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Dozen

A dozen is a unit of quantity representing a group of twelve objects, symbols, or numbers, commonly used in commerce, measurement, and everyday counting.^[1] The term derives from Middle English dozeine, borrowed from Anglo-French duzeine, ultimately tracing back to Latin duodecim ("two" + "ten"), and has been in use since the 14th century to denote exactly twelve items, such as eggs or roses sold by the dozen.^[1] Historically, the dozen emerged as a practical counting unit in ancient civilizations due to twelve's mathematical properties: it is highly divisible (by 1, 2, 3, 4, 6, and 12), facilitating easier fractioning in trade and measurement compared to base-10 systems, which have only four divisors (1, 2, 5, 10).^[2] In ancient Egypt around 1500 B.C., base-12 counting may have arisen from tallying finger joints (excluding the thumb) on one hand, influencing divisions of time like the twelve parts of daylight observed via sundials.^[2] The Romans further embedded the dozen in commerce from the 3rd century B.C., using it for fractional units such as the uncia (1/12 of a libra or as), which shaped later imperial measurements like inches (1/12 of a foot).^[2] During the Middle Ages, European trade under figures like Charlemagne adopted base-12 for efficiency, and it persisted in modern contexts, including timekeeping (12 hours on a clock face) and the 12 lunar cycles approximating a year.^[2] In informal usage, "dozen" can also indicate an indefinitely large but approximate number, as in "dozens of people," reflecting its flexibility beyond strict enumeration.^[1] Additionally, in African American Vernacular English, "the dozens" refers to a ritualized verbal game of trading insults, often about family members, which has influenced hip-hop culture.^[1] Despite the dominance of decimal systems today, advocacy for dozenal (base-12) arithmetic continues through organizations like the Dozenal Society of America, founded in 1944, highlighting its enduring appeal for simplifying calculations.^[2]

Definition and Basic Concepts

Definition

A dozen is a grouping of exactly twelve identical or similar items, objects, or units, serving as a fundamental unit of quantity in everyday counting and measurement.^[1] This unit facilitates the organization of goods into manageable batches, such as produce or merchandise, and is commonly abbreviated as "doz" or "dz."^[3] The dozen originated as a practical unit for counting in batches, predating formal standardization and rooted in early human practices of grouping for trade and daily use.^[4] The term derives from the Latin duodecim, meaning twelve.^[5] In comparison to other traditional grouping units, such as a score (twenty items) or a gross (one hundred forty-four items, equivalent to twelve dozen), the dozen functions as the smallest common batch size, making it particularly suitable for smaller-scale transactions and packaging. Examples of its literal usage include a dozen eggs sold in cartons or a dozen roses arranged in bouquets.^[6]

Notation and Abbreviations

In English, the term "dozen" is commonly abbreviated as "doz." or "dz." in both formal and informal writing, particularly in commercial and inventory contexts where space is limited.^[7]^[8] These abbreviations are often used to denote quantities of twelve items, such as "2 doz. eggs" in retail listings. In other languages, equivalent abbreviations exist for the concept of a dozen. In French, "douzaine" (meaning a group of twelve) is shortened to "douz." or "dz.", as seen in trade documents and product labeling.^[9] In German, "Dutzend" is abbreviated as "Dutz." or "Dtzd.", commonly appearing in inventories and measurement tables.^[10] Numerically, a dozen is represented as 12 items, and in practical notation, it may be written as "1 doz" or "doz 1" in inventories and stock records to indicate one group of twelve.^[11] This shorthand contrasts with more explicit formal notations like "12 pcs" (pieces), which are preferred in precise legal or technical documents to avoid ambiguity, while "doz." suits informal commerce for brevity.^[12] In international trade, the dozen is standardized as a supplementary unit of count under the United Nations Economic Commission for Europe (UNECE) Recommendation No. 20, using the code "DZN" for electronic data interchange and customs declarations.^[13] This code ensures consistency across borders, where a dozen equates to 12 individual units, facilitating global commerce in goods sold by the dozen, such as eggs or baked items.^[14] In the United States, the U.S. Census Bureau also recognizes "DOZ" in trade statistics for conversion purposes.^[11]

