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Dice

Dice

: For other uses, see either Die or Dice (disambiguation). Dice (disambiguation) A die (Old French de, from Latin datum "something given or played" [http://www.askoxford.com/concise_oed/die_2?view=uk]) is a small polyhedral object (usually a cube) suitable as a gambling device (especially for craps or sic bo). Traditionally, a die is seldom seen alone, rather than as one of a pair of identical dice that are sized to be comfortably rolled or thrown, together, from a user's hand. (The singular word "die" is therefore rare, and treating "dice" as interchangeably singular or plural is not uncommon.) A traditional die is a cube (often with corners slightly rounded), marked on each of its six faces with a different number of circular patches or pits called pips. All of these pips have the same appearance within a pair (or larger set) of dice, and are sized for ease of recognizing the pattern the pips on one face form. The design as a whole is aimed at each die providing one randomly determined integer, in the range from one to six, with each of those values being equally likely. More generally, a variety of analogous devices are often described as dice, but necessarily in a context, or with a word or two preceding "die" or "dice", that avoids the assumption that traditional dice are intended. Such specialized dice may have cubical or other polyhedral shapes, with faces marked with various collections of symbols, and be used to produce other random results than one through six. There are also "loaded" or "crooked" dice (especially otherwise traditional ones), meant to produce skewed or even predictable results, for purposes of deception or amusement.

Ordinary dice

integer The most common dice are small cubes 1 to 2 cm along an edge, whose faces are numbered from one to six (usually by patterns of dots called pips). It is traditional to assign pairs of numbers that total seven to opposite faces (it has been since at least classical antiquity); this implies that at one vertex the faces 1, 2 and 3 intersect. It leaves one other abstract design choice: the faces representing 1, 2 and 3 respectively can be placed in either clockwise or anti-clockwise order about this vertex. Dice are thrown to provide (supposedly uniformly distributed) random numbers for gambling and other games and thus are a type of hardware random number generator. However, because the numbers on toy dice are marked with small indentations, slightly more material is removed from the higher numbered faces. This results in a small bias, and they do not provide fair (uniform) random numbers. Casino dice have markings that are flush with the surface and come very close to providing true uniformly distributed random numbers. Dice are thrown, singly or in groups, from the hand or from a cup or box designed for the purpose, onto a flat surface. The face of each die that is uppermost when it comes to rest provides the value of the throw. A typical dice game today is craps, wherein two dice are thrown at a time, and wagers are made on the total value of up-facing spots on the two dice. They are also frequently used to randomize allowable moves in board games such as Backgammon.

Probability

For a single roll, the probability of rolling each value, 1 through 6, is exactly 1 in 6. For a double roll, however, the total of both rolls is not evenly distributed, but is distributed in a triangular curve, as follows: TOTAL PROBABILITY ----- ----------- 2 1/36 3 2/36 4 3/36 5 4/36 6 5/36 7 6/36 8 5/36 9 4/36 10 3/36 11 2/36 12 1/36 For the total of rolls of three or more dice, the curve becomes more bell-shaped with each additional die (according to the central limit theorem). The probability of rolling the same number repeatedly goes down by 1/6 with each additional die: DICE PROBABILITY ---- ----------- 2 1/6 3 1/36 4 1/216 5 1/1296

History

Dice probably evolved from the ankle bones of hoofed animals (such as oxen), colloquially known as "knucklebones", which are approximately tetrahedral. Even today, dice are sometimes colloquially referred to as "bones", as in "shake them bones". Ivory, bone, wood, metal, and stone materials have been commonly used, though the use of plastics is now nearly universal. It is almost impossible to trace clearly the development of dice as distinguished from knucklebones, on account of the confusing of the two games by the ancient writers. It is certain, however, that both were played in times antecedent to those of which we possess any written records. plastic The fact that dice have been used throughout the Orient from time immemorial, as has been proved by excavations from ancient tombs, seems to point clearly to an Asiatic origin. Dicing is mentioned as an Indian game in the Rig-veda. In its primitive form knucklebones was essentially a game of skill played by women and children. In a derivative form of knucklebones, the four sides of the bones received different values and were counted as with modern dice. Gambling with three or sometimes two dice was a very popular form of amusement in Greece, especially with the upper classes, and was an almost invariable accompaniment to banquets (symposium). The Romans were passionate gamblers, especially in the luxurious days of the Roman Empire, and dicing was a favourite form, though it was forbidden except during the Saturnalia. Horace derided what he presented as a typical youth of the period, who wasted his time amid the dangers of dicing instead of taming his charger and giving himself up to the hardships of the chase. Throwing dice for money was the cause of many special laws in Rome. One of these stated that no suit could be brought by a person who allowed gambling in his house, even if he had been cheated or assaulted. Professional gamblers were common, and some of their loaded dice are preserved in museums. The common public-houses were the resorts of gamblers, and a fresco is extant showing two quarrelling dicers being ejected by the indignant host. Tacitus states that the Germans were passionately fond of dicing, so much so, indeed, that, having lost everything, they would even stake their personal liberty. Centuries later, during the middle ages, dicing became the favourite pastime of the knights, and both dicing schools and guilds of dicers existed. After the downfall of feudalism the famous German mercenaries called landsknechts established a reputation as the most notorious dicing gamblers of their time. Many of the dice of the period were curiously carved in the images of men and beasts. In France both knights and ladies were given to dicing. This persisted through repeated legislation, including interdictions on the part of St. Louis in 1254 and 1256. In Japan, China, Korea, India, and other Asiatic countries, dice have always been popular and are so still. The markings on Chinese dominoes evolved from the markings on dice, taken two at a time.

Loaded dice

A loaded or gaffed die is a die that has been tampered with to land with a selected side facing upwards more often than it would simply by chance. There are methods of creating loaded dice, including having some edges round and other sharp and slightly off square faces. If the dice are not transparent, weights can be added to one side or the other. They can be modified to produce winners ("passers") or losers ("miss-outs"). "Tappers" have a drop of mercury in a reservoir at the center of the cube, with a capillary tube leading to another mercury reservoir at the side of the cube. The load is activated by tapping the die on the table so that the mercury leaves the center and travels to the side. Often one can see the circle of the cut used to remove the face and bury the weight. In a professional die, the weight is inserted in manufacture; in the case of a wooden die, this can be done by carving the die around a heavy inclusion, like a pebble around which a tree has grown. A variable loaded die is hollow with a small weight and a semi-solid substance inside, usually wax, whose melting point is just lower than the temperature of the human body. This allows the cheater to change the loading of the die by breathing on it or holding it firmly in hand, causing the wax to melt and the weight to drift down, making the chosen opposite face more likely to land up. A less common type of variable die can be made by inserting a magnet into the die and embedding a coil of wire in the game table. Then, either leave the current off and let the die roll unchanged or run current through the coil to increase the likelihood that the north side or the south side will land on the bottom depending on the direction of the current. Transparent acetate dice, used in all reputable casinos, are harder to tamper with.

Materials

It is unknown of what material the earliest polyhedral dice were made. A pair of icosahedral (20-sided) dice dating from Roman times are on display at the British Museum. It is possible that polyhedral dice were used by even earlier cultures. Precision casino dice, used for the game of craps, are made from cellulose acetate. These dice may have a polished finish, making them transparent, or a sand finish, making them translucent. While red is the most common color, they are also seen in casinos in green, amber, blue, or other colors. Casino dice have their pips drilled, and then filled flush with a paint of the same specific gravity as the acetate, such that the dice remain in perfect balance. In casino play, a stick of 5 dice are used, all stamped with a matching serial number to prevent a cheat from substituting a die. Polyhedral dice are usually made of plastic, though infrequently metal, wooden, and semi-precious stone dice can be found. Early polyhedral dice were made of a soft plastic that would easily wear as the die was used. Typical wear and tear would gradually round the corners and edges of the die until it was unusable. Modern polyhedral dice are typically made of high-impact plastic and can withstand years of use without visible wear. Lou Zocchi and his company Gamescience not only always guaranteed that their high-impact plastic dice would not wear down the way other companies' dice did, but for years criticized major dice manufacturers for crafting unfair, loaded dice through sloppy polishing techniques and substandard materials. Polyhedral dice can be purchased at most hobby stores in numerous combinations. In the early days of role-playing games, most dice came with the numbers unpainted and players took great care in painting their sets of dice. Many early dice came with two sides with the numbers zero through nine on them; half of the sides had to be painted a contrasting color to signify the "high" side.

