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Unit fraction, the Glossary

A unit fraction is a positive fraction with one as its numerator, 1/.^[1]

67 relations: Addition, Ancient Egyptian mathematics, Annals of Mathematics, Apéry's constant, Arthur Eddington, Atomic orbital, Basel problem, Bézout's identity, Bin packing problem, Bohr model, Combinatorial optimization, Coprime integers, Discrete uniform distribution, Division (mathematics), Egyptian fraction, Erdős–Graham problem, Erdős–Straus conjecture, Euler's constant, Extended Euclidean algorithm, Fair division, Fibonacci Quarterly, Fibonacci sequence, Fine-structure constant, Ford circle, Fraction, Geometric group theory, Geometric series, Greatest common divisor, Harmonic bin packing, Harmonic divisor number, Harmonic series (mathematics), Hilbert matrix, Hydrogen atom, Hydrogen spectral series, Invertible matrix, Irrational number, Leibniz formula for π, Main diagonal, Mathematics and Computer Education, Mathematics education, Mathematics Magazine, Modular arithmetic, Multiple (mathematics), Multiplication, Multiplicative inverse, Natural logarithm, Natural logarithm of 2, Natural number, Number line, Number theory, ... Expand index (17 more) »
Elementary arithmetic
Fractions (mathematics)

Addition

Addition (usually signified by the plus symbol) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. Unit fraction and Addition are elementary arithmetic.

See Unit fraction and Addition

Ancient Egyptian mathematics

Ancient Egyptian mathematics is the mathematics that was developed and used in Ancient Egypt 3000 to c., from the Old Kingdom of Egypt until roughly the beginning of Hellenistic Egypt.

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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 Unit fraction and Annals of Mathematics

Apéry's constant

In mathematics, Apéry's constant is the sum of the reciprocals of the positive cubes.

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Arthur Eddington

Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician.

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Atomic orbital

In quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom.

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Basel problem

The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.

See Unit fraction and Basel problem

Bézout's identity

In mathematics, Bézout's identity (also called Bézout's lemma), named after Étienne Bézout who proved it for polynomials, is the following theorem: Here the greatest common divisor of and is taken to be.

See Unit fraction and Bézout's identity

Bin packing problem

The bin packing problem is an optimization problem, in which items of different sizes must be packed into a finite number of bins or containers, each of a fixed given capacity, in a way that minimizes the number of bins used.

See Unit fraction and Bin packing problem

Bohr model

In atomic physics, the Bohr model or Rutherford–Bohr model is an obsolete model of the atom, presented by Niels Bohr and Ernest Rutherford in 1913.

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Combinatorial optimization

Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set.

See Unit fraction and Combinatorial optimization

Coprime integers

In number theory, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1.

See Unit fraction and Coprime integers

Discrete uniform distribution

In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein a finite number of values are equally likely to be observed; every one of n values has equal probability 1/n.

See Unit fraction and Discrete uniform distribution

Division (mathematics)

Division is one of the four basic operations of arithmetic. Unit fraction and Division (mathematics) are elementary arithmetic.

See Unit fraction and Division (mathematics)

Egyptian fraction

An Egyptian fraction is a finite sum of distinct unit fractions, such as \frac+\frac+\frac.

See Unit fraction and Egyptian fraction

Erdős–Graham problem

In combinatorial number theory, the Erdős–Graham problem is the problem of proving that, if the set \ of integers greater than one is partitioned into finitely many subsets, then one of the subsets can be used to form an Egyptian fraction representation of unity.

See Unit fraction and Erdős–Graham problem

Erdős–Straus conjecture

The Erdős–Straus conjecture is an unproven statement in number theory.

See Unit fraction and Erdős–Straus conjecture

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 Unit fraction and Euler's constant

Extended Euclidean algorithm

In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs.

See Unit fraction and Extended Euclidean algorithm

Fair division

Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share.

See Unit fraction and Fair division

Fibonacci Quarterly

The Fibonacci Quarterly is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year.

See Unit fraction and Fibonacci Quarterly

Fibonacci sequence

In mathematics, the Fibonacci sequence is a sequence in which each number is the sum of the two preceding ones.

See Unit fraction and Fibonacci sequence

Fine-structure constant

In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.

See Unit fraction and Fine-structure constant

Ford circle

In mathematics, a Ford circle is a circle in the Euclidean plane, in a family of circles that are all tangent to the x-axis at rational points. Unit fraction and Ford circle are fractions (mathematics).

See Unit fraction and Ford circle

Fraction

A fraction (from fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. Unit fraction and fraction are fractions (mathematics).

See Unit fraction and Fraction

Geometric group theory

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).

See Unit fraction and Geometric group theory

Geometric series

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

See Unit fraction and Geometric series

Greatest common divisor

In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

See Unit fraction and Greatest common divisor

Harmonic bin packing

Harmonic bin-packing is a family of online algorithms for bin packing.

See Unit fraction and Harmonic bin packing

Harmonic divisor number

In mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer.

See Unit fraction and Harmonic divisor number

Harmonic series (mathematics)

In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: \sum_^\infty\frac.

See Unit fraction and Harmonic series (mathematics)

Hilbert matrix

In linear algebra, a Hilbert matrix, introduced by, is a square matrix with entries being the unit fractions For example, this is the 5 × 5 Hilbert matrix: \end.

See Unit fraction and Hilbert matrix

Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen.