Etymology and Historical Development

Linguistic Origins

The word "dozen" entered the English language in the Middle English period around the 14th century, borrowed from Old French dozaine, which denoted a group or set of twelve items. This Old French term derived from doze, the word for the number twelve, ultimately tracing back to Latin duodecim ("twelve"), a compound of duo ("two") and decem ("ten").^[5] The earliest recorded uses of "dozen" in English appear in legal and trade-related texts from approximately 1340–70, such as the alliterative poem Alexander and Dindimus, where it referred to quantities in enumerations.^[15] The Latin duodecim reflects deeper roots in Proto-Indo-European (PIE) counting systems, with duo stemming from the PIE root dwóh₁ (meaning "two"), a fundamental numeral shared across Indo-European languages for denoting duality. Similarly, decem originates from PIE déḱm̥ (meaning "ten"), which likely alluded to the fingers of two hands in early numeral formation. These PIE roots influenced not only Latin but also the broader evolution of number words in Romance and Germanic languages, embedding the concept of twelve as "two tens" in linguistic structures.^[16] Cognates of "dozen" appear in other Romance languages, preserving the Latin heritage. In Spanish, docena ("dozen") evolved from Old Spanish dozena, directly from Latin duodecim via the ordinal form, and is used similarly to denote a set of twelve. Italian dozzina ("dozen") derives from dozza ("twelve"), a Vulgar Latin variant of duodecim, often applied to groupings like eggs or other countable items. These variations highlight how the term spread through medieval European trade and vernaculars, maintaining its core meaning across linguistic boundaries.

Historical Usage in Trade and Measurement

The adoption of the dozen as a unit of count in ancient Mesopotamia is tied to the duodecimal (base-12) system, which complemented the dominant sexagesimal (base-60) framework and enabled efficient arithmetic for trade in grains, textiles, and other goods due to 12's high divisibility by 2, 3, 4, and 6.^[17] This system arose from early numerical practices around 3000 BCE, where merchants used it to tally commodities like barley and wool in cuneiform records, simplifying divisions among partners or laborers without remainders.^[18] In ancient Egypt, base-12 counting, possibly influenced by finger-joint tallying methods dating back to the Old Kingdom (c. 2686–2181 BCE), affected various measurements and divisions, including time observed via sundials.^[19] In medieval European markets, the dozen became a standard for selling countable items like eggs, which were priced and traded at about 1 penny per dozen in late 16th-century England, reflecting its convenience for small-scale farmers and vendors dividing clutches or baskets.^[20] Cloth merchants often bundled bolts or ells in dozens to ease transactions in bustling fairs, while bakers adopted the "baker's dozen" of 13 items—typically loaves or rolls—to exceed the mandated 12 and avoid severe penalties under 13th-century English assize laws regulating short weight or measure in trade.^[21] This practice persisted across continental markets, where the dozen's divisibility supported equitable sharing in guilds and marketplaces from the 12th to 15th centuries. The dozen's role in formal standards is evident in the English Winchester measure, established in 1495 by King Henry VII as a legal benchmark for dry goods like grain to ensure consistent trade volumes until the system's gradual replacement by imperial measures in the 19th century.^[22] These standards, rooted in Anglo-Saxon precedents from Winchester, extended to countable produce until full metrication in Britain during the 1960s–1980s, though remnants lingered in agricultural sales.^[23] In non-metric countries like the United States, the dozen endures in commerce for items such as eggs—routinely packaged and priced per dozen since the 19th century,^[24] as seen in early 20th-century Department of Agriculture records—and baked goods like donuts, sold in dozens to maintain historical packaging efficiencies despite metric adoption elsewhere.^[25] This persistence reflects the unit's practicality in retail produce trade, avoiding the need for decimal reconfiguration in everyday transactions.