Cubical dice with faces representing values other than digits 1 through 6

As noted, the faces of most dice are labelled to using an unbroken series of whole numbers, starting at one (or zero), expressed with either pips or digits. Common exceptions include:
- colour dice (e.g., with the colours of the playing pieces used in a game)
- Poker dice, with the following labels somewhat reminiscent of the names of standard playing cards:
  - Nine (of spades; black)
  - Ten (of diamonds; red)
  - Jack (blue)
  - Queen (blue)
  - King (red)
  - Ace (of clubs; black)
- dice with letters (e.g. in Boggle)
- doubling dice (2, 4, 8, 16, 32, 64)
- average dice (2, 3, 3, 4, 4, 5)
- cheat dice, such as:
  - one face each with two through five, and two with sixes, or
  - for craps, a pair of dice in which one die has five on each face, and its mate has a mixture of twos and sixes, guaranteeing rolls of seven or 11
- so-called "3-sided dice", each a cubical die with each of its faces marked identically to exactly one of the other faces, yielding three equally likely distinguishable outcomes, for example:
  - those (usually abbreviated d3) in some role-playing games, labelled 1, 2, and 3 respectively, or
  - FUDGE dice, with two minus (−) sides, two blank sides, and two plus (+) sides; a throw of n fudge dice yields an integer from −n to n, by reading "−" as "−1" and "+" as "+1" and summing the faces showing.
- random direction dice also known as scatter dice. The dice have arrows on each side, the outcome of a roll is a random direction. Scatter dice are used in tabletop wargames such as Warhammer Fantasy Battle to determine random movements of troops, wind direction or direction of misfired arms.

Non-cubical dice

Warhammer Fantasy Battle Polyhedral dice are dice with more or fewer than six sides. They were once almost exclusively used by fortune-tellers and in other occult practices, but they have become popular lately among players of wargames, trading card games, German-style board games, and role-playing games. Although polyhedral dice are a relative novelty during modern times, some ancient cultures appear to have used them in games (as evidenced by the presence of two icosahedral dice dating from the days of ancient Rome on display in the British Museum). Such dice are typically plastic, and have faces bearing numerals rather than patterns of dots. Reciprocally symmetric numerals are distinguished with a dot in the lower right corner (6. vs 9.) or by being underlined (6 vs 9). Dice with various numbers of faces are often described by their numbers of sides, with a d6 being a six-sided die, a d10 a ten-sided die, and so forth. When more than one die is used, the standard terminology is to have two numbers separated by the 'd' - Number of Dice 'd' Number of sides on each die. Hence 2d6 is simply Two Six-Sided Dice, suitable for games of Monopoly or Craps. The platonic solids are commonly used to make dice of 4, 6, 8, 12, and 20 faces. Other shapes can be found to make dice with 5, 7, 10, 16, 24, 30, 34, 50, or 100 sides, but other than the 10 sided, they are rarely used. (See Zocchihedron.) A large number of different probability distributions can be obtained using these dice in various ways; for example, 10-sided dice (or 20-sided dice labeled with single digits) are often used in pairs to produce a linearly-distributed random percentage. Summing multiple dice approximates a normal distribution (a "bell curve"), while eliminating high or low throws can be used to skew the distribution in various ways. Using these techniques, games can closely approximate the real probability distributions of the events they simulate. There is some controversy over whether manufacturing processes create genuinely "fair" dice (dice that roll with even distributions over their number span). Casino dice are legally required to be fair; those used by all others hold no such requirement. Spherical dice also exist; these function like the plain cubic dice, but have an octahedral internal cavity in which a weight moves which causes them to settle in one of six orientations when rolled. Cowry shells or coins may be used as a kind of two-sided dice ("d2"). (Because of their shape, cowry shells probably do not yield a uniform distribution.)

Standard variations

uniform distribution The most common non-cubical dice — often sold in sets of five or six that are each differently shaped but with the same pair of background and marking colors — include one each of the five Platonic solids, which are highly symmetrical. The six-die versions add the pentagonal trapezohedron, in which the faces (identical to one another as to angles and edge lengths) each have two different lengths of side, and three different sizes of angle; the corners at which multiple faces meet are also of two different kinds.

Rarer variations

Often the names of the dice appear in formulas for calculating game parameters: e.g., hit points. '6d8+10', for example, will yield a number between 16 (6×1+10) and 58 (6×8+10), as it means 'Roll an eight-sided die six times and add ten to the total of all the rolls'. Occasionally they may be written '10×d6+20' or '1d6×10+20'; this means 'roll one six-sided die. Multiply it by ten and add twenty', and avoids boring repetitive dice-rolling at the expense of reducing the number of possible results (i.e., 30, 40, 50, 60, 70, and 80 are the only possible outcomes) compared to rolling the die 10 times (yielding any number between 30 and 80).

Application in role-playing games

trapezohedron The fantasy role-playing game Dungeons & Dragons introduced the use of polyhedral dice during modern times and paved the way for their use in other role-playing games, using 20, 12, 10, 8 and 4 sided dice in addition to the traditional 6 sided die. Players use polyhedral dice together in a number of ways. For example, often a d10 is used in conjunction with a d6 instead of using a d20. If the d6 displays a 1, 2 or 3, the number on the d10 is resolved as 1–10. If the d6 displays a 4, 5 or 6, the number shown on the d10 is resolved to 11-20 ("1" is 11, "2" is 12, etc.). In cases like this, almost any sided die can be used as a "resolver". Two d10 are often used to generate a number between 1 and 100. When tossing these dice, the player indicates which die is "high" (representing the tens position). Dungeons & Dragons

Use of Dice for Divination

Some people believe that dice can be used for divination. Using dice for such a purpose is called cleromancy. A pair of standard 6-sided dice is generally used. Astrological dice are a specialized set of three 12-sided dice for divination, using the concepts of astrology and containing astrological symbols for the planets, the zodiac signs and the astrological houses. The first die represents planets, the Sun, the Moon, and two nodes (North Node and South Node). The second die represents the 12 zodiac signs, and the third represents the 12 houses. In simplified terms, the planets, etc. could represent the 'actor'; the zodiac signs could represent the 'role' being played by the actor; and the house could represent the 'scene' in which the actor plays. Rune dice are a specialized set of dice for divination (runecasting), using the symbols of the runes printed on the dice.

See also


- Fuzzy dice
- Craps - on the casino game.

References


- Persi Diaconis and Joseph B. Keller. "Fair Dice". The American Mathematical Monthly, 96(4):337-339, 1989. (Discussion of dice that are fair "by symmetry" and "by continuity".)
- Bias and Runs in Dice Throwing and Recording: A Few Million Throws. G. R. Iverson. W. H. Longcour, et al. Psychometrika, Vol. 36, No. 1, March 1971
- Knizia, Reiner (1999). Dice Games Properly Explained. Elliot Right Way Books. ISBN 0716021129.

External links


- [http://mathworld.wolfram.com/Dice.html MathWorld: Dice] Analysis of dice probabilities.
- [http://www.maa.org/editorial/mathgames/mathgames_05_16_05.html Fair Dice] is an illustrated [http://www.maa.org/news/mathgames.html Math Games] column about all the possible fair dice, and the mathematical reasons why other shapes are not fair.
- [http://www.personal.psu.edu/users/w/x/wxk116/roma/rbgames.html Roman Board Games] (See, in particular, [http://www.personal.psu.edu/users/w/x/wxk116/roma/tali.html Tali] and [http://www.personal.psu.edu/users/w/x/wxk116/roma/tesserae.html Tesserae].)
- [http://hjem.get2net.dk/Klaudius/Dice.htm Properties of Dice] is a page describing all solids that make for provably fair dice.
- [http://www.openroleplaying.org/tools/dieroller/ Openroleplaying.org's automated Die Roller] - allows rolling any combination of any die using standard RPG 'Dice Equations')
- Category:Dice games Category:Randomness Category:Consumer goods ko:주사위 ja:サイコロ simple:Dice th:ลูกเต๋า

Die

Die may mean:
- Die (manufacturing), any of several material-forming tools
- Die (plural dice), a polyhedral object used in games
- Die, integrated circuit unit resulting from die cutting a wafer
- Die, Drôme, a commune and sous-préfecture of France
- Die, to undergo death (ie:William Li)
- DIE, think tank with full name Deutsches Institut für Entwicklungspolitik or German Development Institute

See also:


- Dye, coloring substance
- Dai people, Chinese ethnic group
- DAI, Distributed artificial intelligence

Dice (disambiguation)

Dice are polyhedral objects used in games. Dice may also mean:
- Dice food, the process of chopping food into small cubes for cooking.
- Die cutting, or dicing, process for integrated circuits.
- Digital Illusions CE (DICE), a Swedish computer game developer.
- Dice coefficient, a correlation coefficient for discrete events

Old French

Old French is a term sometimes used to refer to the langue d'oïl, the continuum of varieties of Romance language spoken in territories corresponding roughly to the northern half of modern France and parts of Belgium and Switzerland during the period roughly from 1000 to 1300 A.D. It was known at the time as the langue d'oïl to distinguish it from the langue d'oc, (also then called Provençal) which bordered these areas to the south. Provençal to Charlemagne; from a manuscript of a chanson de geste.]]

