Copyright © Philip M. Parker, INSEAD. Terms of Use.

Pi

Definition: Pi

Pi

Noun

1. The ratio of the circumference to the diameter of a circle.

2. Someone who can be employed as a detective to collect information.

3. The scientist in charge of an experiment or research project.

4. The 16th letter of the Greek alphabet.

Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.
 

Date "pi" was first used in popular English literature: sometime before 1880. (references)

 

Specialty Definition: Pi

DomainDefinition

Computing

PI An interface between Prolog application programs and the X Window System that aims to be independent from the Prolog engine, provided that it has a Quintus foreign function interface (e.g. SICStus and YAP). It is mostly written in Prolog and is divided in two libraries: Edipo - the lower level interface to the Xlib functions; and Ytoolkit - the higher level user interface toolkit. (ftp://ftp.ncc.up.pt/pub/prolog/ytoolkit.tar.Z) E-mail: Ze' Paulo Leal . (1993-03-02). Source: The Free On-line Dictionary of Computing.

Census

Designation for the (Pacific Islands). For census purposes, this includes persons who identify themselves as Polynesian, Micronesian, or Melanesian. (references)

Physics

The constant equal to the ratio of the circumference of a circle to its diameter, which is approximately 3.141593. (references)
 Principal Investigator. (references)

Space

Principal Investigator, scientist in charge of an experiment. (references)

Source: compiled by the editor from various references; see credits.

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Specialty Definition: List of people by name: Pi

(From Wikipedia, the free Encyclopedia)

List of people by name: A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z Pa-Pd - Pe - Pf-Pg - Ph - Pi - Pj-Pn - Po - Pp-Pr - Ps - Pt - Pu - Pv-Pz

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Pi

(From Wikipedia, the free Encyclopedia)

The number '\pi (denoted with the lower-case Greek letter π) is a mathematical constant which occurs in many areas of mathematics and physics. It is also known as Archimedes' constant or Ludolph's number' and is equal to the ratio of a circle's circumference to its diameter in Euclidean geometry. Alternatively, π can be defined as the area of a circle of radius 1, or as the smallest positive number x for which sin(x) = 0.

The value of π to the first sixty-four digits is:

3.14159 26535 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 592...

Properties

The number π is an irrational number: that is, it cannot be written as the ratio of two integers. This was proved in 1761 by Johann Heinrich Lambert. In fact, the number is transcendental, as was proved by Ferdinand Lindemann in 1882. This means that there is no polynomial with integer (or rational) coefficients of which π is a root. As a consequence, it is impossible to express π using only a finite number of integers, fractions and their roots.

This result establishes the impossibility of squaring the circle: it is impossible to construct, using ruler and compass alone, a square whose area is equal to the area of a given circle. The reason is that the coordinates of all points that can be constructed with ruler and compass are special algebraic numbers.

Formulae involving π

Geometry:

Circumference of circle of radius r: C = 2 π r
Area of circle of radius r: A = π r2
Area of ellipse with semiaxes a and b: A = π ab
Volume of sphere of radius r: V = (4/3) π r3
Surface area of sphere of radius r: A = 4 π r2
Angles: 180 degrees is equivalent to π radians

Analysis:

(Leibniz' formula)

(Wallis' product)

(Euler)

(Stirling's formula)

(Euler's identity, also called "The most remarkable formula in the world")

π has beautiful continued fractional representations:

(You can see 12 other representations at [1] )

Number theory:

The probability that two randomly chosen integers are relatively prime is 6/π2.
The probability that a randomly chosen integer is square-free is 6/π2.
The average number of ways to write a positive integer as the sum of two perfect squares (order matters) is π/4.

Dynamical Systems / Ergodic Theory:

for almost every x0 in [0, 1] where the xi are iterates of the Logistic map for r=4.
Physics:

(Heisenberg's uncertainty principle)

(Einstein's field equation of general relativity)

Statistics:

(The probability density function for the normal distribution.)

Computing the value of pi

Due to the transcendental nature of π there are no nice closed expressions for π. Therefore calculations have to use approximations to the number. For many purposes, 3.14 or 22/7 is close enough, although engineers often use 3.1416 (5 significant figures) or 3.14159 (6 significant figures) for more accuracy. 355/113, with two each of the first 3 odd digits, is a simple and easily memorised fraction which is good for 7 significant figures.