Mathematical Properties

Divisibility and Composite Nature

The number 12 is classified as a highly composite number, meaning it possesses more positive divisors than any smaller positive integer.^[26] Specifically, the positive divisors of 12 are 1, 2, 3, 4, 6, and 12, totaling six divisors, which exceeds the count for all integers from 1 to 11 (the maximum being four for numbers like 6, 8, and 10).^[26] This abundance of divisors facilitates practical divisions, such as into halves (6 units), thirds (4 units), quarters (3 units), or sixths (2 units), making 12 an efficient grouping for partitioning quantities without remainders.^[27] The prime factorization of 12 is

12 = [2^2](/page/2_+_2_=_?) \times [3](/page/3)

, which underscores its composite structure with small prime factors that contribute to its high divisor count relative to its magnitude.^[26] This factorization allows for a balanced distribution of factors, enabling multiple ways to express 12 as a product of integers greater than 1, such as $2 \times 6, $3 \times 4, or $2 \times 2 \times 3.^[28] In comparison to other composite numbers, 12 strikes a practical balance: it has more divisors than 6 (divisors: 1, 2, 3, 6) but fewer than 24 (divisors: 1, 2, 3, 4, 6, 8, 12, 24), positioning it as an optimal choice for everyday grouping without excessive complexity.^[26] For instance, a dozen items can be readily divided into 6 pairs for distribution or 4 sets of 3 for balanced sharing, illustrating its utility in scenarios requiring equitable subdivision.^[29] This mathematical convenience historically favored the dozen in trade practices, where easy divisibility simplified transactions and inventory management.^[27]

Applications in Number Systems

The dozenal system, also known as base-12 or duodecimal, serves as an alternative positional numeral system to the more common decimal (base-10) system, utilizing twelve as its radix. In this framework, numbers beyond nine are represented using additional symbols for the values ten and eleven, such as "dek" (often symbolized as X or a rotated 2) and "el" (often symbolized as E or an inverted 3), allowing seamless extension to higher counts where 10_{12} denotes twelve in decimal. This system leverages the composite nature of 12, which has more divisors (1, 2, 3, 4, 6, 12) than 10 (1, 2, 5, 10), facilitating easier division and fraction representation in everyday arithmetic.^[30]^[31] A key advantage of dozenal lies in its superior handling of fractions due to 12's greater divisibility, reducing the occurrence of repeating decimals compared to base-10. For instance, one-third is exactly 0.4_{12} in dozenal (since 4_{12} / 10_{12} = 4/12 = 1/3), whereas in decimal it is the infinite 0.[overline](/page/Overline){3}_{10}. This property minimizes computational overhead in divisions by 2, 3, 4, and 6, making dozenal theoretically more efficient for applications involving partitioning or modular operations.^[32]^[33] Historical advocacy for the dozenal system dates to the 19th century, when philosopher Herbert Spencer argued against the metric system's decimal basis, promoting base-12 for its practical divisibility in measurements and trade, as outlined in his 1896 essays reprinted in Popular Science Monthly. Spencer's influence helped lay groundwork for later organizations, culminating in the founding of the Dozenal Society of America (DSA) in 1944, initially as the Duodecimal Society of America, to research and promote base-12 numeration. The DSA continues to publish resources demonstrating dozenal's computational benefits, such as simplified multiplication tables.^[34]^[35] In modern contexts, dozenal remains rare in mainstream computing, where binary and hexadecimal dominate due to hardware alignment. Enthusiast communities, including the DSA, have developed dozenal-based games like custom card decks and board games to illustrate its arithmetic ease, as well as software tools for dozenal arithmetic, though adoption is limited to educational and recreational settings.^[36]

