# Baker's dozen

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Rectangular-13-disk-packing.png
Thirteen items in a rectangular space

A baker's dozen, also known as Long dozen, is 13, one more than a proper dozen. It may be rooted in the tidy way 13 disks (cookies, biscuits, etc) can pack a rectangle (baking tray) of appropriate proportions. Standard 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.

The term may also originate from the practice of baking 13 items for an intended dozen to prevent short measure. This was on the basis that one of the 13 would be lost, ruined or burnt in some way, leaving the baker with the original dozen.

Another explanation dates back to ancient times, where bakers — who, aside from selling bread, also baked the dough of housewives — were punished if they were discovered to be cheating by selling less bread (bread was sold by weight) or by pinching dough for their own use (often with the help of a boy and a trap door on the counter). As such, to prevent the crude punishment of getting their hands chopped off, bakers always gave 13 for the price of 12 to be certain of not being known as cheats.

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