An Egyptian scribe called Ahmes is the source of the oldest known text to give an approximate value for π. The Rhind Papyrus dates from the 17th century BC and describes the value in such a way that the result obtained comes out to 256 divided by 81 or 3.160.

Liu Hui computed π to 3.141014 (incorrect in the fourth decimal digit) in 263 A.D. and suggested that 3.14 was a good approximation.

Ludolph van Ceulen (circa 1600) computed the first 35 decimals. He was so proud of this accomplishment that he had them inscribed on his tombstone.

The Slovene mathematician Jurij Vega in 1789 calculated the first 140 decimal places for π of which 137 were correct and held the world record for over 50 years at that time. He improved John Machin's formula from 1706 and his method is still mentioned today.

None of the formulas given above can serve as an efficient way of approximating π. For fast calculations, one may use formulas like Machin's:

together with the Taylor series expansion of the function arctan(x). This formula is most easily verified using polar coordinates of complex numbers, starting with
(5+i)4 · (-239 + i) = -114244-114244 i.
Formulas of this kind are known as Machin-like formulas.

Extremely large numbers of digits of π are typically computed with the Gauss-Legendre algorithm and Borwein's algorithm; the Salamin-Brent algorithm which was invented in 1976 has also been used in the past.

The first one million digits of π and 1/π are available from Project Gutenberg (see external links below). The current record (December 2002) stands at 1,241,100,000,000 digits, which were computed in September 2002 on a 64-node Hitachi supercomputer with 1 Terabyte of main memory, which carries out 2 trillion operations per second, nearly twice as many as the computer used for the previous record (206 billion digits); the following Machin-like formulas were used for this:

(K. Takano, 1982)

(F. C. W. Störmer, 1896)

These approximations have so many digits that they are no longer of any practical use, except for testing new supercomputers.

In 1996 David H. Bailey, together with Peter Borwein and Simon Plouffe, discovered a new formula for π as an infinite series:

This formula permits one to easily compute the nth binary or hexadecimal digit of π, without having to compute the preceeding n-1 digits. Bailey's website contains the derivation as well as implementations in various programming languages.

Other formulas that have been used to compute pi include:

(Ramanujan)

(David Chudnovsky and Gregory Chudnovsky)

Open questions

The most pressing open question about π is whether it is normal, i.e. whether any digit block occurs in the expansion of π just as often as one would statistically expect if the digits had been produced completely randomly. This should be true in any base, not just in base 10.

It isn't even known which of the digits 0,...,9 occur infinitely often in the decimal expansion of π.

Bailey and Crandall showed in 2000 that the existence of the above mentioned Bailey-Borwein-Plouffe formula and similar formulas imply that the normality in base 2 of π and various other constants can be reduced to a plausible conjecture of chaos theory. See Bailey's above mentioned web site for details.

The nature of π

In non-Euclidean geometry the sum of the angles of a triangle may be more or less than π, and the ratio of a circle's circumference to its diameter may also differ from π. This doesn't change the value of π, but does affect many formulae in which it appears. So in particular, the shape of the universe does not affect the value of π at all: it is a mathematical constant, not a physical value.

Pi culture

There is an entire field of humorous yet serious study that involves the use of mnemonic techniques to remember the digits of π, which is known as Piphilology. This is obviously a play on Pi itself and the linguistic field of philology.

The most common mnemonic technique is to memorise a sentence in which the number of letters in each word in turn is equal to the corresponding digit of π. The most famous example of this is from Isaac Asimov:

How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics!

If less accuracy is required an easy one is also:

How I wish I could recollect pi easily today!

Part of the school cheer of MIT is: "Cosine, secant, tangent, sine! 3 point 1 4 1 5 9!"

There are piphilologists who have written poems which encode 100s of digits. This is an example of constrained writing.

March 14 marks Pi Day which is celebrated by many lovers of π. On July 22, Pi Approximation Day is celebrated (22/7 is a popular approximation of π).

Related articles

External Links

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Pi (letter)

(From Wikipedia, the free Encyclopedia)

Pi (Π π) is the 16th letter of the Greek alphabet and has a numeric value of 80. In words it is pronounced /p/.