Cultural and Symbolic Significance

In Religion and Mythology

In Christianity, the number 12 symbolizes completeness and divine order, prominently featured in key scriptural narratives. Jesus selected twelve apostles—Simon Peter, Andrew, James, John, Philip, Bartholomew, Thomas, Matthew, James son of Alphaeus, Thaddaeus, Simon the Zealot, and Judas Iscariot—to serve as his closest disciples and the foundation of the early church.^[37] This choice echoes the twelve tribes of Israel, descending from Jacob's sons—Reuben, Simeon, Levi, Judah, Dan, Naphtali, Gad, Asher, Issachar, Zebulun, Joseph, and Benjamin—which represent the covenant community in the Hebrew Bible.^[38] In eschatological imagery, the Book of Revelation depicts the New Jerusalem with a high wall featuring twelve gates, each guarded by an angel and inscribed with the names of Israel's twelve tribes, signifying eternal inclusion and protection.^[39] In Islam, 12 carries profound theological weight, particularly in Shia tradition and calendrical structure. Shia Muslims revere the Twelve Imams as infallible successors to Prophet Muhammad, starting with Ali ibn Abi Talib and culminating in Muhammad al-Mahdi, whom they believe is in occultation and will return as the awaited savior; this doctrine underscores spiritual guidance and justice post-prophecy.^[40] The Quran establishes the Islamic lunar calendar with exactly twelve months, fixed since creation, of which four—Dhul-Qa'dah, Dhul-Hijjah, Muharram, and Rajab—are sacred, prohibiting warfare to emphasize piety and reflection.^[41] Ancient Greek mythology elevates 12 as a marker of cosmic harmony and heroic endeavor. The Twelve Olympians—Zeus, Hera, Poseidon, Demeter, Athena, Apollo, Artemis, Ares, Aphrodite, Hephaestus, Hermes, and either Hestia or Dionysus—constitute the principal deities ruling from Mount Olympus, embodying dominion over natural and human realms as described in Hesiod's Theogony.^[42] The demigod Heracles (Hercules in Roman tradition) atoned for his sins through twelve divinely imposed labors, including slaying the Nemean Lion, destroying the Lernaean Hydra, and capturing Cerberus, trials that tested his prowess and affirmed his path to apotheosis, as detailed in Apollodorus' Library. The zodiac's division into twelve signs—Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces—originates from Babylonian astronomy around the 5th century BCE, where the ecliptic was segmented into equal 30-degree portions for celestial tracking, later integrated into Greek and global astrological systems to interpret human fate through stellar influences.^[43] This framework's symbolic completeness, rooted in 12's high divisibility, permeates mythic and spiritual cosmologies across cultures.

Idiomatic Expressions

The phrase "half a dozen" denotes exactly six items, representing half of a standard dozen of twelve, and is often employed for rhetorical emphasis in everyday language, such as "she bought half a dozen eggs."^[5] This usage stems from the collective sense of "dozen" as a grouping of twelve, with the earliest recorded idiomatic extension in phrases like "six of one and half a dozen of the other," meaning two options that are equivalent and make no difference, appearing in English by 1833.^[44] A "baker's dozen" refers to thirteen items rather than the usual twelve, a practice originating in medieval England where bakers added an extra loaf—known as the "in-bread" or "vantage loaf"—to customer orders to avoid severe penalties for underweight goods under the Assize of Bread and Ale, a regulation revived in 1266 during the reign of Henry III and enforced by guilds like the Worshipful Company of Bakers.^[45] The term first appears in print in 1599 in John Cooke's play Tu Quoque, reflecting the longstanding custom among bakers to ensure compliance with weight laws that could result in fines, public pillorying, or flogging, as documented in a 1477 case involving baker John Mundew.^[45] The expression "dozens of" conveys an approximate large quantity, emphasizing abundance without specifying an exact number, as in "dozens of books lined the shelves."^[46] This idiomatic shift from the literal grouping of twelve to a sense of multiplicity evolved in English by the 19th century, building on the word's historical use for collections and appearing in modern contexts to denote "very many," such as "dozens of homes were affected by the storm."^[1] "A dime a dozen" describes something commonplace, abundant, and thus of little value or uniqueness, originating in the United States after the introduction of the dime coin in 1796, when merchants advertised bulk goods—like eggs or produce—at this low price of ten cents for twelve items to attract buyers. The phrase gained popularity in the 20th century, as seen in early 20th-century American print, to highlight oversupply, for example, "talented singers are a dime a dozen in this city." The "dirty dozen" signifies a group of twelve individuals considered undesirable, troublesome, or villainous, a term coined in the title of E.M. Nathanson's 1965 novel The Dirty Dozen and popularized by Robert Aldrich's 1967 film adaptation, which depicted a squad of military convicts on a suicide mission during World War II.^[47] Since then, the phrase has entered broader idiom to label any set of twelve problematic entities, such as in environmental contexts referring to persistent organic pollutants targeted by the United Nations in 1995.^[48]

