Thirteen items in a rectangular space, 3+2+3+2+3 arrangement with aspect ratio near 3:2

Thirteen items in a rectangular space, 4+5+4 arrangement with aspect ratio near 11:6

A baker's dozen, also known as a long dozen, is 13, one more than a proper dozen. The aspect ratio of a Shape is the ratio of its longer Dimension to its shorter dimension 45 ( forty-five) is the Natural number following 44 and followed by 46. Dozen is another word for the Number twelve. The dozen may be one of the earliest primitive groupings perhaps because there are approximately a dozen cycles of the The expression found its genesis in 13th-century England. England is a Country which is part of the United Kingdom. Its inhabitants account for more than 83% of the total UK population whilst its mainland

It is also known as Devil's dozen, because 13 is considered an unlucky number. Triskaidekaphobia (from Greek tris=three kai=and deka=ten is an irrational fear of the number 13; it is a Superstition and related to a specific fear

Origin

The oldest known source and most probable origin for the expression "baker's dozen" dates to the 13th century in one of the earliest English statutes, instituted during the reign of Henry III (r. A statute is a formal written enactment of a Legislative authority that governs a Country, State, City, or County. Henry III (1 October 1207 &ndash 16 November 1272 was the son and successor of John "Lackland" as King of England, reigning for fifty-six years from 1216 1216-1272), called the Assize of Bread and Ale. The Assize of Bread and Ale (Assisa panis et cervisiæ was a 13th-century Statute ( Assize) in late medieval English law that set standards of Bakers who were found to have shortchanged customers could be liable 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 to prevent "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 dozen. The practice can be seen in the guild codes of the Worshipful Company of Bakers in London. The Worshipful Company of Bakers is one of the Livery Companies of the City of London.

Modern uses

While modern bakers no longer fear medieval law, they have found other reasons for a baker's dozen, as seen in the tidy way 13 disks (loaves, cookies, biscuits, etc. This article refers to the cooking profession For other uses see Baker (disambiguation A baker is someone who primarily Bakes In Geometry, a disk (also spelled disc) is the region in a plane bounded by a Circle. In the United States and Canada, a cookie is a small flat-baked treat usually round containing milk flour eggs and sugar etc A biscuit (ˈbɪskɨt is a small baked product the exact meaning varies markedly in different parts of the world ) can pack a rectangle (baking tray) of appropriate proportions. Packing problems are one area where Mathematics meets Puzzles ( Recreational mathematics) In Geometry, a rectangle is defined as a Quadrilateral where all four of its angles are Right angles A rectangle with vertices ABCD would be denoted as Modern standard-sized 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 neighbors. 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. Continued use also stems from tradition, and some customers see it as a sign of appreciation from the baker for continued patronage.

Dungeons & Dragons writer Keith Baker often references the number 13, especially in the form "thirteen minus one", where a group of 13 lost one of its number, resulting in 12. Dungeons & Dragons (abbreviated as D&D or DnD) is a Fantasy Role-playing game (RPG originally designed by For the American and Canadian football player of the same name see Keith Baker (football player. Fans of his work refer to this as a "Baker's dozen"

See also

• Poulter's measure
• Decimal dozen
• Banker's dozen