 1868 by Alfred Clebsch and Carl Neumann.
See Irrational number and Mathematische Annalen
Method of exhaustion
The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
See Irrational number and Method of exhaustion
Metric space
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points.
See Irrational number and Metric space
Middle Ages
In the history of Europe, the Middle Ages or medieval period (also spelt mediaeval or mediæval) lasted from approximately 500 to 1500 AD.
See Irrational number and Middle Ages
Morris Kline
Morris Kline (May 1, 1908 – June 10, 1992) was a professor of mathematics, a writer on the history, philosophy, and teaching of mathematics, and also a popularizer of mathematical subjects.
See Irrational number and Morris Kline
Natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0. Irrational number and natural number are sets of real numbers.
See Irrational number and Natural number
New York Academy of Sciences
The New York Academy of Sciences (originally the Lyceum of Natural History) is a nonprofit professional society that claims to, “Advance scientific research and knowledge, support scientific literacy, and promote science-based solutions to global challenges.” Founded in January 1817 as the Lyceum of Natural History, it is the fourth-oldest scientific society in the United States.
See Irrational number and New York Academy of Sciences
Nth root
In mathematics, an th root of a number is a number (the root) which, when raised to the power of the positive integer, yields: r^n.
See Irrational number and Nth root
Number
A number is a mathematical object used to count, measure, and label.
See Irrational number and Number
Numeral system
A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
See Irrational number and Numeral system
Octal
Octal (base 8) is a numeral system with eight as the base.
See Irrational number and Octal
Paul Gordan
Paul Albert Gordan (27 April 1837 – 21 December 1912) was a Jewish-German mathematician, a student of Carl Jacobi at the University of Königsberg before obtaining his PhD at the University of Breslau (1862),.
See Irrational number and Paul Gordan
Paul Tannery
Paul Tannery (20 December 1843 – 27 November 1904) was a French mathematician and historian of mathematics.
See Irrational number and Paul Tannery
Pentagram
A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon.
See Irrational number and Pentagram
Periodic continued fraction
In mathematics, an infinite periodic continued fraction is a continued fraction that can be placed in the form x.
See Irrational number and Periodic continued fraction
Persians
The Persians--> are an Iranian ethnic group who comprise over half of the population of Iran.
See Irrational number and Persians
Pi
The number (spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.
Polynomial
In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.
See Irrational number and Polynomial
Positional notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system).
See Irrational number and Positional notation
Prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers.
See Irrational number and Prime number
Proof by contradiction
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction.
See Irrational number and Proof by contradiction
Proof that e is irrational
The number ''e'' was introduced by Jacob Bernoulli in 1683. Irrational number and Proof that e is irrational are irrational numbers.
See Irrational number and Proof that e is irrational
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
See Irrational number and Pythagorean theorem
Pythagoreanism
Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans.
See Irrational number and Pythagoreanism
Quadratic equation
In mathematics, a quadratic equation is an equation that can be rearranged in standard form as ax^2 + bx + c.
See Irrational number and Quadratic equation
Quadratic irrational number
In mathematics, a quadratic irrational number (also known as a quadratic irrational or quadratic surd) is an irrational number that is the solution to some quadratic equation with rational coefficients which is irreducible over the rational numbers.
See Irrational number and Quadratic irrational number
Ratio
In mathematics, a ratio shows how many times one number contains another.
See Irrational number and Ratio
Rational number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator. Irrational number and rational number are sets of real numbers.
See Irrational number and Rational number
Rational root theorem
In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or theorem) states a constraint on rational solutions of a polynomial equation a_nx^n+a_x^+\cdots+a_0.
See Irrational number and Rational root theorem
Real number
In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.
See Irrational number and Real number
Reductio ad absurdum
In logic, reductio ad absurdum (Latin for "reduction to absurdity"), also known as argumentum ad absurdum (Latin for "argument to absurdity") or apagogical arguments, is the form of argument that attempts to establish a claim by showing that the opposite scenario would lead to absurdity or contradiction.
See Irrational number and Reductio ad absurdum
Remainder
In mathematics, the remainder is the amount "left over" after performing some computation.
See Irrational number and Remainder
Repeating decimal
A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.