Uses in Various Fields

In Time and Calendar

The division of the day into 12 hours on analog clocks traces its origins to ancient Egyptian timekeeping practices around 1500 BCE, where daylight and nighttime were each divided into 12 parts using sundials and observations of decans (groups of stars), forming a 24-hour day. This structure was later influenced by the Babylonian sexagesimal (base-60) system, which subdivided hours into 60 minutes and seconds, facilitating the AM/PM format still used today. This division simplified the tracking of daylight and nighttime periods, building on the use of 12 as a highly divisible number for temporal measurements.^[49]^[50]^[51]^[52]^[53] In calendrical systems, the 12-month structure of the Gregorian calendar approximates the solar year of approximately 365.25 days, providing a practical division that aligns agricultural and seasonal cycles with human activity. This format evolved from earlier Roman traditions, where King Numa Pompilius around 713 BCE reformed the calendar to include 12 lunar months of 29 or 30 days each, totaling about 355 days, to better reflect lunar phases while attempting solar synchronization. [Julius Caesar](/page/Julius Caesar) further adjusted this in 45 BCE through the Julian reform, establishing fixed month lengths totaling 365 days with a leap year every four years, directly influencing the modern 12-month framework.^[54]^[55]^[56] Culturally, the dozen manifests in temporal festivals such as the 12 Days of Christmas, spanning from December 25 to January 6, commemorating the period from Jesus' birth to the arrival of the Magi on Epiphany, a tradition rooted in early Christian adaptations of Roman and pre-Christian winter celebrations. Similar 12-day observances appear in various traditions, including ancient Mesopotamian festivals honoring deities through extended ritual periods that marked seasonal transitions.^[57]^[58]

In Measurements and Standards

In the imperial system of measurement, the foot is standardized as 12 inches, a subdivision that originated from the Roman foot (pes) divided into 12 unciae, which was adopted and adapted in medieval England for its practicality in everyday and trade measurements. This base-12 structure facilitated easy divisions—such as halves (6 inches), thirds (4 inches), and quarters (3 inches)—making it suitable for constructing tools, buildings, and land surveys without complex fractions. The system was formalized in the British Weights and Measures Act of 1824, establishing the imperial foot as a legal standard that influenced global practices in non-metric countries.^[59]^[60] For weighing precious metals and gemstones, the troy system defines the pound as 12 troy ounces, distinct from the 16-ounce avoirdupois pound used for general commodities; this 12-ounce structure dates to medieval European markets, particularly in Troyes, France, where it supported fair trade in high-value goods by aligning with duodecimal counting conventions. The troy ounce, approximately 31.1035 grams, remains the international standard for gold, silver, and platinum, retained in modern assay offices.^[61]^[62] In scientific education, particularly chemistry, the dozen serves as an analogy for the mole concept, where a gross (12 dozens or 144 units) illustrates counting vast quantities of particles, much like Avogadro's number (6.022 × 10^{23}) defines the entities in one mole of a substance. This pedagogical tool helps students grasp molar mass and stoichiometry by comparing it to familiar groupings, such as a dozen molecules versus Avogadro's number of atoms, with approximations like 6 × 10^{23} sometimes used in introductory contexts to emphasize scale without full precision.^[63]^[64]^[65] Despite the global shift to the metric system, the dozen persists in contemporary packaging standards for its efficiency and historical inertia from trade practices, as seen in cases of 12 wine or beer bottles that fit standard crates (three rows of four) or cartons of a dozen eggs designed for protection and transport. These conventions endure in both metric and imperial nations, prioritizing logistical compatibility over decimal uniformity.^[66]^[67]

