Dozenal Wiki
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The base-dozen numbering system and its applications.

What is Dozenal?[]

The dozenal system (also known as base-dozen) is positional notation numeral system using dozen as its base. In dozenal, the number ten (also known as dek) may be written as "A", "X", "T" or a rotated "2" (introduced by Sir Isaac Pitman); the number eleven (also known as el, elv, lev, or ven) may be written as "B", "E", or a rotated "3" (introduced by Sir Isaac Pitman).

The number dozen (also known as doh, doz, zen, or unqua) is written as "10" in dozenal (meaning "1 dozen and 0 units", instead of "1 dek and 0 units"). whereas the number "12" means "1 dozen and 2 units". As well, in dozenal, "100" means "1 gross" (also known as gro, gross, grosan, or biqua) and "1000" means "1 great gross" (also known as grand gross, great gross, mo, megro, unand, migross , meg-gross or triqua).

The number twelve is a superior highly composite number, is the smallest number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4) within the subitizing range.

Symbols used in this wiki[]

"X" is the digit used for dek (dekranary 10)

"E" is the digit used for el (dekranary 11)

"." for the dozenal point

Overline for repeating dozenal fractions (e.g. 0.1 = 0.111111111111..., 47.539 = 47.5393939393939...)

"%" for the dozenal percent (e.g. 34.5% = 0.345)

"‰" for the dozenal permille (e.g. 345‰ = 0.345)

"ln" for the natural logarithm (base e = 2.875236069822...)

"log" for the dozenal common logarithm (base 10)

"//" for concatenation (in dozenal) (e.g. 47//39//5 = 47395, (2×9)//(3+5) = 16//8 = 168)

"an" for exponentiation (a^n) (e.g. 35 = 183)

"an" for concatenation of a, n times with itself (in dozenal) (e.g. 35 = 33333, 917 = 9999999999999999999, 586 = 5888888, 568 = 5555558, (58)6 = 585858585858, 1754 = 1777774, 6(497)382 = 649749749782)

"sin(x)" for the sine function with the angle x in radians (a turn, or a cycle, is 2π = 6.349416967E64... radians)

"sin(x°)" for the sine function with the angle x in dozenal degrees (a turn, or a cycle, is 400 dozenal degrees, a right angle is 100 dozenal degrees) (also called “dozenal gradian” or “dozenal gon”)

"aΔn" for the dozenal scientific notation, i.e. a×10n, with real number 1≤a<10 and integer n

In dozenal world:

  • A turn, or a cycle, is 400 degrees
  • A degree is 100 angle minutes
  • A angle minute is 100 angle seconds
  • A day (the usual day on Earth) is 20 hours (in fact, this is the same as an hour on Earth)
  • A hour is 60 minutes
  • A minute is 60 seconds
  • A week is 6 days
  • A month is 4 weeks (= 20 dozenal days)
  • A year is 10 months
  • A dozade is 10 years
  • A century is 10 dozades (= 100 years)
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