See Unit fraction and Hydrogen atom

Hydrogen spectral series

The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula.

See Unit fraction and Hydrogen spectral series

Invertible matrix

In linear algebra, an -by- square matrix is called invertible (also nonsingular, nondegenerate or rarely regular) if there exists an -by- square matrix such that\mathbf.

See Unit fraction and Invertible matrix

Irrational number

In mathematics, the irrational numbers (in- + rational) are all the real numbers that are not rational numbers.

See Unit fraction and Irrational number

Leibniz formula for π

In mathematics, the Leibniz formula for pi, named after Gottfried Wilhelm Leibniz, states that \frac.

See Unit fraction and Leibniz formula for π

Main diagonal

In linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix A is the list of entries a_ where i.

See Unit fraction and Main diagonal

Mathematics and Computer Education

Mathematics and Computer Education was a peer-reviewed academic journal in the fields of mathematics and computer science education, published from 1982 to 2016.

See Unit fraction and Mathematics and Computer Education

Mathematics education

In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.

See Unit fraction and Mathematics education

Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

See Unit fraction and Mathematics Magazine

Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus.

See Unit fraction and Modular arithmetic

Multiple (mathematics)

In mathematics, a multiple is the product of any quantity and an integer. Unit fraction and multiple (mathematics) are integers.

See Unit fraction and Multiple (mathematics)

Multiplication

Multiplication (often denoted by the cross symbol, by the mid-line dot operator, by juxtaposition, or, on computers, by an asterisk) is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division. Unit fraction and Multiplication are elementary arithmetic.

See Unit fraction and Multiplication

Multiplicative inverse

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

See Unit fraction and Multiplicative inverse

Natural logarithm

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

See Unit fraction and Natural logarithm

Natural logarithm of 2

The decimal value of the natural logarithm of 2 is approximately The logarithm of 2 in other bases is obtained with the formula The common logarithm in particular is The inverse of this number is the binary logarithm of 10: By the Lindemann–Weierstrass theorem, the natural logarithm of any natural number other than 0 and 1 (more generally, of any positive algebraic number other than 1) is a transcendental number.

See Unit fraction and Natural logarithm of 2

Natural number

In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0. Unit fraction and natural number are integers.

See Unit fraction and Natural number

Number line

In elementary mathematics, a number line is a picture of a straight line that serves as spatial representation of numbers, usually graduated like a ruler with a particular origin point representing the number zero and evenly spaced marks in either direction representing integers, imagined to extend infinitely.

See Unit fraction and Number line

Number theory

Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.

See Unit fraction and Number theory

Photon

A photon is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force.

See Unit fraction and Photon

Pinwheel scheduling

In mathematics and computer science, the pinwheel scheduling problem is a problem in real-time scheduling with repeating tasks of unit length and hard constraints on the time between repetitions.

See Unit fraction and Pinwheel scheduling

Principle of indifference

The principle of indifference (also called principle of insufficient reason) is a rule for assigning epistemic probabilities.

See Unit fraction and Principle of indifference

Probability theory

Probability theory or probability calculus is the branch of mathematics concerned with probability.

See Unit fraction and Probability theory

Quantization (physics)

Quantisation (in American English quantization) is the systematic transition procedure from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics.

See Unit fraction and Quantization (physics)

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. Unit fraction and rational number are fractions (mathematics).

See Unit fraction and Rational number

Rydberg formula

In atomic physics, the Rydberg formula calculates the wavelengths of a spectral line in many chemical elements.

See Unit fraction and Rydberg formula

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 Unit fraction and Series (mathematics)

Square matrix

In mathematics, a square matrix is a matrix with the same number of rows and columns.

See Unit fraction and Square matrix

Subtraction

Subtraction (which is signified by the minus sign) is one of the four arithmetic operations along with addition, multiplication and division. Unit fraction and Subtraction are elementary arithmetic.

See Unit fraction and Subtraction

Superparticular ratio

In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers.

See Unit fraction and Superparticular ratio

Tangent circles

In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point.

See Unit fraction and Tangent circles

The American Mathematical Monthly

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

See Unit fraction and The American Mathematical Monthly

The Mathematical Intelligencer

The Mathematical Intelligencer is a mathematical journal published by Springer Science+Business Media that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.

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Triangle group

In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle.

See Unit fraction and Triangle group

Zipf's law

Zipf's law is an empirical law that often holds, approximately, when a list of measured values is sorted in decreasing order.

See Unit fraction and Zipf's law

17-animal inheritance puzzle

The 17-animal inheritance puzzle is a mathematical puzzle involving unequal but fair allocation of indivisible goods, usually stated in terms of inheritance of a number of large animals (17 camels, 17 horses, 17 elephants, etc.) which must be divided in some stated proportion among a number of beneficiaries.

See Unit fraction and 17-animal inheritance puzzle

References

[1] https://en.wikipedia.org/wiki/Unit_fraction

Also known as Adjacent fractions, Any rational number is a sum of unit fractions, Unit Fractions.

, Photon, Pinwheel scheduling, Principle of indifference, Probability theory, Quantization (physics), Rational number, Rydberg formula, Series (mathematics), Square matrix, Subtraction, Superparticular ratio, Tangent circles, The American Mathematical Monthly, The Mathematical Intelligencer, Triangle group, Zipf's law, 17-animal inheritance puzzle.

Unit fraction, the Glossary

Table of Contents

See also

Elementary arithmetic

Fractions (mathematics)

References