References

[1]
Definition of DOZEN
### Extracted Definition of 'Dozen'
[2]
[PDF] A look into the mystical properties of the dozenal counting system
Oct 11, 2024 · The Roman fractional system was derived from the units of measure for weight and land. The unica was the basic unit of weight; twelve unica ...
[3]
Dozen - Math.net
A dozen (doz or dz) is a set (or group) of 12 items. Groupings of twelve are thought to be one of the earliest primitive groupings (eg 12 months in a year).
[4]
Dozen | Definition & Meaning - The Story of Mathematics
In conclusion, the term “a dozen” refers to a measurement unit that is equal to 12 objects. Many ancient cultures employed the number 12 as the basis for ...
[5]
Dozen - Etymology, Origin & Meaning
Originating c.1300 from Old French dozaine, meaning "a collection of twelve," derived from Latin duodecim ("twelve") combining duo ("two") and decem ...
[6]
What Is a Dozen? Definition, Unit, Examples, Facts - SplashLearn
A dozen is one of the oldest units of measurement. A dozen is a grouping of twelve objects, shapes, or numbers. It is abbreviated as doz or dz. The dozen unit ...
[7]
DOZEN | definition in the Cambridge English Dictionary
dozen | Business English ( abbreviation doz.) a group of twelve things: Most people know only a few big-name insurers but there are about two dozen.
[8]
Abbreviation for dozen | Learn English - Preply
Sep 10, 2016 · The abbreviation of 'dozen' in English is 'dz', both letters in lowecase. I suggest you look up www.merriam-webster.com whenever you need to learn about word ...A dime a dozenDime a dozenMore results from preply.com
[9]
dozen - English-French Dictionary - WordReference.com
written, abbreviation (dozen) (douzaine), douz., dz ... Le prix pour une demi-douzaine de petits pains est de trois et de cinq dollars pour une douzaine.
[10]
German-English Glossary of Popular German Abbreviations
Feb 27, 2021 · German (adj.) Dtzd. Dutzend, dozen. DVU, Deutsche Volksunion, German People's Union. D-Zug, Direkt-Zug, fast, through train (stops only in ...
[11]
List of German abbreviations - Wikipedia
List of German abbreviations ; dt. deutsch, German ; Dtzd. Dutzend, dozen ; e.h., ehrenhalber, hon., honorary ; ehem. ehemals/ehemalig, formerly/former ...
[12]
Conversion Tables and Units of Quantity - U.S. Census Bureau
Conversion Tables ; Dozen (DOZ), Gross (GR), 0.08333 ; Dozen (DOZ), Thousand (THS), 0.0120 ; Dozen (DOZ), Number (NO), 12.00 ; Dozen pair (DPR), Dozen (DOZ), 2.000.Missing: ISO | Show results with:ISO
[13]
[PDF] Abbreviation / symbol Meaning $ Canadian dollars $/doz Canadian ...
The following table lists symbols and abbreviations with their corresponding meaning which may be found throughout the Customs Tariff. Abbreviation / symbol.
[14]
[PDF] UNECE - Annex II (Informative) Units of Measure: Code elements ...
20 - Units of Measure used in International Trade. Page 1/57. The table column ... A unit of count defining the number of rolls, expressed in twelve roll units.
[15]
Units of measurement codes - Clover Docs
The following table lists the Unit of Measurement codes that are used for international trade. ... Dozen, DZN. Dozenpacks, DZP. Dozen pairs, DZR. Dozen pieces ...
[16]
dozen, n. meanings, etymology and more - Oxford English Dictionary
The earliest known use of the noun dozen is in the Middle English period (1150—1500). OED's earliest evidence for dozen is from around 1340–70, in Alexander and ...
[17]
Two - Etymology, Origin & Meaning
From Old English "twa" (feminine/neuter), meaning the number one more than one; "two" denotes the numeral 2 and its symbol.
[18]
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The combination of the duodecimal system (base 12) and the base. 10 system leads naturally to a base 60 system. Moreover, duodeci- mal systems have their ...
[19]
World of Patterns - Project MUSE
This “duodecimal system” is ... This property facilitated all kinds of arithmetic operations that were necessary for the growing trade in Mesopotamia.
[20]
[PDF] A look into the mystical properties of the dozenal counting system
Oct 11, 2024 · It is also believed the Egyptians counted to twelve using the number of finger joints on one hand (excluding the thumb). Between the fourth and ...
[21]
List of price of medieval items
Retainers could get money, but they would also get food, lodging, weapons (sometimes), and cloth. ... Dozen Eggs 1d " " " Goose (in London) 6d (legal) 7d ...
[22]
Why Is a Baker's Dozen 13? | Britannica
There are a few theories as to why a baker's dozen became 13, but the most widely accepted one has to do with avoiding a beating.Missing: European markets cloth
