Welcome to the Dozenal Wiki
The base-twelve numbering system and its applications.
What is Dozenal?
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, gros, grosan, or biqua) and "1000" means "1 great gross" (also known as grand gross, mo, grand, unand, migross 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 using of this wiki
"X" for ten (decimal 10)
"E" for eleven (decimal 11)
";" for the dozenal point
Overline for repeating dozenal (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