## 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)

"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)