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Welcome to the Dozenal Wiki!Edit

The base-twelve numbering system and its applications.

What is Dozenal?Edit

The dozenal system (also known as base-twelve or duodecimal) is positional notation numeral system using twelve 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 twelve (also known as doh, doz, zen, or unqua) is written as "10" in dozenal (meaning "1 dozen and 0 units", instead of "1 ten 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 highly composite number, is the smalled number with four non-trivial factors (2, 3, 4, 6), and the smallest to include as factors all four numbers (1 to 4, the number n’s such that general algebraic equation with degree n have algebraic solutions) within the subitizing range.

Symbols used in this wikiEdit

"↊" (or X) is the digit used for dek (decimal 10)

"Ɛ" (or E) is the digit used for elve (decimal 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 100; dozenal degrees)

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

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