In mathematics, the reciprocal of a non-zero number x is the number 1/x which it must be multiplied by to give the product 1. The reciprocal function, the function f(x): x -> 1/x, is one the simplest examples of a function which is self-inverse. Image File history File links Hyperbola_one_over_x. ... Image File history File links Hyperbola_one_over_x. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... In mathematics, an inverse function is in simple terms a function which does the reverse of a given function. ...
One may also speak of taking the reciprocal of an equation: if (u+v)=(x+y), then 1/(u+v) = 1/(x+y).
Etymology
The term was in common use at least as far back as the third edition of Encyclopaedia Britannica (1797) to describe two numbers whose product is 1; two figures in plane geometry are described as reciprocall in a 1570 translation of Euclid's Elements.[1] ... 1797 (MDCCXCVII) was a common year starting on Sunday (see link for calendar) of the Gregorian calendar (or a common year starting on Wednesday of the 11-day-slower Julian calendar). ... Events January 23 - The assassination of regent James Stewart, Earl of Moray throws Scotland into civil war February 25 - Pope Pius V excommunicates Queen Elizabeth I of England with the bull Regnans in Excelsis May 20 - Abraham Ortelius issues the first modern atlas. ... Euclid(Greek: ), also known as Euclid of Alexandria, was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BC). ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise, consisting of 13 books, written by the Hellenistic mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems...
References
^ Jeff Miller, Earliest Known Uses of Some of the Words of Mathematics. Accessed 2007-03-03.
Reciprocity (international relations), a principle that favours, benefits, or penalties that are granted by one state to the citizens or legal entities of another, should be returned in kind.
Reciprocity (Canadian politics), 19th Century concept of free trade with the United States of America.
Reciprocity (photography), the relationship between the intensity of the light and duration of the exposure that result in identical exposure.
Positive reciprocal actions differ from altruistic actions as they only follow from other positive actions and they differ from social gift giving in that they are not actions taken with the hope or expectation of future positive responses.
Reciprocal actions are important to social psychology as they can help explain the maintenance of social norms.
In public good experiments, behavioral economists have demonstrated that the potential for reciprocal actions by players increases the rate of contribution to the public good, providing evidence for the importance of reciprocity in social situations (Fehr and Gatcher, 2003).
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