Grammar and phonology

Historical influences

Gaulish

The Gaulish language, a Celtic language, slowly became extinct during the long centuries of Roman domination. A handful of Gaulish words survive in contemporary French: words like chêne, "oak tree", and charrue, "plough", mon, "my", are Gaulish survivals, but fewer than two hundred words of modern French have a Gaulish etymology; Delamarre (2003 pp.389-90) lists 167. Latin was the common language of the western Roman world, and opened up a wider world to its speakers than Gaulish did, so it grew at the expense of Gaulish.

Latin

In one sense, Old French began when the Roman Empire conquered the territory it called Gaul during the conquests of Julius Caesar, which were substantially completed by 51 BC. The Romans introduced the Latin language into southern France starting in around 120 BC, when they occupied southern Gaul during the Punic Wars. Starting during the period when Plautus was writing, the common Latin of the Roman world, the phonological structure of classical Latin began to change, yielding the vulgar Latin that was the common spoken language of the western Roman world. This vulgar Latin began to vary strongly from the classical language in its phonology; spoken Latin, rather than the somewhat artificial literary language of classical Latin, was the ancestor of the Romance languages including Old French. Some Gaulish words influenced Vulgar Latin and thus, not only Old French but also other Romance languages. For example classical latin equus was replaced in comon parlance by vulgar Latin caballus, derived from Gaulish caballos (Delamare 2003 p.96) thus giving Modern French cheval, Italian cavallo and (borrowed from French) English cavalry.

Frankish

The Frankish language had a much larger impact on the vocabulary of Old French as a result of the Frankish conquest of much of the territory of modern France by the Franks during the Migration Period. The current and older names of the language, français, derives from the name of the Franks. A number of other Germanic peoples, including the Burgundians, were active in the territory at that time; the Germanic languages spoken by the Franks, Burgundians, and others were not written languages, and at this remove it is often difficult to identify from which specific Germanic source a given Germanic word in French is derived. Philologists such as Pope (1934) estimate that perhaps fifteen percent of the vocabulary of modern French derives from Germanic sources; this vocabulary includes a large number of common words like haïr, "to hate"; bateau, "boat", and hache, "axe", all derive from Germanic sources. It has been suggested that the passé composé and other compound verbs used in French conjugation are also the result of Germanic influences. It is important to distinguish however words which came from Germanic initially, via Frankish, and those that were introduced later, via the Normans in the 10th century.

Earliest written Old French

The earliest documents said to be in French are the Oaths of Strasbourg, which are treaties and charters entered by king Charles the Bald in 842. These documents are written in a mixture of vulgar Latin and early Romance, and it is hard to determine from the text we have how they were pronounced: :Pro Deo amur et pro christian poblo et nostro commun salvament, d’ist di en avant, in quant Deus savir et podir me dunat, si salvarai eo cist meon fradre Karlo, et in aiudha et in cadhuna cosa. . . ::(For the love of God and for the christian people, and our common salvation, from this day forward, as God will give me the knowledge and the power, I will defend my brother Charles with my help in everything. . .) Beginning with the Capetian dynasty, which was begun by Hugh Capet in 987, the culture of northern France began to develop, and its political ascendency over the southern areas of Aquitaine and Toulouse was slowly but firmly asserted. The current French language, however, did not begin to become the common speech of the entire nation of France until after the French revolution.

From Vulgar Latin to Old French

One profound change that affected French, and every other Romance language, reordered the vowel system of classical Latin. Latin had ten distinct vowels: long and short versions of A, E, I, O, U, and three (or four) diphthongs, AE, OE, AU, and according to some, UI.1 What happened to Vulgar Latin is set forth in the table. Both the diphthongs AE and OE also fell in with /e/. AU was initially retained, and turned into /O/ after the original /O/ fell victim to further changes. Thus, the ten vowel system of Classical Latin, which relied on phonemic vowel length was new-modelled into a system in which vowel length distinctions were suppressed and alterations of vowel quality became phonemic. Because of this change, the stress on accented syllables became much more pronounced in Vulgar Latin than in Classical Latin. This tended to cause unaccented syllables to become less distinct, while working further changes on the sounds of the accented syllables. Old French underwent more thorough alterations of its sound system than did the other Romance languages. Vowel breaking was something that occurred generally in Proto-Western-Romance (here, Proto-Romance), although with different results in each of the daughter languages; Latin FOCU(M) (originally "hearth") becomes Italian fuoco, Spanish fuego, French feu (all meaning "fire"). But in Old French the phenomenon went further than in any other Romance language; of the seven vowels inherited from Latin, only remained essentially unchanged. In stressed syllables:
- The sound of Latin E (short), turning to in Proto-Romance, became ie in Old French: Latin MEL, "honey" > OF miel
- The sound of Latin O (short) > Proto-Romance > OF uo: COR > cuor, "heart"
- Latin Ê > Proto-Romance > OF ei: HABÊRE > aveir, "to have"; this later becomes /oi/ in many words, as in avoir
- Latin Ô > Proto-Romance > OF ou: FLÔRE(M) > flour, "flower"
- Latin > OF , probably through an intervening stage of ; MARE > mer, "sea" This change is found in no other Romance language. Note that Latin AU did not share the fate of or ; Latin AURUM > OF or, "gold": not
- oeur nor
- our. Latin AU must have been retained at the time these changes were affecting Proto-Romance. Changes affecting the consonants were also quite pervasive in Old French. Old French shared with the rest of the Vulgar Latin world the loss of final -M. Since this sound was basic to the Latin noun case system, its loss levelled the distinctions upon which the synthetic Latin syntax relied, and forced the Romance languages to adapt a more analytic syntax based on word order. Old French also dropped many internal consonants when they followed the strongly stressed syllable; Latin PETRA

Modern French

French (French: français) is the third of the Romance languages in terms of number of speakers, after Spanish and Portuguese, being spoken by about 67 million people as a mother tongue, and altogether by some 128 million people, which includes second-language speakers who use French for daily communication. French is thus the 18th most spoken language in the world by number of native speakers, and 9th in terms of daily speakers. It is an official language in 29 countries. It is also an official or administrative language in various communities and organisations (such as the European Union, IOC, United Nations and Universal Postal Union). Before World War II, French was considered the international language, particularly in such fields as diplomacy, trade, shipping, and transportation.

History

The Roman invasion of Gaul

The French language is a Romance language, meaning that it is descended from Latin. Before the Roman invasion of what is modern-day France by Julius Cæsar (58–52 BC), France was inhabited largely by a Celtic people that the Romans referred to as Gauls, although there were also other linguistic/ethnic groups in France at this time, such as the Iberians in southern France and Spain, the Ligurians on the Mediterranean coast, Greek colonies such as Massalia (i.e. present-day Marseille), Phoenician outposts, and the Vascons on the Spanish/French border. Although in the past many Frenchmen liked to refer to their descent from Gallic ancestors (nos ancêtres les Gaulois), perhaps fewer than 200 words with a Celtic etymological origin remain in French today (largely place and plant names and words dealing with rural life and the earth). In the reverse direction, some words for Gallic objects which were new to the Romans and for which there were no words in Latin were imported into Latin – for example, clothing items such as les braies. Latin quickly became the lingua franca of the entire Gallic region for mercantile, official and educational purposes, yet it should be remembered that this was Vulgar Latin, the colloquial dialect spoken by the Roman army and its agents and not the literary dialect of Cicero.