The upper-case letter Π is used as a symbol for:

The lower-case letter π is used as a symbol for: See also:

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Pi (movie)

(From Wikipedia, the free Encyclopedia)

π (pronounced, and often written as, Pi) is a 1998 American science fiction film directed by Darren Aronofsky. The film is about an aloof genius who believes that mathematics is the language of nature, and pursues the fundamental formula for it. He finds the golden spiral occurring everywhere, including in an analysis of the stock exchange which he is carrying out. A number of mysterious people become interested in his research, including a Go-playing mathematician who seems his mentor, a woman from a Wall Street firm with access to powerful new computer hardware, and a group of kabbalistic Jews who believe that the Torah, when represented as numbers instead of letters, contains the true name of God.

The film is in monochrome and stars Sean Gullette, Mark Margolis, Ben Shenkman, Pamela Hart, Stephen Pearlman, and Samia Shoaib.

π had an extremely low budget ($60,000), and made huge profits ($3.2 million gross in the U.S.). Darren Aronofsky made the movie Requiem for a Dream after π.

While the film contains several mathematical "goofs", such as claiming that the kabbalists could recite the phonetic equivalents of all 216-digit numbers in only two thousand years, it is notable that Sean Gullette's character pursues a legitimate scientific goal. His belief that diverse systems embodying highly nonlinear dynamics share a unifying pattern is much in the tradition of James Clerk Maxwell, whose equations unified the description of electricity and magnetism, in the process predicting that light is an electromagnetic wave.

π launched the film scoring career of Clint Mansell.

See also

External Links

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Piauí

(From Wikipedia, the free Encyclopedia)

Piauí is one of the states of Brazil, located in the northeastern part of the country, in the arid region of Sertão. It has an area of 250,934 sq. km. and a population of approximately 2,750,000.

Capital: Teresina

Flag:

Other cities include:

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Pion

(From Wikipedia, the free Encyclopedia)

In physics, pion is a shortened form of the name Pi meson; this subatomic particle comes in three forms: the pi-zero (π0), pi-plus (π+) and pi-minus (π-). Pi mesons are the lightest mesons.

Pi mesons have zero spin and are composed of first generation quarks. An up and an anti-down quark compose a pi-plus (π+), while a down and an anti-up quark compose the pi-minus (π-), its antiparticle. Combinations of up and anti-up, or down and anti-down, would both be neutral, but because they have the same quantum numbers are only found in superpositions. The lowest energy superposition is the pi-zero, and it is its own antiparticle.

The pi-plus (π+) and pi-minus (π-) may combine to form an exotic atom called pionium, if they are created close to each other with a small relative momentum.

External Link

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Abbreviations & Acronyms: Pi

The following table is compiled from various sources, across various languages. When English abbreviations or acronyms come from a non-English source, this is noted.
EntrySourceExpressionField

PI

EnglishProduction instructionN/A

PI

FrenchPneumopathies interstitiellesMedicine

PI

GermanProduktivitätsindexMining

PI

ItalianDivisione pianificazione e sviluppo dell'impresaN/A
pionEnglishPi mesonChemistry, Physics

Source: compiled by the editor, based on several corpora (additional references).

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Synonyms: Pi

Synonyms: operative (n), principal investigator (n), private detective (n), private eye (n), private investigator (n), shamus (n), sherlock (n). (additional references)

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Synonyms within Context: Pi

ContextSynonyms within Context (source: adapted from Roget's Thesaurus).

Evidence

Admission; (assent); authority, warrant, credential, diploma, voucher, certificate, doquet, docket; testamur; record; document; pi

Printing

Typography; stereotype, electrotype, aprotype; type, black letter, font, fount; pi, pie; capitals; (letters); brevier, bourgeois, pica;

Source: adapted from Roget's Thesaurus.

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Crosswords: Pi

English words defined with "pi": Pieing. (references)
Specialty definitions using "pi": alpha 1-Antitrypsin ♦ for values of ♦ parameter group identifier ♦ schedule numbers, suitably small ♦ VCC filtering. (references)
Etymologies containing "pi": Pie. (references)
Non-English Usage: "Pi" is also a word in the following languages with English translations in parentheses.

