Dozen
Encyclopedia
A dozen is a grouping of approximately twelve
12 (number)
12 is the natural number following 11 and preceding 13.The word "twelve" is the largest number with a single-morpheme name in English. Etymology suggests that "twelve" arises from the Germanic compound twalif "two-leftover", so a literal translation would yield "two remaining [after having ten...

. The dozen may be one of the earliest primitive groupings, perhaps because there are approximately a dozen cycles of the moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...

or month
Month
A month is a unit of time, used with calendars, which was first used and invented in Mesopotamia, as a natural period related to the motion of the Moon; month and Moon are cognates. The traditional concept arose with the cycle of moon phases; such months are synodic months and last approximately...

s in a cycle of the sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

or year
Year
A year is the orbital period of the Earth moving around the Sun. For an observer on Earth, this corresponds to the period it takes the Sun to complete one course throughout the zodiac along the ecliptic....

. The dozen is convenient because its multiple
Multiple (mathematics)
In mathematics, a multiple is the product of any quantity and an integer. In other words, for the quantities a and b, we say that b is a multiple of a if b = na for some integer n , which is called the multiplier or coefficient. If a is not zero, this is equivalent to saying that b/a is an integer...

s and divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...

s are convenient: 12 = 2 × 2 × 3, 3 × 4 = 2 × 6, 60
60 (number)
60 is the natural number following 59 and preceding 61. Being three times twenty, 60 is called "three score" in some older literature.-In mathematics:...

= 12 × 5, 360
360 (number)
360 or three sixty is the natural number following 359 and preceding 361.-In mathematics:*Divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 and 360. *360 makes a highly composite number...

= 12 × 30
30 (number)
30 is the natural number following 29 and preceding 31.-In mathematics:30 is the sum of the first four squares, which makes it a square pyramidal number.It is a primorial and is the smallest Giuga number....

. The use of twelve as a base number, known as the duodecimal
Duodecimal
The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written as 'A', 'T' or 'X', and the number eleven as 'B' or 'E'...

system (also as dozenal), probably originated in Mesopotamia
Mesopotamia
Mesopotamia is a toponym for the area of the Tigris–Euphrates river system, largely corresponding to modern-day Iraq, northeastern Syria, southeastern Turkey and southwestern Iran.Widely considered to be the cradle of civilization, Bronze Age Mesopotamia included Sumer and the...

(see also sexagesimal). Twelve dozen (122 = 144
144 (number)
144 is the natural number following 143 and preceding 145. 144 is a dozen dozens, or one gross.-In mathematics:It is the twelfth Fibonacci number, and the largest one to also be a square, as the square of 12 , following 89 and preceding 233.144 is the smallest number with exactly 15 divisors.144 is...

, the duodecimal 100) are known as a gross
Gross (unit)
A gross is equal to a dozen dozen, i.e. 12 × 12 = 144.It can be used in duodecimal counting. The use of gross likely originated from the fact that 144 can be counted on the fingers using the fingertips and first two joints of each finger when marked by the thumb of one hand. The other hand...

; and twelve gross (123 = 1,728
1728 (number)
1728 is the natural number following 1727 and preceding 1729. 1728 is a dozen gross, one great gross .-In mathematics:...

, the duodecimal 1,000) are called a great gross, a term most often used when shipping or buying items in bulk. A great hundred, also known as a small gross
Small gross
Archaically, a small gross or short gross is a quantity equal to ten dozen, i.e. 10 × 12 = 120.This number is also known as a great hundred or a duodecimal hundred....

, is 120
120 (number)
120 is the natural number following 119 and preceding 121. 120 was known as "the great hundred", especially prior to the year 1700, from the Teutonic Hundert which equalled 120. The number 100, now known commonly as "one hundred" was then known as "the small hundred". It is also known as...

or ten
10 (number)
10 is an even natural number following 9 and preceding 11.-In mathematics:Ten is a composite number, its proper divisors being , and...

dozen (a dozen for each finger
Finger
A finger is a limb of the human body and a type of digit, an organ of manipulation and sensation found in the hands of humans and other primates....

on both hand
Hand
A hand is a prehensile, multi-fingered extremity located at the end of an arm or forelimb of primates such as humans, chimpanzees, monkeys, and lemurs...

s). A baker's dozen, also known as a long dozen, is thirteen
13 (number)
13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers....