See Irrational number and Repeating decimal
Richard Dedekind
Julius Wilhelm Richard Dedekind (6 October 1831 – 12 February 1916) was a German mathematician who made important contributions to number theory, abstract algebra (particularly ring theory), and the axiomatic foundations of arithmetic.
See Irrational number and Richard Dedekind
Salvatore Pincherle
Salvatore Pincherle (March 11, 1853 – July 10, 1936) was an Italian mathematician.
See Irrational number and Salvatore Pincherle
Samhita
Samhita (IAST: Saṃhitā) literally means "put together, joined, union", a "collection", and "a methodically, rule-based combination of text or verses".
See Irrational number and Samhita
Series (mathematics)
In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity.
See Irrational number and Series (mathematics)
Shulba Sutras
The Shulva Sutras or Śulbasūtras (Sanskrit: शुल्बसूत्र;: "string, cord, rope") are sutra texts belonging to the Śrauta ritual and containing geometry related to fire-altar construction.
See Irrational number and Shulba Sutras
Special right triangle
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist.
See Irrational number and Special right triangle
Springer Science+Business Media
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
See Irrational number and Springer Science+Business Media
Square number
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.
See Irrational number and Square number
Square root
In mathematics, a square root of a number is a number such that y^2.
See Irrational number and Square root
Square root of 2
The square root of 2 (approximately 1.4142) is a real number that, when multiplied by itself or squared, equals the number 2.
See Irrational number and Square root of 2
Square root of 3
The square root of 3 is the positive real number that, when multiplied by itself, gives the number 3.
See Irrational number and Square root of 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.
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Tetration
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation.
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The Mathematical Gazette
The Mathematical Gazette is a triannual peer-reviewed academic journal published by Cambridge University Press on behalf of the Mathematical Association.
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Theodorus of Cyrene
Theodorus of Cyrene (Theódōros ho Kyrēnaîos) was an ancient Greek mathematician who lived during the 5th century BC.
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Topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.
See Irrational number and Topological space
Transcendental number
In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients.
See Irrational number and Transcendental number
Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
See Irrational number and Trigonometric functions
Uncountable set
In mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable.
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Unique factorization domain
In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds.
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Vedic period
The Vedic period, or the Vedic age, is the period in the late Bronze Age and early Iron Age of the history of India when the Vedic literature, including the Vedas (–900 BCE), was composed in the northern Indian subcontinent, between the end of the urban Indus Valley Civilisation and a second urbanisation, which began in the central Indo-Gangetic Plain BCE.
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Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.
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Yuktibhāṣā
Yuktibhāṣā (lit), also known as Gaṇita-yukti-bhāṣā and (English: Compendium of Astronomical Rationale), is a major treatise on mathematics and astronomy, written by the Indian astronomer Jyesthadeva of the Kerala school of mathematics around 1530.
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Zeno of Elea
Zeno of Elea (Ζήνων ὁ Ἐλεᾱ́της) was a pre-Socratic Greek philosopher.
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Zeno's paradoxes
Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia.
See Irrational number and Zeno's paradoxes
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, the function f attains the value of 0 at x, or equivalently, x is a solution to the equation f(x).
See Irrational number and Zero of a function
Zero-dimensional space
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space.
See Irrational number and Zero-dimensional space
See also
Irrational numbers
- Apéry's constant
- Copeland–Erdős constant
- Diophantine approximation
- Erdős–Borwein constant
- Exact trigonometric values
- Hippasus
- Irrational number
- Irrational rotation
- Irrationality sequence
- Liouville number
- Normal number
- Particular values of the Riemann zeta function
- Prime constant
- Proof that π is irrational
- Proof that e is irrational
- Quadratic irrational numbers
- Real transcendental numbers
- Reciprocal Fibonacci constant
- Schizophrenic number
- Twelfth root of two
Sets of real numbers
- Bernstein set
- Cantor set
- Fractal string
- Gregory number
- Integer
- Integers
- Interval (mathematics)
- Irrational number
- Irrational numbers
- Natural number
- Nested intervals
- Normal number
- Rational number
- Rational numbers
- Smith–Volterra–Cantor set
- Stoneham number
- Unit interval
- Vitali set
References
Also known as First Crisis of Mathematics, History of irrational numbers, Incommensurable magnitudes, Irrational Numbers, Irrational.number, Irrationals.