Albanian (boose, booze, bouse, consume, drink, imbibe, liquor, lush, take a drink, take to drink, tipple, tope), Dutch (pi), French (pi), German (pi), Haitian Creole (more), Italian (pi), Samoan (bee, peas), Spanish (pi), Swedish (pi), Welsh (magpie).

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Modern Usage: Pi

DomainUsage

Screenplays

As in the words of Porky pig, pi pi pi pi piss off Lou (Mrs. Doubtfire; writing credit: Randi Mayem Singer)

Clever

Ratio of an igloo's circumference to its diameter: Eskimo Pi. (references; author: unknown)

Movie/TV Titles

Pi li quan (1972)

Ren pi guo zheng xie (1996)

Heng wen dao pi niu wen chai (1995)

Guang Zhou sha ren wang zhi ren pi ri ji (1995)

Lezioni di pi...ano (1995)

Source: compiled by the editor from various references; see credits.

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Commercial Usage: Pi

DomainTitle

Books

  

Periodicals

  

Theater & Movies

  

High Tech

Source: compiled by the editor from various references; see credits.

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Image Slideshow: Pi

Computer Images:
Pi

More pictures...

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Photo Album: Pi

ThumbnailDescription & CreditThumbnailDescription & Credit

Beta Theta Pi House, Amherst College, Mass. Credit: Library of Congress.

Lumber manufacture. Boise Payette Lumber Company, Boise, Idaho. As the rough logs enter the sawmill from the bull chain conveyor they are first sawed into the proper length on this circular power saw. This sawmill at Emmet, Idaho is producing Ponderosa pi. Credit: Library of Congress.

Conversion. Hosiery factory. This mechanic used to tend machines which produced some of America's sheerest hosiery. Today he's working for America's armed forces on these same machines, which are producing mosquito netting for the Army and Navy. In the pi. Credit: Library of Congress.

Margy. "Am I blue? I've invited Margy to the Bita Pi dinner tonight". Credit: Library of Congress.

Source: pictures compiled by the editor from various references; see picture credits.

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Digital Photo Gallery: Pi
 

"Pi 1" by Keith M.
Commentary: "The key of a circle on a digital display."		"Pipi 3" by Ron Dc
Commentary: "A boy got pi."

Source: photographs selected by the editor, with permission from the photographers.

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Non-Fiction Usage: Pi

SubjectTopicQuote

Health

PI diseases are usually inherited. (references)

The exact number of persons with PI is not known. (references)

Some cases of PI are the result of a combined deficiency. (references)

Source: compiled by the editor from ICON Group International, Inc.; see credits.

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Spoken Usage: Pi

SpeakerPhrase(s)

Dennis Miller

Tebbi, the nice man in the New York Yankees turban, told us it'll be ready in the year Pi.

Source: compiled by the editor from various references; see credits.

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Usage Frequency: Pi

"Pi" is generally used as an alphabetical symbol -- approximately 91.87% of the time. "Pi" is used about 614 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted)
Parts of SpeechPercentUsage per
100 Million Words		Rank in English
Alphabetical Symbol91.87%56411,138
Unclassified Items8.13%5048,117
                    Total100.00%614N/A

Source: compiled by the editor from several corpora; see credits.

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Name Usage Frequency: Pi

The following table summarizes the usage of "pi" based on a population census conducted in the United States. Ranks and frequencies are based on all names reported and classified.
NameUsage/GenderUsage per 100
million Persons		Rank in USA
PiLast name13069,127
Source: compiled by the editor from several corpora; see credits.

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Expressions: Pi

Expressions using "pi": pi character ♦ PI disc ♦ pi font ♦ two pi. Additional references.

Hyphenated Usage

Beginning with "pi": Pi-beseth, pi-calculus, pi-dock, Pi-hahiroth, pi-hinkeeeee, Pi-i-i-i-i-i-sssss, pi-jaw, pi-meson, pi-mesons, pi-n, pi-pi-pi-pi-pi, Pi-rho.

Ending with "pi": lifespan-pi, pi-pi-pi-pi-pi, sigma-pi.

Source: compiled by the editor from various references; see credits.

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Frequency of Internet Keywords: Pi

The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com.
 