, while a decimal dozen is only ten.

## Etymology

The English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

word dozen comes from the old form of the French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...

word douzaine, meaning "a group of twelve" ("Assemblage de choses de même nature au nombre de douze" - (translation: A group of twelve things of the same nature as defined in the eighth edition of the Dictionnaire de l'Académie française
Dictionnaire de l'Académie française
The Dictionnaire de l'Académie française is the official dictionary of the French language.The Académie française is France's official authority on the usages, vocabulary, and grammar of the French language, although its recommendations carry no legal power...

). This French word is a derivation from the cardinal number
Cardinal number
In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a finite set is a natural number – the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite...

douze ("twelve", from Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

duodĕcim) and the collective
Collective number
In linguistics, singulative number and collective number are terms used when the grammatical number for multiple items is the unmarked form of a noun, and the noun is specially marked to indicate a single item...

suffix
Suffix
In linguistics, a suffix is an affix which is placed after the stem of a word. Common examples are case endings, which indicate the grammatical case of nouns or adjectives, and verb endings, which form the conjugation of verbs...

-aine (from Latin -ēna), a suffix also used to form other words with similar meanings such as quinzaine (a group of fifteen), vingtaine (a group of twenty), centaine (a group of one hundred), etc. These French words have synonymous cognate
Cognate
In linguistics, cognates are words that have a common etymological origin. This learned term derives from the Latin cognatus . Cognates within the same language are called doublets. Strictly speaking, loanwords from another language are usually not meant by the term, e.g...

s in Spanish
Spanish language
Spanish , also known as Castilian , is a Romance language in the Ibero-Romance group that evolved from several languages and dialects in central-northern Iberia around the 9th century and gradually spread with the expansion of the Kingdom of Castile into central and southern Iberia during the...

: docena, quincena, veintena, centena, etc. English dozen, French douzaine, German Dutzend, Dutch dozijn and Spanish docena, are also used as indefinite quantifiers to mean "about twelve" or "many" (as in "a dozen times", "dozens of people").

## Baking

A baker's dozen, devil's dozen, long dozen, or long measure is 13
13 (number)
13 is the natural number after 12 and before 14. It is the smallest number with eight letters in its name spelled out in English. It is also the first of the teens – the numbers 13 through 19 – the ages of teenagers....

, one more than a standard dozen. The oldest known source, but questionable explanation for the expression "baker's dozen" dates to the 13th century in one of the earliest English statute
Statute
A statute is a formal written enactment of a legislative authority that governs a state, city, or county. Typically, statutes command or prohibit something, or declare policy. The word is often used to distinguish law made by legislative bodies from case law, decided by courts, and regulations...

s, instituted during the reign of Henry III
Henry III of England
Henry III was the son and successor of John as King of England, reigning for 56 years from 1216 until his death. His contemporaries knew him as Henry of Winchester. He was the first child king in England since the reign of Æthelred the Unready...

(1216–1272), called the Assize of Bread and Ale
Assize of Bread and Ale
The Assize of Bread and Ale was a 13th-century statute in late medieval English law, which regulated the price, weight and quality of the bread and beer manufactured and sold in towns, villages and hamlets. This statute is usually attributed to act 51 Hen. III, occurring about 1266–1267. It was...

. Bakers who were found to have shortchanged customers (some variations say that they would sell hollow bread) could be subject to severe punishment. To guard against the punishment of losing a hand to an axe, a baker would give 13 for the price of 12, to be certain of not being known as a cheat. Specifically, the practice of baking 13 items for an intended dozen was insurance against "short measure", on the basis that one of the 13 could be lost, eaten, burnt, or ruined in some way, leaving the baker with the original legal dozen. The practice can be seen in the guild
Guild
A guild is an association of craftsmen in a particular trade. The earliest types of guild were formed as confraternities of workers. They were organized in a manner something between a trade union, a cartel, and a secret society...