The Franks

From the third century on, Western Europe was invaded by Germanic tribes from the east, and some of these groups settled in Gaul. For the history of the French language, the most important of these groups are the Franks in northern France, the Alemanni in the German/French border, the Burgundians in the Rhone valley and the Visigoths in the Aquitaine region and Spain. These Germanic-speaking groups had a profound effect on the Latin spoken in their respective regions, altering both the pronunciation and the syntax. They also introduced a number of new words: perhaps as much as 15% of modern French comes from Germanic words, including many terms and expressions associated with their social structure and military tactics.

Langue d'Oïl

Linguists typically divide the languages spoken in medieval France into three geographical subgroups: Langue d'oïl and Langue d'oc are the two major groups; the third group, Franco-Provençal, is considered a transitional language between the two other groups. The Oïl–Oc divide is broadly comparable to the divide illustrated by the use of "yes" in English and "aye" in Scots. Langue d'oïl, the languages which use oïl (in modern usage, oui) for "yes", is the language group in the north of France. These languages, like Picard, Walloon, Francien and Norman, were influenced by the Germanic languages spoken by the Frankish invaders. From the time period Clovis I on, the Franks extended their rule over northern Gaul. Over time, the French language developed from either the Oïl language found around Paris (the Francien theory) or from a standard administrative language based on common characteristics found in all Oïl languages (the lingua franca theory). Langue d'oc, the languages which use oc for "yes", is the language group in the south of France and northern Spain. These languages, such as Gascon and Provençal, have relatively little Frankish influence. (Modern French has two words for "yes", oui and si; the latter is used to contradict negative statements. Si derives from Latin sic "thus", and is cognate to the word for "yes" in Spanish, Italian, and Catalan. Oïl/oui derive, according to Larousse, from Latin hoc ille "thus he (did)".)

Other linguistic groups

The early middle ages also saw the influence of other linguistic groups on the dialects of France: From the 5th to the 8th centuries, Celtic-speaking peoples from southwestern Britain (Wales, Cornwall, Devon) travelled across the English Channel, both for reasons of trade and as a result of the Anglo-Saxon invasions of England. They established themselves in Bretagne (Brittany). Their language was a dialect of the Brythonic languages, which has been named Breton in more recent centuries. It is part of the larger Celtic language family, though the modern dialects reflect a noticeable influence from French in their vocabulary. From the 6th to the 7th centuries, the Vascons crossed over the Pyrénées, a mountain range in the south of France. Their presence influenced the Occitan language spoken in southwestern France, resulting in the dialect called Gascon. Scandinavian vikings invaded France from the 9th century onwards and established themselves in what would come to be called Normandie (Normandy). They took up the langue d'oïl spoken there and contributed many words to French related to maritime activities, amongst other things. With their conquest of England in 1066, the Normans brought their language. The dialect that developed there as a language of administration and literature is referred to as Anglo-Norman. Anglo-Norman served as the language of the ruling classes and commerce in England from the time of the conquest until 1362, when the use of English became dominant again. Because of the Norman Conquest, the English language has borrowed a considerable amount of its vocabulary from French. The Arab peoples also supplied many words to French around this time period, including words for luxury goods, spices, trade stuffs, sciences and mathematics.

History of French

For the period up to around 1300, some linguists refer to the oïl languages collectively as Old French (ancien français). The earliest extant text in French is the Oaths of Strasbourg from 842; Old French became a literary language with the chansons de geste that told tales of the paladins of Charlemagne and the heroes of the Crusades. By the Ordinance of Villers-Cotterêts in 1539 King Francis I made French the official language of administration and court proceedings in France, ousting the Latin that had been used before then. With the imposition of a standardised chancery dialect and the loss of the declension system, the dialect is referred to as Middle French (moyen français). Following a period of unification, regulation and purification, the French of the 17th to the 18th centuries is sometimes referred to as Classical French (français classique), although many linguists simply refer to French language from the 17th century to today as Modern French (français moderne). The foundation of the Académie française (French Academy) in 1634 by Cardinal Richelieu created an official body whose goal has been the purification and preservation of the French language. This group of 40 members is known as the Immortals, not, as some erroneously believe, because they are chosen to serve for the extent of their lives (which they are), but because of the inscription engraved on the official seal given to them by their founder Richelieu—"À l'immortalité" ("to the Immortality (of the French language)"). The foundation still exists and contributes to the policing of the language and the adaptation of foreign words and expressions. Some recent modifications include the change from software to logiciel, packet-boat to paquebot, and riding-coat to redingote. The word ordinateur for computer was however not created by the Académie, but by a linguist appointed by IBM (see :fr:ordinateur). From the 17th to the 19th centuries, France was the leading power of continental Europe; thanks to this, together with the influence of the Enlightenment, French was the lingua franca of educated Europe, especially with regards to the arts, literature, and diplomacy; monarchs like Frederick II of Prussia and Catherine the Great of Russia could both speak and write in French. Through the Académie, public education, centuries of official control and the role of media, a unified official French language has been forged, but there remains a great deal of diversity today in terms of regional accents and words. For some critics, the "best" pronunciation of the French language is considered to be the one used in Touraine (around Tours and the Loire River valley), but such value judgments are fraught with problems, and with the ever increasing loss of lifelong attachments to a specific region and the growing importance of the national media, the future of specific "regional" accents is difficult to predict.

Modern issues

There is some debate in today's France about the preservation of the French language and the influence of English (see franglais), especially with regard to international business, the sciences and popular culture. There have been laws (see Toubon law) enacted which require that all print ads and billboards with foreign expressions include a French translation and which require quotas of French-language songs (at least 40%) on the radio. There is also pressure, in differing degrees, from some regions as well as minority political or cultural groups for a measure of recognition and support for their regional languages.

Geographic distribution

regional language
French is an official language in the following countries or parts thereof: La Francophonie is an international organization of French-speaking countries and governments.

Legal status in France

Per the Constitution of France, French is the official language of the Republic since 1792 [http://www.languefrancaise.net/dossiers/dossiers.php?id_dossier=50]. France mandates the use of French in official government publications, public education outside of specific cases (though these dispositions are often ignored) and legal contracts; advertisements must bear a translation of foreign words. See Toubon Law. Contrary to a misunderstanding common in the American and British media, France does not prohibit the use of foreign words in websites or any other private publication, which would anyway contradict constitutional guarantees on freedom of speech. The misunderstanding may have arisen from a similar prohibition in the Canadian province of Quebec which made strict application of the Charter of the French Language between 1977 and 1993, although these regulations addressed language used in advertising and the provision of commercial services offered within the province, not the language of private communication. There exist in addition to French a variety of languages spoken in France by minorities; see Languages of France.

Legal status in Canada

About 12% of the world's francophones are Canadian, and French is one of Canada's two official languages, with English; various provisions of the Canadian Charter of Rights and Freedoms deal with the right of Canadians to access services in English and French all across Canada. By law, the federal government must operate and provide services in both English and French; proceedings of the Parliament of Canada must be translated into both English and French; and all Canadian products must be labelled in both English and French. Overall about 22% of Canadians speak French as a first language and 18% are bilingual. French has been the only official language of Quebec since 1974, although it is commonly (and incorrectly) believed that the designation of French as the sole official language occurred in 1977 with the adoption of the Charter of the French Language (which is popularly referred to as Bill 101). By far the provision of Bill 101 with the most significant impact has been that which mandates French-language education, unless a child's parents or siblings have received the major part of their own education in English within Canada. That provision has reversed a historical trend whereby a large number of immigrant children were being sent to English schools by their parents. In so doing, Bill 101 has greatly contributed to the "visage français" (French face) of Quebec. Other provisions of Bill 101, on the other hand, have been ruled unconstitutional over the years, including those mandating French-only commercial signs, court proceedings, and debates in the legislature. Some of those provisions have remained in effect, for a while, using the constitutional "notwithstanding" clause that permits a non-compliant law to temporarily remain. No "notwithstanding provision" is currently in effect. In 1993 the Charter was changed to allow signage in other languages so long as French is markedly "predominant". The Charter also provides for a measure of access by Anglophones to health and social services in their own language. The only province which has French as an official language is New Brunswick. In Ontario and Manitoba, French does not have full official status, although the provincial governments do provide full French-language services in all communities where significant numbers of francophones live. All of the other provinces do make some effort to accommodate the needs of their francophone citizens, although the level and quality of French-language service varies significantly from province to province.