ExpressionFrequency
per Day		ExpressionFrequency
per Day

seattle pi

1,951

file pi

28

pi

1,585

nu phi pi

28

life of pi

214

pi school

27

magnum pi

193

canon optura pi

25

alpha delta pi

157

pi super

25

pi kappa alpha

123

pi water

23

pi beta phi

108

math pi

23

pi kappa phi

87

pi symbol

23

alpha omicron pi

81

newspaper pi seattle

23

pi the movie

71

pi lambda phi

22

history of pi

65

alpha epsilon pi

21

life pi

60

cala pi

21

beta theta pi

59

beta pi tau

20

delta sigma pi

54

pi engineering

20

digit pi

49

alpha pi sigma

18

kappa delta pi

46

alpha delta pi sorority

17

sigma pi

42

formula pi

17

the number pi

37

calculate pi

17

phi sigma pi

36

life pi review

15

value of pi

35

pi schools.gr

15

day pi

15
Source: compiled by the editor from various references; see credits.

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Modern Translation: Pi

Language Translations for "pi"; alternative meanings/domain in parentheses.

Albanian

  

pigrek, p greke, numri pi, fetar (pious, religious, spiritual). (various references)

   

Arabic 

  

‏مغتبط, ‏متزمت (austere, prim, puritan, puritanical, rigid, rigorous, severe, stick in the mud, strict), ‏متعصب (bigot, bigoted, devout, factional, fanatic, fanatical, fundamentalist, hard liner, illiberal, intolerant, narrow minded, orthodox, prejudiced, sectarian, zealot), ‏سعيد (auspicious, blessed, blissful, blithe, carefree, felicitous, fortuitous, fortunate, gay, glad, happy, happy go lucky, high, in high spirits, joyful, joyous, lucky, merry, pollyanna, providential, thankful, unstressed, upbeat), ‏راض عن نفسه (complacent, puffed up, self-complacent, smug). (various references)

   

Bulgarian 

  

хрисим (amenable, quiet, submissive, tractable), куп размесени букви (pie), гръцката буква пи, набожен (devotional, devout, godly, pious, prayerful, religious), мирен (amicable, halcyon, law abiding, peaceable, peaceful, piping, quiet, restful, still), пи. (various references)

   

Danish

  

pseudo-isotrop skive (PI disc, pseudo-isotropic disc), pion (pi-meson, pion), pi-meson (pi-meson, pion), specialtegn (peculiar, pi character, pi font, sort, special sort). (various references)

   

Dutch

  

pi. (various references)

   

Finnish

  

pseudo-isotrooppinen kiekko (PI disc, pseudo-isotropic disc), erikoismerkki (peculiar, pi character, pi font, sort, special sort). (various references)

   

French

  

pi, satisfait de soi, béat. (various references)

   

German

  

pi (Productivity index). (various references)

   

Greek 

  

πι (course). (various references)

   

Hebrew 

  

אותיות דפוס מעורבבות. (various references)

   

Hungarian

  

pi betû, ludolf-féle szám, ájtatos (devout, godly, religious). (various references)

   

Italian

  

pi. (various references)

   

Japanese Kanji 

  

パール編み (full cup, parentheses, parenthesis, pie, pineapple, pioneer, pioneer spirit, pipe, pipe-line, pipe-organ, piping, purl stitch, tart, tube, vasectomy), 円周率 . (various references)

   

Japanese Katakana 

  

パイ (pie, tart), えんしゅうりつ. (various references)

   

Pig Latin

  

ipay.(various references)

   

Portuguese

  

pio (bird call, bump, cheep, peep, pious, whistle), piedoso (believer, devotional, devout, godly, holy, merciful, pious, prayerful, sainted), devoto (ascetic, devotee, devotional, devout, godly, obedientiary, pious, prayerful, votary). (various references)

   

Romanian

  

sãpunealã (knock, pi-jaw, punishment, roast, soaping, wigging), mustrare (dressing, lash, lecture, pi-jaw, prick, rebuke, remonstrance, reprehension, reprimand, reproach, reproof, row, scolding, slur, snub, trim, trimming, wigging). (various references)

   

Russian 

  

набожный (devotional, devout, godly, pious, prayerful), примерный (exemplary), пи. (various references)

   

Serbo-Croatian

  

pobožan (devout, pious, prayerful, religious, saintlike, sanctimonious), grčko slovo. (various references)

   

Spanish

  

pi, pastel (baked goods, cake, pastel, pasty, pie, tart). (various references)

   

Swedish

  

pi, skenhelig (hypocritical, sanctimonious), hymlande. (various references)

   

Turkish

  

pi sayısı. (various references)

   

Ukrainian

  

удавальник (dissimulator, make believe, pretendant, pretender, shammer), мораль (ethic, ethics, moral, morality), зразковий (banner, classic, exemplary, model, paradigmatic). (various references)

Source: compiled by the editor from various translation references.