codes of the Worshipful Company of Bakers
Worshipful Company of Bakers
The Worshipful Company of Bakers is one of the Livery Companies of the City of London. The Bakers' Guild is known to have existed in the twelfth century. From the Corporation of London, the Guild received the power to enforce regulations for baking, known as the Assize of Bread and Ale. The...

in London.
However, there is some doubt over whether this is the real explanation for the expression, because baking 13 instead of 12 units has been good practice all over Europe, not only in England. It also seems unusual that only bakers deliver 13 in a dozen, and not, for example, butchers. An alternative explanation for why specifically bakers deliver 13 in a dozen has been found in the tidy way 13 disks
Disk (mathematics)
In geometry, a disk is the region in a plane bounded by a circle.A disk is said to be closed or open according to whether or not it contains the circle that constitutes its boundary...

In the United States and Canada, a cookie is a small, flat, baked treat, usually containing fat, flour, eggs and sugar. In most English-speaking countries outside North America, the most common word for this is biscuit; in many regions both terms are used, while in others the two words have...

s, biscuit
Biscuit
A biscuit is a baked, edible, and commonly flour-based product. The term is used to apply to two distinctly different products in North America and the Commonwealth Nations....

s, etc.) can pack
Packing problem
Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together , as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues...

a rectangle
Rectangle
In Euclidean plane geometry, a rectangle is any quadrilateral with four right angles. The term "oblong" is occasionally used to refer to a non-square rectangle...

(baking tray) of appropriate proportion
Aspect ratio
The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements,...

s. Packing trays have a 3:2 aspect ratio, and the most efficient two-dimensional array is hexagonal close packing, which has sixfold symmetry, such that each baked item is equidistant from its six nearest neighbours. The corners of a cookie sheet heat up and cool off faster than the edges and interior, so any item placed near a corner will not bake at the same rate as the other items. A 4+5+4 arrangement provides the dense hexagonal packing while avoiding corners, and would have been discovered empirically by bakers with the goal of baking the maximum number per batch with optimal uniformity.

According to the 1811 Dictionary of the Vulgar Tongue, by Capatin Grose, a Baker's Dozen is "Fourteen; that number of rolls being allowed to the purchaser of a dozen".

## Wine

A decimal dozen is a design of carton
Carton
Carton is the name of certain types of containers typically made from paperboard which is also sometimes known as cardboard. Many types of cartons are used in packaging. Sometimes a carton is also called a box.-Folding cartons:...

s for bottled wine
Wine
Wine is an alcoholic beverage, made of fermented fruit juice, usually from grapes. The natural chemical balance of grapes lets them ferment without the addition of sugars, acids, enzymes, or other nutrients. Grape wine is produced by fermenting crushed grapes using various types of yeast. Yeast...

that holds two rows of five bottles, developed by the Helm Wines winery
Winery
A winery is a building or property that produces wine, or a business involved in the production of wine, such as a wine company. Some wine companies own many wineries. Besides wine making equipment, larger wineries may also feature warehouses, bottling lines, laboratories, and large expanses of...

, Canberra
Canberra
Canberra is the capital city of Australia. With a population of over 345,000, it is Australia's largest inland city and the eighth-largest city overall. The city is located at the northern end of the Australian Capital Territory , south-west of Sydney, and north-east of Melbourne...

, Australia
Australia
Australia , officially the Commonwealth of Australia, is a country in the Southern Hemisphere comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands in the Indian and Pacific Oceans. It is the world's sixth-largest country by total area...

, to replace traditional dozen-bottle cartons. The quoted motivation is that demographics reports show that women buy more than 50 percent of wine in Australia. According to the OH&S regulations, a woman should not lift more than 15 kilogram
Kilogram
The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

s (33 lbs), which is only the minimum gross weight of a standard 12-bottle carton, which can weigh up to 20 kg for some types of bottles.

In 2005 it was a nominee for the ACT
Australian Capital Territory
The Australian Capital Territory, often abbreviated ACT, is the capital territory of the Commonwealth of Australia and is the smallest self-governing internal territory...

Occupational Health and Safety Award in the category "Best Solution to an Identified Workplace Health and Safety Issue" for addressing "the manual handling issues by introducing a ten bottle carton in a 2 X 5 configuration".