baker's dozen

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 and a "long measure", is 13, one more than a proper dozen. The expression found its genesis in 13th-century England, when an Assize of Bread and Ale was introduced. At that time, it was commonly called "the long measure".

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 (1216-1272), called the Assize of Bread and Ale. 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 legal dozen. The practice can be seen in the guild codes of the Worshipful Company of Bakers in London.

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"^[1]

Modern uses

While modern bakers no longer fear medieval laws, they have found other reasons for a baker's dozen, as seen in the tidy way 13 disks (loaves, cookies, biscuits, etc.) can pack a rectangle (baking tray) of appropriate proportions. 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.

References

1. ^ Francis Grose (2007). Classical dictionary of the vulgar tongue (Unabridged from the original 1811 ed.). p. 18. 

See also

• Poulter's measure
• Decimal dozen