Legal status in Switzerland

French is an official language in Switzerland. It is spoken in the part of Switzerland called Romandy.

Dialects of French


- Acadian French
- African French
- Belgian French
- Cajun French
- Canadian French
- Cambodian French
- Louisiana Creole French
- français d'Aoste
- français-germanique
- Indian French
- Levantine French
- Maghreb French
- Newfoundland French
- North American French
- Oceanic French
- Quebec French
- South East Asian French
- Swiss French
- West Indian French
- [http://www.linguasphere.org/langues_romanes.pdf linguasphere on Romance languages]

Languages derived from French


- Antillean Creole
- Haitian Creole
- Lanc-Patuá
- Mauritian Creole
- Michif
- Louisiana Creole French
- Réunionese Creole
- Seychellois Creole
- Tay Boi

Sounds

:Main article: French phonology and orthography French pronunciation follows strict rules based on spelling, but French spelling is often based more on history than phonology. The rules for pronunciation vary between dialects, but the standard rules are:
- liaison or linking: Final single consonants, in particular s, x, z, t, d, n and m, are normally silent. (The final letters 'c', 'r', 'f', and 'l' however are normally pronounced.) When the following word begins with a vowel, though, a silent consonant may once again be pronounced, to provide a "link" between the two words and avoid a glottal stop between them. Some liaisons are mandatory, for example the s in les amants or vous avez; some are optional, depending on dialect and register, for example the first s in deux cents euros or euros irlandais; and some are forbidden, for example the s in beaucoup d'hommes aiment. The t of et is never pronounced and the silent final consonant of a noun is only pronounced in the plural and in set phrases like pied-à-terre. Doubling a final consonant and adding a silent e at the end of a word (e.g. Parisien → Parisienne) makes it clearly pronounced, always.
- elision or vowel dropping: Monosyllabic words such as je or que drop their final vowel before another word beginning with a vowel. The missing vowel is replaced by an apostrophe. (e.g. je ai is instead pronounced and spelt → j'ai)
- nasal "n" and "m". When "n" or "m" follows a vowel combination, the "n" and "m" become silent and cause the preceding vowel to become nasalized (i.e. pronounced with the soft palate extended downward so as to allow part of the air to leave through the nostrils). Exceptions are when the "n" or "m" is doubled, or immediately followed by a vowel. The prefixes en- and em- are always nasalized. The rules get more complex than this but may vary between dialects.
- digraphs French does not introduce extra letters or diacritics to specify its large range of vowel sounds and diphthongs, rather it uses specific combinations of vowels, sometimes with following consonants, to show which sound is intended. (See French phonology and orthography or [http://www.languageguide.org/francais/grammar/pronunciation/ French Pronunciation Guide] for more details.)
- accents are used sometimes for pronunciation, sometimes to distinguish similar words, and sometimes for etymology alone.
  - Accents that affect pronunciation:
    - "é", is pronounced instead of the defaults or,
    - "è" (e.g., secrète) means that the vowel is pronounced (as usual),
    - dieresis (e.g. naïve, Noël) as in English, specifies that this vowel is pronounced separately from the preceding one (or following one in some cases), not combined,
    - the "ç" means that the letter c is pronounced in front of A, O, or U. ("c" is otherwise hard before a hard vowel.)
    - The circumflex (e.g. pâté, forêt) shows that an e is pronounced and that an o is pronounced . In some dialects it also signifies a pronunciation of for the letter a, but this differentiation is disappearing. It usually indicates a former long vowel created by the dropping of an "s" from the Latin root (as in English "paste", "forest"),
  - Accents with no pronunciation effect:
    - The circumflex does not affect the pronunciation of the letters i or u, and in most dialects, a as well.
    - All other accents are used only to distinguish similar words or for etymological reasons, as in the case of distinguishing the adverbs là and où ("there", "where") from the article la and the conjunction ou ("the fem. sing.", "or") respectively.

Grammar

:Main article: French grammar French grammar shares several notable features with most other Romance languages, including:
- the loss of Latin's declensions
- only two grammatical genders
- the development of grammatical articles from Latin demonstratives
- new tenses formed from auxiliaries French word order is Subject Verb Object, except when the object is a pronoun, in which case the word order is Subject Object Verb.

Vocabulary

Word origins

The majority of French words derive from vernacular or "vulgar" Latin or were constructed from Latin or Greek roots. There are often pairs of words, one form being popular (noun) and the other one savant (adjective), both originating from Latin. Example:
- brother: frère (brother) / fraternel
- finger: doigt / digital
- faith: foi (faith) / fidèle
- cold: froid / frigide
- eye: œil / oculaire The French words which have developed from Latin are usually less recognisable than Italian words of Latin origin because as French developed into a separate language from Vulgar Latin, the unstressed final syllable of many words was dropped or elided into the following word. It is estimated that 12 percent (4,200) of common French words found in a typical dictionary such as the Petit Larousse or Micro-Robert Plus (35,000 words) are of foreign origin. About 25 percent (1,054) of these foreign words come from English and are fairly recent borrowings. The others are some 707 words from Italian, 550 from ancient Germanic languages, 481 from ancient Gallo-Romance languages, 215 from Arabic, 164 from German, 160 from Celtic languages, 159 from Spanish, 153 from Dutch, 112 from Persian and Sanskrit, 101 from Native American languages, 89 from other Asian languages, 56 from Afro-Asiatic languages, 55 from Slavic languages and Baltic languages, and 144 from other languages (3 percent of the total). Source: Henriette Walter, Gérard Walter, Dictionnaire des mots d'origine étrangère, 1998.

Levels of register

French, like many other languages, possesses a continuum of several levels of register. The colloquial register is used in almost any circumstance of life, and should not be confused with slang or rude talk. Formal French is used in writing or in formal occasions (when people make official speeches or when they are interviewed on television, for instance). Some level of formality is also normally used in classrooms in France, although colloquial French is now spoken by more and more professors with their students. Colloquial French differs from formal French in terms of grammar. For instance, the negation in formal French is "ne... pas", whereas in colloquial French it is simply "... pas", such as "I don't think so", which is "Je ne crois pas" in formal French, and "Je crois pas" in colloquial French. Another example of change in grammar is the way to ask a question: by inverting verb and subject in formal French, or also by using "est-ce que", whereas in colloquial French a question is phrased exactly as an affirmation, with the voice rising in the end. E.g.: "Is he sick?" would be "Est-il malade?" or "Est-ce qu'il est malade?" in formal French, and "Il est malade?" in colloquial French. On the other hand, questions with "est-ce que" are more colloquial than using inversion. Secondly, colloquial French differs from formal French in terms of pronunciation. Some words undergo shortening, or sound change, whereas some syllables are dropped altogether. For instance, "yes" is "oui" in formal French, and becomes "ouais" in colloquial French; "I" is "je" in formal French, but becomes "j' " in colloquial French; so a sentence like "I think he'll come" is "Je pense qu'il viendra" in formal French, and "J'pense qu'i'viendra" in colloquial French. There are many instances of shortening of words, such as "teacher", which is "professeur" in formal French, but becomes "prof'" in colloquial French.

Counting system

The French counting system is partially vigesimal: twenty () is used as a base number in the names of numbers from 70-99. So for example, means 4 times 20, i.e. is the French word for 80, and (literally "sixty-fifteen") means 75. This is comparable to archaic English use of "score", as in "fourscore and seven" (87), or "threescore and ten" (70). Belgian French and Swiss French are different in this respect.

