## Welcome to the Dozenal Wiki![]

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)

"*a ^{n}*" for exponentiation (

*a*^

*n*) (e.g. 3

^{5}= 183)

"*a _{n}*" for concatenation of

*a*,

*n*times with itself (in dozenal) (e.g. 3

_{5}= 33333, 9

_{17}= 9999999999999999999, 58

_{6}= 5888888, 5

_{6}8 = 5555558, (58)

_{6}= 585858585858, 17

_{5}4 = 1777774, 6(497)

_{3}82 = 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”)

"*a*Δ*n*" for the dozenal scientific notation, i.e. *a*×10^{n}, 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)