# reciprocal

## Definitions

• WordNet 3.6
• adj reciprocal of or relating to the multiplicative inverse of a quantity or function "the reciprocal ratio of a:b is b:a"
• adj reciprocal concerning each of two or more persons or things; especially given or done in return "reciprocal aid","reciprocal trade","mutual respect","reciprocal privileges at other clubs"
• n reciprocal hybridization involving a pair of crosses that reverse the sexes associated with each genotype
• n reciprocal (mathematics) one of a pair of numbers whose product is 1: the reciprocal of 2/3 is 3/2; the multiplicative inverse of 7 is 1/7
• n reciprocal something (a term or expression or concept) that has a reciprocal relation to something else "risk is the reciprocal of safety"
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Webster's Revised Unabridged Dictionary
• Reciprocal Done by each to the other; interchanging or interchanged; given and received; due from each to each; mutual; as, reciprocal love; reciprocal duties. "Let our reciprocal vows be remembered."
• Reciprocal Mutually interchangeable. "These two rules will render a definition reciprocal with the thing defined."
• Reciprocal Recurring in vicissitude; alternate.
• Reciprocal (Gram) Reflexive; -- applied to pronouns and verbs, but sometimes limited to such pronouns as express mutual action.
• Reciprocal That which is reciprocal to another thing. "Corruption is a reciprocal to generation."
• Reciprocal (Arith. & Alg) The quotient arising from dividing unity by any quantity; thus 1/4 is the reciprocal of 4; 1/(a + b is the reciprocal of a + b. The reciprocal of a fraction is the fraction inverted, or the denominator divided by the numerator.
• Reciprocal (Math) Used to denote different kinds of mutual relation; often with reference to the substitution of reciprocals for given quantities. See the Phrases below.
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Century Dictionary and Cyclopedia
• reciprocal Moving backward and forward; alternating; reciprocating.
• reciprocal Mutually exchanged or exchangeable; concerning or given or owed by each (of two or more) with regard to the other or others: as, reciprocal aid; reciprocal rights, duties, or obligations; reciprocal love or admiration.
• reciprocal Having an interchangeable character or relation; mutually equivalent or correspondent; concordant; agreeing.
• reciprocal Synonyms Reciprocal, Mutual. There is a theoretical difference between these words, although it often is not important. That is mutual which is a common act on the part of both persons at the same time. Mutual is not properly applicable to physical acts or material things, as blows or gifts. Reciprocal means that one follows another, being caused by it, with emphasis upon that which is viewed as caused: as, reciprocal love or hate. See remarks under mutual as to the propriety of using mutual for common.
• n reciprocal That which is reciprocal to another thing.
• n reciprocal In mathematics, the quotient resulting from the division of unity by the quantity of which the quotient is said to be the reciprocal. Thus, the reciprocal of 4 is ¼, and conversely the reciprocal of ¼ is 4; the reciprocal of 2 is ½, and that of a + x is 1/ (a + x). A fraction made by inverting the terms of another fraction is called the reciprocal of that other fraction: thus, is the reciprocal of
• reciprocal In geometry, definitely dual, so that the dual of each element is fixed and constructible.
• n reciprocal In geometry, the dual.
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Chambers's Twentieth Century Dictionary
• adj Reciprocal rē-sip′rō-kal acting in return: mutual: alternating: interchangeable: giving and receiving
• n Reciprocal that which is reciprocal:
• v.i Reciprocal to move backward and forward:
• n Reciprocal (math.) the quotient resulting from the division of unity by any given quantity
• v.i Reciprocal (coll.) to make a return or response
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## Quotations

• Samuel Johnson
“Life cannot subsist in society but by reciprocal concessions.”
• Washington Irving
“Love is never lost. If not reciprocated, it will flow back and soften and purify the heart.”
• Louis K. Anspacher
“Marriage is that relation between man and woman in which the independence is equal, the dependence mutual, and the obligation reciprocal.”