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Oct 30, 2025 · Early royal standards established to enforce uniformity took the name Winchester, after the ancient capital of Britain, where the 10th-century ...
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Weights and Measures | Hampshire Cultural Trust Online Collections
Winchester measure, used for grains, Troy weight for precious metals, and Avoirdupois weight for goods, were used for trade. Winchester measure was used until ...
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Spotlight: Eggs through the Ages - The Unwritten Record
Mar 25, 2016 · Check out the story of eggs, as told by these 1920's through the 1950's images from the Department of Agriculture.
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Highly Composite Number -- from Wolfram MathWorld
Highly composite numbers are numbers such that divisor function d(n)=sigma_0(n) (i.e., the number of divisors of n) is greater than for any smaller n.
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Do You Know What a Dozen Is? - Smartick
Oct 21, 2019 · A dozen is twelve units of something in a collection together. So we can have dozens of things, for example, twelve eggs are a dozen eggs.
[28]
Highly Composite Numbers - GeeksforGeeks
Jul 15, 2025 · A number N is highly composite if it has more divisors than any smaller numbers than N. Few Highly composite numbers are: 1, 2, 4, 6, 12, 24, 36, 48, 60, 120.
[29]
Quantity Converter - Check How Much Is a Dozen - Omni Calculator
Originating in Mesopotamia, a dozen is one of the oldest grouping measures. It's a convenient number as it has many divisors (1,2,3,4,6,12). The dozen ...
[30]
[PDF] Manual Dozenal System
Dozenal is counting numbers by twelves, rather than tens, also known as base twelve. It uses X for ten, E for eleven, and 10 for a dozen.Missing: games | Show results with:games
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The base-12 number system composed of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B. Such a system has been advocated by no less than Herbert Spencer.
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Why We Should Use Base-12 Instead Of Base-10? - ScienceABC
Jun 16, 2018 · The decimal system is favored because we have ten fingers. However, the dozenal system would fare much better. It is more divisible, ...
[33]
Duodecimal: The Base-12 Counting System
Duodecimal (or dozenal) is a counting system based on the number 12, and it has some advantages over the base-10 decimal method of counting. One of them is ...
[34]
Against the Metric System - Dozenal Society of America
Written by Herbert Spencer during one of the earlier pushes toward the metric system in Britain, this piece attacks the metric system on a number of grounds. ...Missing: advocacy | Show results with:advocacy
[35]
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The Dozenal Society of America is an international non-profit dedicated to researching, using, and teaching about dozenals (duodecimals) and other ...
[36]
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The Duodecimal Bulletin is an official publication of the Dozenal Society of America, which researches and educates about base twelve.<|separator|>
[37]
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There are a dozen and one cards in each suit. I would be interested in seeing your card game. The card game goes like this. ***.
[38]
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This article is in reference to the question that: Where did the twelve Imams (as) come from and why should the number of Imams be twelve and twelve only?
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There were twelve principal deities in the Greek pantheon. Foremost was Zeus, the sky god and father of the gods, to whom the ox and the oak tree were sacred; ...
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The earliest records we have of such a system seem to have been left by the Babylonians, or Sumerians, though there are theories that it came from a race ...
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Six - Etymology, Origin & Meaning
Six of one and half-a-dozen of the other "little difference" is recorded from 1833. Six-figure (adj.) in reference to hundreds of thousands (of dollars, etc ...Missing: idiom | Show results with:idiom
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Baker's Dozen - Meaning & Origin Of The Phrase
What's the origin of the phrase 'Baker's dozen'?. It's widely believed that this phrase originated from the practice of medieval English bakers giving an extra ...
[47]
dozen noun - Definition, pictures, pronunciation and usage notes