Writing system

French is written using the Latin alphabet, plus five diacritics (the circumflex accent, acute accent, grave accent, diaeresis, and cedilla) and two ligatures (æ, œ). French spelling, like English spelling, tends to preserve obsolete pronunciation rules. This is mainly due to extreme phonetic changes since the Old French period, without a corresponding change in spelling. However, some conscious changes were also made to restore Latin orthography:
- Old French doit > French doigt "finger" (Latin digitum)
- Old French pie > French pied "foot" (Latin pedem) As a result, it is nearly impossible to predict the spelling on the basis of the sound alone. Final consonants are generally silent, except when the following word begins with a vowel. For example, all of these words end in a vowel sound: nez, pied, aller, les, finit, beaux. The same words followed by a vowel, however, may sound the consonants, as they do in these examples: beaux-arts, les amis, pied-à-terre. On the other hand, a given spelling will almost always lead to a predictable sound, and the Académie française works hard to enforce and update this correspondence. In particular, a given vowel combination or diacritic predictably leads to one phoneme. The diacritics have phonetic, semantic, and etymological significance.
- grave accent (à, è, ù): Over a or u, used only to distinguish homophones: à ("to") vs. a ("has"), ou ("or") vs. où ("where"). Over an e, indicates the sound .
- acute accent (é): Over an e, indicates the sound , the ai sound in such words as English hay or neigh. It often indicates the historical deletion of a following consonant (usually an s): écouter < escouter.
- circumflex (â, ê, î, ô û): Over an e or o, indicates the sound or , respectively. Most often indicates the historical deletion of an adjacent letter (usually an s or a vowel): château < castel, fête < feste, sûr < seur, dîner < disner. By extension, it has also come to be used to distinguish homophones: du ("of the") vs. dû (past participle of devoir "to owe"; note that dû is in fact written thus because of a dropped e: deu).
- diaeresis or tréma (ë, ï, ü): Indicates that a vowel is to be pronounced separately from the preceding one: naïve, Noël. Diaeresis on ÿ only occurs in some proper names (such as l'Haÿ-les-Roses) and in modern editions of old French texts. Since the 1990 orthographic rectifications, the diaeresis in words containing guë (such as aiguë or ciguë) was moved onto the u: aigüe, cigüe. Words coming from German retain the old Umlaut if applicable but uses French pronounciation, such as capharnaüm(mess).
- cedilla (ç): Indicates that an etymological c is pronounced when it would otherwise be pronounced /k/. Thus je lance "I throw" (with c = before e), je lançai "I threw" (c would be pronounced before a without the cedilla). The ligature œ is a mandatory contraction of oe in certain words (sœur "sister" , œuvre "work [of art]" , cœur "heart" , cœlacanthe "Coelacanth" ), sometimes in words of Greek origin, spelled with an οι diphthong which became oe in Latin, pronounced in French (and other Romance languages): œsophage , œnologie . It may also appear in œu digraph (or œ alone in œil "eye"), in words that were once written with eu digraph (which could be read or , depending on the word): bœuf "ox" (Old French buef or beuf), mœurs "custom", œil "eye" , etc. In these cases, the Latin etymon must be spelled with an o where the French word has œu: bovem > bœuf, mores > mœurs, oculum > œil. Some attempts have been made to reform French spelling, but few major changes have been made over the last two centuries.

Some common phrases


- French: français ("fran-seh")
- hello: bonjour ("bon-zhoor")
- I love you.: Je t'aime. ("jhe tem")
- My name is _____: Je m'appelle _____ ("jhe-ma-pelle")
- good-bye: au revoir ("o-ruh-vwar")
- please: s'il vous plaît (Literally: if it please you) ("sill voo pleh")
- thank you: merci ("mairr-see")
- you are welcome: de rien (Literally: Of nothing) ("duh ryeh"), je vous en prie, il n'y a pas de quoi (France); bienvenue ("byeh-venuh") (Quebec)
- that one: celui-là ("su-lwee la"), colloq. ("swee la"), or celle-là (feminine) ("cell-la")
- how much?: combien? ("kom-byen")
- English: anglais ("ahng-gleh")
- yes: oui ("wee"), colloq. ouais (seldom written) ("way")
- no: non ("non")
- I am sorry: Je suis désolé(e). (add the "e" if the speaker is feminine); ("zhahn swee deh-zo-leh"), colloq. ("shswee deh-zo-leh"). Pardon ("par-dohn")
- I do not understand: Je ne comprends pas. ("zhuh nuh comprahn pa"), colloq. Je comprends pas (with dropping of "ne") ("shcomprahn pa")
- Where are the toilets?: Où sont les toilettes ? ("oo son leh twa-let")
- Cheers (toast to someone's health): Tchin ("chin"), Santé ("san-teh") or À la vôtre ("a la votr")
- Do you speak English?: Parlez-vous anglais ? ("par-leh voo ang-gleh") OR "Est-ce que vous parlez anglais?" ("voo par-leh ang-leh")
- Excuse me: Excusez-moi. ("eh-skyu-zay mwa")
- Good night: Bonne nuit ("bun nwee")
- Hi!: Salut ! ("sal-oo")
- I am tired: Je suis fatigué(e). (add the "e" if the speaker is feminine) ("jhe swee fah-tee-gay")
- Are you coming?: Venez vous ?, Est-ce que vous venez ? (or with close friends and relatives: tu viens?)
- I am thinking about it: J'y pense. ("jhee pahnss")
- I am going to the grocery store: Je vais à l'épicerie. ("jhe vay a lay-pee-ser-ee")
- We are going to school: On va à l'école. (colloquial) ("ohn va a lay-cohl")
- She is so pretty.: Elle est si jolie. ("el ay see jho-lee")
- our neighbors to the South: Nos voisins du sud ("noh vwah-zen due sued")
- Could you help me?: Pourriez-vous m'aider ? ("poo-ree-ay voo may-day")
- May I help you?: Puis-je vous aider? ("pwee-jha voo zay-day")
- It is the best of worlds: C'est le meilleur des mondes. ("say le may-yuhr day mohnd")
- Go to bed!: Va te coucher ! ("vah te coo-shay")
- I'm watching TV.: Je regarde la télé. ("jhe re-gard lah tay-lay")
- Wikipedia, the free encyclopedia: Wikipédia, l'encyclopédie libre. ("wee-kee-pay-dee-ah, lahns-ee-kloh-pay-dee lee-bruh")
- I am the state.: L'État, c'est moi. ("leh-tah seh-mwa")

See also


- Académie française
- common phrases in different languages
- List of English words of French origin
- List of French phrases
- French in the United States
- French Language Wikipedia
- French phrases used by English speakers
- French proverbs
- Reforms of French orthography
- Morphology of the French verb
- Louchebem
- Verlan
- French Creole languages

External links


-
- [http://www.dicts.info/dictlist1.php?k1=33 All free French dictionaries] Collection of free French dictionaries.
- [http://www.declan-software.com/french French language learning audio software]
- [http://www.window.to/french/ Learn French online]
- [http://www.academie-francaise.fr/ Académie Française]
- [http://french.about.com/library/begin/bl_begin_vocab.htm Beginning French Vocabulary]
- [http://radio-canada.ca/education/francaismicro/ Capsules linguistiques - Radio-Canada.ca]
- [http://www.moelc.moe.edu.sg/french/ Département de Français, Ministry of Education Language Centre, Singapore]
- [http://www.ethnologue.com/show_language.asp?code=fra Ethnologue report for French]
- [http://www.sprachprofi.de.vu/english/f.htm Free online resources for learners]
- [http://www.lexilogos.com/french_language_dictionary.htm French-English : all online dictionaries]
- [http://www.jump-gate.com/languages/french/ French Language Course]
- [http://www.ielanguages.com/french.html French Language Tutorial at ielanguages.com]
- [http://www.intuxication.org/~webtypo/le_francais_facile.htm Le français facile]
- [http://portal.wikinerds.org/rapidfrench How to learn French in 10 months]
- [http://dhost.info/defu/wiki/index.php?id=French_accentuation_rules Basic tips of French accentuation]
- [http://www.languagehelpers.com/words/french/basics.html LanguageHelpers]
- [http://www.lightandmatter.com/french/ Liberté, an online first-year French textbook]
- [http://www.listenandlearn.org/learn/french/index.php Learn French by reading and listening]
- [http://www.how-to-learn-any-language.com/e/languages/french/index.html A profile of the French language]
- [http://dhost.info/defu/wiki/index.php?id=Virtual_French_Keyboard A virtual French keyboard]
- [http://linearb.co.uk:8080/memory/ Searchable French-English dictionary, with example sentences]
- [http://atilf.atilf.fr/ Le Trésor de la Langue Française informatisé] (very comprehensive)
- [http://truckspeak.monsite.wanadoo.fr Truck Drivers' French - English, English - French Dictionary]
- [http://www.loecsen.com/travel/discover_pop.php?lang=en&to_lang=3&learn-French/ Listen to useful French expressions]
- [http://www.FrenchLanguageTips.com/ Learn French Fast & Easy]
- [http://www.wordreference.com/ Wordreference.com dictionary]
- [http://www.my-french-dictionary.com/ My French Picture Dictionary] Category:French language Category:Oïl languages Category:Languages of Belgium Category:Languages of Canada Category:Languages of France Category:Languages of Luxembourg Category:Languages of Switzerland Category:Languages of French Guiana Category:Languages of Morocco Category:Languages of French Polynesia Category:Languages of Wallis and Futuna Category:Languages of New Caledonia Category:Synthetic languages Category:Guttural R als:Französische Sprache zh-min-nan:Hoat-gí ko:프랑스어 ja:フランス語 simple:French language th:ภาษาฝรั่งเศส

Polyhedron

A polyhedron is a geometric shape which in mathematics is defined by three related meanings. In the traditional meaning it is a 3-dimensional polytope, and in a newer meaning that exists alongside the older one it is a bounded or unbounded generalization of a polytope of any dimension. Further generalizing the latter, there are topological polyhedra.