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Derivations: Pi

Derivations

Words beginning with "pi": pia, piacular, piaffe, piaffed, piaffer, piaffers, piaffes, piaffing, pial, pian, pianic, pianism, pianisms, pianissimi, pianissimo, pianissimos, pianist, pianistic, pianistically, pianists, piano, pianoforte, pianofortes, pianos, pians, pias, piasaba, piasabas, piasava, piasavas, piassaba, piassabas, piassava, piassavas, piaster, piasters, piastre, piastres, piazza, piazzas, piazze, pibal, pibals, pibroch, pibrochs, pic, pica, picacho, picachos, picador, picadores. (additional references)

Words ending with "pi": campi, carpi, euripi, hippocampi, impi, kepi, metacarpi, octopi, okapi, palpi, pappi, pithecanthropi, platypi, polypi, priapi, principi, rhizopi, scampi, tempi, tipi, topi. (additional references)

Words containing "pi": abapical, accipiter, accipiters, accipitrine, accipitrines, adipic, adrenocorticotropic, adrenocorticotropin, adrenocorticotropins, affenpinscher, affenpinschers, afterpiece, afterpieces, airdropping, allotropic, allotropies, allotypic, allotypically, allotypies, allspice, allspices, alpine, alpinely, alpines, alpinism, alpinisms, alpinist, alpinists, altarpiece, altarpieces, amblyopia, amblyopias, amblyopic, ametropia, ametropias, ametropic, ampicillin, ampicillins, anisometropia, anisometropias, anisometropic, anisotropic, anisotropically, anisotropies, anisotropism, anisotropisms, anopia, anopias, anthropic, anthropical, anticapitalism. (additional references)

Source: compiled by the editor, based on several corpora (additional references).

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Rhyming with "Pi"

# of Phoneme MatchesPronunciationWord(s) rhyming with "pi" (pronounced pī")
2p ī"pie, Pye, spy.

Source: compiled by the editor (additional references); see credits.

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Anagrams: Pi

Scrabble® Enable2K-Verified Anagrams

 Words containing the letters "i-p"
 

+1 letter: dip, gip, hip, imp, kip, lip, nip, phi, pia, pic, pie, pig, pin, pip, pis, pit, piu, pix, poi, psi, rip, sip, tip, yip, zip.

 

+2 letters: blip, chip, clip, dips, dipt, drip, epic, flip, gimp, gips, grip, hips, impi, imps, jimp, kepi, kips, limp, lipa, lipe, lips, lisp, nipa, nips, padi, paid, paik, pail, pain, pair, pein, peri, pfui, phis, phiz, pial, pian, pias, pica, pice, pick, pics, pied, pier, pies, pigs, pika, pike, piki, pile, pili, pill, pily, pima, pimp, pina, pine, ping, pink, pins, pint, piny, pion, pipe, pips, pipy, pirn, pish, piso, piss, pita, pith, pits, pity, pixy, plie, pois, prig, prim, psis, puli, puri, pyic, pyin, quip, ripe, rips, ship, simp, sipe, sips, skip, slip, snip, spic, spik, spin, spit, spiv, tipi, tips, topi, trip, whip, wimp, wipe, wisp, yipe, yips, zips.

Source: compiled by the editor from various references; see credits.

SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro.

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INDEX

1. Definition
2. Synonyms
3. Crosswords
4. Usage: Modern 		5. Usage: Commercial
6. Images: Slideshow
7. Images: Photo Album
8. Images: Digital Art 		9. Quotations: Non-fiction
10. Quotations: Spoken
11. Usage Frequency
12. Names: Frequency 		13. Expressions
14. Expressions: Internet
15. Translations: Modern
16. Abbreviations 		17. Acronyms
18. Derivations
19. Rhymes
20. Anagrams 		21. Bibliography


  

Copyright © Philip M. Parker, INSEAD. Terms of Use.