dozens of something I've been there dozens of times. · We interviewed dozens and dozens of people. · in dozens They arrived in dozens (= in large numbers).
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The Dirty Dozen (1967) - Turner Classic Movies - TCM
Based on the novel The Dirty Dozen by E. M. Nathanson (New York, 1965). Technical Specs. Duration. 2h 29m. Sound. Stereo. Color.Missing: origin | Show results with:origin
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Persistent Organic Pollutants (POPs) and Pesticides - UNEP
In 1995. the United Nations Environment Programme expanded its research and investigation on POPs with an initial focus on what became known as the “Dirty Dozen ...
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[PDF] Egyptian and Babylonian mathematics
The Babylonians used a 12 hour clock, with 60 minute hours. 3. The base 60 provided a convenient way to express fractions from a variety of systems as may ...Missing: influence | Show results with:influence
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A Brief History of Time(Keeping) – Science Technology and Society ...
The concept of the twelve-hour day and twelve month year originated from Babylonian culture, which associated the number twelve with the mystical or the divine.
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Roman Calendar
According to Livy, it was Numa Pompilius, the second king of Rome (715–673 BC), who divided the year into twelve lunar months (History of Rome, I.19). Fifty ...<|control11|><|separator|>
[53]
Lecture 11: The Calendar
Sep 29, 2007 · Julius Caesar asked the Alexandrine astronomer Sosigenes to reform the Roman calendar. He started with the solar year of 365.25d: Year divided ...
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Chronology | Gregorian Calendar - The Galileo Project
The year was made up of twelve months of thirty days each, and five days were added at the end. Since this meant an error of about 1/4 day per year, the ...
[55]
Who arrives on the 12th day of Christmas? Three Wise Men, of course
Jan 6, 2014 · The Kings (Melchior from Europe, Caspar from Arabia, and Balthazar from Africa) arrived twelve days after Jesus' birth.
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Christmas Origin | Celebrating Immigration
With respect to connections to the most ancient Pagan groups, Mesopotamians held a 4,000 year old, 12 day festival called Zagmuth for their prime god, Marduk.
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[PDF] History of the Measurement of Length - UChicago Library
The foot unit passed to Rome and so to Britain where its division of twelfths or "unciae became "inches". In Britain the Roman Foot became merged with the Anglo ...
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[PDF] units and systems of weights and measures their origin ... - GovInfo
and Romans. I. 2. Page 3. The Roman foot was divided into both 12 unciae (inches) and 16 digits. The Romans also introduced the mile of 1. 000* paces or double ...
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Early Modern Measurements - Folgerpedia
Nov 2, 2020 · Dry Amounts, Money, and Weight ; pounds (Troy): 12 ounces ; pounds (Apothecaries') ; pounds (Avoirdupois) ; pennyweight: a Troy unit containing 24 ...
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Troy Ounces: The Pound Connection - University Innovation Hub
May 29, 2025 · One troy pound (lb t) is equal to 12 troy ounces. This means that the troy pound is essentially a larger unit of the troy ounce, allowing for ...
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Redefining the Mole - inChemistry - American Chemical Society
May 20, 2019 · But other numbers have no errors associated with them: A pair is 2, a dozen is 12, and a gross is 144. What if Avogadro's number could be ...
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Analogies
A mole (6.02 x 1023) is a counting number like dozen (12), gross (144), ream (500), etc. used to count objects such as eggs, pencils, or sheets of paper ...
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Stoich8
Avogadro's number is equal to 6.02 x 1023 to three significant figures. So, a mole of something, not unlike a dozen, baker's dozen, or gross, refers to a ...
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How Many Bottles Are In A Case Of Wine? - Tasting Table
Oct 20, 2024 · Although some believe the number twelve was chosen for symbolic reasons, it's likely because three rows of four bottles fit in a crate that's ...
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history notes--eggs - The Food Timeline
The price of eggs was about 1s.1d. a dozen in the late 1580s, and 62 per cent higher by 1617-21." ---Prices, Food and Wages in Scotland 1550 ...