Classical polyhedron

polytope In classical mathematics, a polyhedron (from Greek πολυεδρον, from poly-, stem of πολυς, "many," + -edron, form of εδρον, "base", "seat", or "face") is a three-dimensional shape that is made up of a finite number of polygonal faces which are parts of planes, the faces meet in edges which are straight-line segments, and the edges meet in points called vertices. Cubes, prisms and pyramids are examples of polyhedra. The polyhedron surrounds a bounded volume in three-dimensional space; sometimes this interior volume is considered to be part of the polyhedron. A polyhedron is a three-dimensional analog of a polygon. The general term for polygons, polyhedra and even higher dimensional analogs is polytope. Names of polyhedra by number of faces are tetrahedron, pentahedron, hexahedron, octahedron, decahedron, etc. Such terms are in particular used with "regular" in front or implied (in the five cases in which this is applicable) because for each there are different types which have not much in common except having the same number of faces. For a tetrahedron this applies to a much lesser extent, it is always a triangular pyramid.

Characteristics

A polyhedron is:
- Convex if the line segment joining any two points of the polyhedron is contained in the polyhedron or its interior
- Vertex-uniform if all vertices are the same, in the sense that for any two vertices there exists a symmetry of the polyhedron mapping the first isometrically onto the second
- Edge-uniform if all edges are the same, in the sense that for any two edges there exists a symmetry of the polyhedron mapping the first isometrically onto the second
- Face-uniform if all faces are the same, in the sense that for any two faces there exists a symmetry of the polyhedron mapping the first isometrically onto the second
- Regular if it is vertex-uniform, edge-uniform and face-uniform; this implies that every face is a regular polygon
- Quasi-regular if it is vertex-uniform and edge-uniform but not face-uniform, and every face is a regular polygon
- Semi-regular if it is vertex-uniform but neither edge-uniform nor face-uniform, and every face is a regular polygon
- Uniform if it is vertex-uniform and every face is a regular polygon, i.e. it is regular, quasi-regular, or semi-regular. The Euler characteristic relates the number of edges E, vertices V, and faces F of a simply connected polyhedron: V - E + F = 2.

Uniform polyhedra

As conjectured by H. S. M. Coxeter et al. in 1954 and later confirmed by J. Skilling, there are exactly 75 uniform polyhedra, plus an infinite number of prisms and antiprisms. Uniform polyhedra can be organized as follows:
- 9 regular polyhedra:
  - 5 convex solids: Platonic solids
  - 4 non-convex solids: Kepler-Poinsot solids
- 15 quasi-regular polyhedra:
  - 2 convex solids
  - 13 non-convex solids
- semi-regular polyhedra:
  - Semi-regular convex polyhedra:
    - An infinite number of prism and antiprisms
    - 11 other convex solids
  - 40 semi-regular non-convex polyhedra:
    - 17 stellated Archimedean solids
    - 23 other semi-regular non-convex solids Based on this organisation, except the prisms and antiprisms, there are exactly 13 convex semi-regular and quasi-regular polyhedra; they are called the Archimedean solids. As shown here, there are exactly 53 non-convex semi-regular and quasi-regular polyhedra.

Regular polyhedra

Regular polyhedra are vertex-uniform, edge-uniform and face-uniform -- this implies that every face is a regular polygon.
Platonic solids
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There are exactly five regular convex polyhedra. These have been known since ancient times, and are called the Platonic solids:
- Tetrahedron
- Hexahedron or cube
- Octahedron
- Dodecahedron
- Icosahedron
Kepler-Poinsot solids
250px There are exactly four regular non-convex polyhedra: the Kepler-Poinsot solids:
- Small stellated dodecahedron
- Great stellated dodecahedron
- Great icosahedron
- Great dodecahedron

Quasi-regular polyhedra

Quasi-regular means vertex- and edge-uniform but not face-uniform, and every face is a regular polygon; this implies that there are two "kinds" of faces, and that at every edge one of each meet; also that at every vertex four faces meet: alternatingly two of each kind.
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There are exactly two quasi-regular convex polyhedra; both are also Archimedean solids:
- Cuboctahedron (with triangles and squares)
- Icosidodecahedron (with triangles and pentagons) No other convex edge-uniform polyhedra composed of regular polygons exist than the five regular and two quasi-regular convex polyhedra, so edge uniformity and face regularity with convexity implies vertex-uniformity. (There are two other edge-uniform convex polyhedra, the rhombic dodecahedron and the rhombic triacontahedron, but they are not face-regular and not vertex-uniform. These are the duals of the quasi-regular convex polyhedra, and are both members of the Catalan solids.) There are exactly 13 quasi-regular non-convex polyhedra (Hart):
- Dodecadodecahedron
- Great icosidodecahedron
- 3 triambic polyhedra:
  - Small triambic icosidodecahedron
  - Triambic dodecadodecahedron
  - Great triambic icosidodecahedron
- 9 Hemihedra:
  - Tetrahemihexahedron
  - Octahemioctahedron
  - Cubohemioctahedron
  - Small icosihemidodecahedron
  - Small dodecahemidodecahedron
  - Great dodecahemiicosahedron
  - Small dodecahemiicosahedron
  - Great dodecahemidodecahedron
  - Great icosihemidodecahedron

Semi-regular polyhedra

Semi-regular means vertex-uniform but not edge-uniform. There are infinitely many semi-regular convex polyhedra due to two infinite series:
- Prisms (with 2 n-gons and n squares) and
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- Antiprisms (with 2 n-gons and 2n triangles)
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The others are 11 of the Archimedean solids:
- Truncated cube
- Truncated dodecahedron
- Truncated tetrahedron
- Truncated octahedron
- Truncated icosahedron
- Truncated cuboctahedron
- Truncated icosidodecahedron
- Snub cube or snub cuboctahedron
- Snub dodecahedron or
- Rhombicuboctahedron
- Rhombicosidodecahedron
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The semi-regular non-convex polyhedra include the 17 stellated Archimedean solids:
- 3 have cubic symmetry:
  - Great cubicuboctahedron
  - Cuboctatruncated cuboctahedron or cubitruncated cuboctahedron
  - Quasitruncated hexahedron or stellated truncated cube
- 11 have icosahedral symmetry:
  - Quasitruncated small stellated dodecahedron or small stellated truncated dodecahedron
  - Quasitruncated great stellated dodecahedron or great stellated truncated dodecahedron
  - Great truncated dodecahedron
  - Great truncated icosahedron
  - Rhombidodecadodecahedron
  - Icosidodecatruncated icosidodecahedron
  -
  - Small ditrigonal icosidodecahedron
  -
  - Great ditrigonal icosidodecahedron
  -
  - Great quasitruncated icosidodecahedron or great truncated icosidodecahedron
  - Great dodecicosidodecahedron
  - Great ditrigonal dodecicosidodecahedron
  -
- 3 have the symmetry of the snub dodecahedron:
  - Snub dodecadodecahedron
  - Great inverted snub icosidodecahedron or great vertisnub icosidodecahedron
  - Great inverted retrosnub icosidodecahedron or great retrosnub icosidodecahedron In addition to the 17 stellated Archimedean solids, there are 23 more semi-regular non-convex polyhedra:
- ? have octahedral symmetry:
  - Small cubicuboctahedron
  - Small rhombicube
  - Great rhombicube
  - Great truncated cuboctahedron
- ? have icosahedral symmetry:
  - Rhombicosahedron
  - Small rhombidodecahedron
  - Great rhombidodecahedron
  - Small dodecicosahedron
  - Great dodecicosahedron
  - Small dodecicosidodecahedron
  - Icositruncated dodecadodecahedron
  - Great truncated dodecadodecahedron
  - Vertisnub dodecadodecahedron
  - Icosidodecadodecahedron
  - Snub icosidodecadodecahedron
  - Small dodekic icosidodecahedron ??
  - Great dodekic icosidodecahedron ??
  - Small icosic icosidodecahedron ??
  - Great icosic icosidodecahedron ??
  - Great snub icosidodecahedron
  - Snub disicosidodecahedron
  - Retrosnub disicosidodecahedron
  - Great snub icosidisdodecahedron
  - Great snub disicosidisdodecahedron TODO: Check this list for duplicates/alternate names Given two polyhedra of equal volume, one may ask whether it is then always possible to cut the first into polyhedral pieces which can be reassembled to yield the second polyhedron. This is a version of Hilbert's third problem; the answer is "no", as was shown by Dehn in 1900.