## Etymology

Webster's Revised Unabridged Dictionary
L. reciprocus,; of unknown origin

## Usage

### In literature:

I knew how much I cared for them and it was pleasing to know that they reciprocated my feelings.
"Autobiography of Andrew Carnegie" by Andrew Carnegie
One good turn deserves another and he may have a chance later to reciprocate.
"The Boston Terrier and All About It" by Edward Axtell
The difference between the two nations, the two sovereigns, and their reciprocal position, were remarked in these proclamations.
"History of the Expedition to Russia" by Count Philip de Segur
Furthermore, Austria-Hungary would insist on full reciprocity for the Poles resident in Ukraine.
"In the World War" by Count Ottokar Czernin
Commercial reciprocity between the United States and Canada is desirable.
"Carnegie Library of Pittsburgh Debate Index" by Carnegie Library of Pittsburgh
A list of all reciprocal relations is a desideratum of Logic.
Hence, the perfect peace of reciprocated love.
"The People's Common Sense Medical Adviser in Plain English" by R. V. Pierce
The plan might well be reciprocal.
"The War and Unity" by Various
Friendships live and thrive upon a system of reciprocal benefit.
"The Vicomte de Bragelonne" by Alexandre Dumas
This obligation was reciprocal.
"The History of England in Three Volumes, Vol.II. From William and Mary to George II." by Tobias Smollett
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### In poetry:

My friends will me forget;
But why should I regret?
Nor human love nor hate
I then reciprocate.
"Of Death And Life" by Alfred Gibbs Campbell
"I doubt it not," said John, "and I
Reciprocate the feeling,
And here, with one despairing cry,
I kneel, and love you, kneeling."
"John And Jane" by Thomas Frederick Young
OUR hero felt a thousand times more blessed
Than when he first the beauteous fair caressed;
For when a flame reciprocal is raised,
The bliss redoubles, and by all is praised.
"Richard Minutolo" by Jean de La Fontaine
Theft is theft and raid is raid
Lovers, the conclusion is
Doubled sighs and jealousies
In a single heart that grieves For lost honour among thieves.
"The Thieves" by Robert Graves
Who seek a friend should come dispos’d
To exhibit, in full bloom disclos’d,
The graces and the beauties
That form the character he seeks,
For ‘tis a union that bespeaks
Reciprocated duties.
"Friendship" by William Cowper
The worthy priest, he up and drew his cowl upon his crown,
And started off in haste to tell the news to ROBBER BROWN -
To tell him how his daughter, who was now for marriage fit,
Had winked upon a sorter, who reciprocated it.
"Gentle Alice Brown" by William Schwenck Gilbert

### In news:

Wisconsin, Minnesota use tuition reciprocity to lure best students.
Harper Says Takeover Reciprocity Is Challenge, Post Reports.
WIS.- MIN TAX RECIPROCITY UNLIKELY IN 2013.
Talks on reinstating income tax reciprocity with Minnesota have stalled and an agreement likely will not be reached before 2013.
Tax Reciprocity Deal Unlikely by Oct 1st Deadline.
State officials hit a major road block in the efforts to reinstate reciprocity between Minnesota and Wisconsin.
It's time to set a price for reciprocity .
Wisconsin and Minnesota are far apart on how much the Badger State should pay for tax reciprocity .
Which agencies are poorest in contractor clearance reciprocity .
And Melissa Leo Take On Sexual Reciprocity on Louie.
Iran looking for respect and reciprocity .
Reciprocity makes the adage "It's better to give than to receive" literally true.
State legislators and the revenue commissioners of both Minnesota and Wisconsin met this week to discuss reinstatement of the income tax reciprocity between the two states.
Hats off to Reciprocity 's luncheon.
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### In science:

The emission frequency is deﬁned by the spatial period and by the volume geometry (by the direction of the reciprocal vectors for example).
Influence of guiding magnetic field on emission of stimulated photons in generators utilizing periodic slow-wave structures
Here we suggest a new approach for description of this solution in more clear form by using suitable reciprocal transformation.
The Calogero equation and Liouville type equations
In third section we describe another reciprocal transformation from the generalized HunterSaxton equation into the Liouville equation.
The Calogero equation and Liouville type equations
This leads to a fermionic representation of the hamiltonian with, in reciprocal space, the fermions operators αq (α+ q ) and βq (β+ q ).
Elementary Excitations in Quantum Antiferromagnetic Chains: Dyons, Spinons and Breathers
Quantum toroidal algebras were introduced by Ginzburg-Kapranov-Vasserot [GKV] in the study of the Langlands reciprocity for algebraic surfaces.
$U_q(\hat{\frak{gl}}_{{}_N})$ action on $\hat{\frak{gl}}_{{}_N}$ -modules and quantum toroidal algebras
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