Polyhedron duals

75px For every polyhedron there is a dual polyhedron which can be obtained by connecting the midpoints of the faces. Face-uniformity of a polyhedron corresponds to vertex-uniformity of the dual and conversely, and edge-uniformity of a polyhedron corresponds to edge-uniformity of the dual. Thus the regular polyhedra come in natural pairs: the dodecahedron with the icosahedron, the cube with the octahedron, and the tetrahedron with itself. In most duals of uniform polyhedra, faces are irregular polygons. The exceptions are:
- Cube, which is a special trapezohedron, hence dual to an antiprism (namely the octahedron).
- Triangular dipyramid, the octahedron and the pentagonal dipyramid, which are special bipyramids, hence dual to prisms.
- Icosahedron and Dodecahedron, which are dual to one another.

Quasi-regular duals

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The duals of the quasi-regular polyhedra are edge- and face-uniform. These are, correspondingly:
- Rhombic dodecahedron
- Rhombic triacontahedron and 13 other, nonconvex ones.

Semi-regular duals

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The duals of the semi-regular polyhedra are face-uniform. These are, correspondingly:
- Bipyramids
- trapezohedra
- 11 of the Catalan solids →

Other polyhedra with regular faces

:See main entries: Johnson solid and Deltahedron Norman Johnson sought which non-uniform polyhedra had regular faces. In 1966, he published a list of 92 convex solids, the Johnson solids, and gave them their names and numbers. He did not prove there were only 92, but he did conjecture that there were no others. Victor Zalgaller in 1969 proved that Johnson's list was complete. A deltahedron (plural deltahedra) is a polyhedron whose faces are all equilateral triangles. There are infinitely many deltahedra, but only eight of these are convex:
- 3 regular convex polyhedra (3 of the Platonic solids)
  - Tetrahedron
  - Octahedron
  - Icosahedron
- 5 non-uniform convex polyhedra (5 of the Johnson solids)
  - Triangular dipyramid
  - Pentagonal dipyramid
  - Snub disphenoid
  - Triaugmented triangular prism
  - Gyroelongated square dipyramid With regard to polyhedra whose faces are all squares: if coplanar faces are not allowed, even if they are disconnected, there is only the cube. Otherwise there is also the result of pasting six cubes to the sides of one, all seven of the same size; it has 30 square faces (counting disconnected faces in the same plane as separate). This can be extended in one, two, or three directions: we can consider the union of arbitrarily many copies of these structures, obtained by translations of (expressed in cube sizes) (2,0,0), (0,2,0), and/or (0,0,2), hence with each adjacent pair having one common cube. The result can be any connected set of cubes with positions (a,b,c), with integers a,b,c of which at most one is even. There is no special name for polyhedra whose faces are all equilateral pentagons or pentagrams. There are infinitely many of these, but only one is convex: the dodecahedron. The rest are assembled by (pasting) combinations of the regular polyhedra described earlier: the dodecahedron, the small stellated dodecahedron, the great stellated dodecahedron and the great icosahedron. There exists no polyhedron whose faces are all regular polygons with six or more sides. There exist an infinite number of non-uniform non-convex polyhedra.

General polyhedron

More recently mathematics has defined a polyhedron as a set in real affine (or Euclidean) space of any dimensional n that has flat sides. It could be defined as the union of a finite number of convex polyhedra, where a convex polyhedron is any set that is the intersection of a finite number of half-spaces. It may be bounded or unbounded. In this meaning, a polytope is a bounded polyhedron. All classical polyhedra are general polyhedra, and in addition there are examples like:
- A quadrant in the plane. For instance, the region of the cartesian plane consisting of all points above the horizontal axis and to the right of the vertical axis: . Its sides are the two positive axes.
- An octant in Euclidean 3-space,
- A prism of infinite extent. For instance a doubly-infinite square prism in 3-space, consisting of a square in the xy-plane swept along the z-axis:
- Each cell in a Voronoi tessellation is a convex polyhedron. In the Voronoi tessellation of a set S, the cell A corresponding to a point c∈S is bounded (hence a classical polyhedron) when c lies in the interior of the convex hull of S, and otherwise (when c lies on the boundary of the convex hull of S) A is unbounded.

Topological polyhedron

A topological polyhedron is a topological space given along with a specific decomposition into shapes that are topologically equivalent to convex polytopes and that are attached to each other in a regular way that needs better description.

Relation with graphs

Any polyhedron gives rise to a graph, called skeleton, with corresponding vertices and edges. Thus graph terminology and properties can be applied to polyhedra:
- The Archimedean solids give rise to regular graphs: 7 Archimedean solids are degree 3, 4 solids are degree 4, and the remaining 2 are chiral pairs of degree 5.
- The octahedron gives rise to a strongly regular graph, because adjacent vertices have always two common neighbors, and non-adjacent vertices always four.
- Only the tetrahedron gives rise to a complete graph (K4).
- Due to Steinitz theorem convex polyhedra are in one-to-one correspondence with 3-connected planar graphs.

See also


- Antiprism
- Archimedean solid
- Bipyramid
- Defect
- Deltahedron
- Deltohedron
- M. C. Escher
- Johnson solid
- Kepler-Poinsot solid
- Platonic solid
- Polyhedral compound
- Polyhedron models
- Prism
- Semiregular polyhedra
- Spidron
- Trapezohedron
- Zonohedron
- Overview of many polyhedra, with images

External links


- [http://www.queenhill.demon.co.uk/polyhedra/ Polyhedra Index Page]
- [http://www.software3d.com/Stella.html Stella: Polyhedron Navigator]
- [http://www.mathconsult.ch/showroom/unipoly/ The Uniform Polyhedra]
- [http://www.georgehart.com/virtual-polyhedra/vp.html Virtual Reality Polyhedra] - The Encyclopedia of Polyhedra
- [http://www.korthalsaltes.com/ Paper Models of Polyhedra] Many links
- [http://www.polyedergarten.de/ Paper Models of Uniform (and other) Polyhedra]
- [http://ibiblio.org/e-notes/3Dapp/Convex.htm Interactive 3D polyhedra in Java]
- ko:다면체 ja:多面体

Gambling

:This article is about wagering. For other senses of the word 'gamble', see gamble (disambiguation). Gambling (or betting) is any behavior involving risking money or property (making a wager or placing a stake) on the outcome of a game, contest, or other event in which the outcome of that activity depends partially or totally upon chance or upon one's ability to do something. In extended usage, gambling may also refer to engaging in any high-risk behavior in which decisions occur based upon incomplete knowledge - for example, high-risk stock investments (see speculation), difficult and potentially costly business or non-business ventures, or even personal relationships. Gambling games may predate recorded history, with examples recorded in virtually all of the ancient civilizations.

Legal aspects

Because religious authorities generally frown on gambling to some extent, and because of various perceived social costs, most legal jurisdictions censure gambling to some extent. Islamic nations officially prohibit gambling; most other countries regulate it. In particular, in the majority of circumstances - and perhaps all cases - the law does not recognise wagers as contracts, and views any consequent losses as debts of honour, unenforceable by legal process. Thus organized crime often takes over the enforcement of large gambling debts, sometimes using violent methods. Because contracts of insurance have many features in common with wagers, legislation generally makes a distinction, typically defining any agreement in which either one of the parties has an interest in the outcome bet upon, beyond the specific financial terms, as a contract of insurance. Thus a bet on whether one's house will burn down becomes a contract of insurance, as one has an independent interest in the security of one's home.