Mayan numerals
- Task
Present numbers using the Mayan numbering system (displaying the Mayan numerals in a cartouche).
- Mayan numbers
Normally, Mayan numbers are written vertically (top─to─bottom) with the most significant numeral at the top (in the sense that decimal numbers are written left─to─right with the most significant digit at the left). This task will be using a left─to─right (horizontal) format, mostly for familiarity and readability, and to conserve screen space (when showing the output) on this task page.
- Mayan numerals
Mayan numerals (a base─20 "digit" or glyph) are written in two orientations, this task will be using the "vertical" format (as displayed below). Using the vertical format makes it much easier to draw/construct the Mayan numerals (glyphs) with simple dots (.) and hyphen (-); (however, round bullets (∙) and long dashes (─) make a better presentation on Rosetta Code).
Furthermore, each Mayan numeral (for this task) is to be displayed as a
cartouche (enclosed in a box) to make it easier to parse (read); the box may be
drawn with any suitable (ASCII or Unicode) characters that are presentable/visible in all web browsers.
- Mayan numerals added to Unicode
Mayan numerals (glyphs) were added to the Unicode Standard in June of 2018 (this corresponds with version 11.0). But since most web browsers don't support them at this time, this Rosetta Code task will be constructing the glyphs with "simple" characters and/or ASCII art.
- The "zero" glyph
The Mayan numbering system has the concept of zero, and should be shown by a glyph that represents an upside─down (sea) shell, or an egg. The Greek letter theta (Θ) can be used (which more─or─less, looks like an egg). A commercial at symbol (@) could make a poor substitute.
- Mayan glyphs (constructed)
The Mayan numbering system is a [vigesimal (base 20)] positional numeral system.
- The Mayan numerals (and some random numbers) shown in the vertical format would be shown as
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║ ║ ║ ║ ║
║ ║ ║ ∙ ║ ║ ║ ║
1──► ║ ║ 11──► ║────║ 21──► ║ ║ ║
║ ∙ ║ ║────║ ║ ∙ ║ ∙ ║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║ ║ ║ ║ ║
║ ║ ║ ∙∙ ║ ║ ║ ║
2──► ║ ║ 12──► ║────║ 22──► ║ ║ ║
║ ∙∙ ║ ║────║ ║ ∙ ║ ∙∙ ║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║ ║ ║ ║ ║
║ ║ ║∙∙∙ ║ ║ ║ ║
3──► ║ ║ 13──► ║────║ 40──► ║ ║ ║
║∙∙∙ ║ ║────║ ║ ∙∙ ║ Θ ║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║ ║ ║ ║ ║
║ ║ ║∙∙∙∙║ ║ ║ ║
4──► ║ ║ 14──► ║────║ 80──► ║ ║ ║
║∙∙∙∙║ ║────║ ║∙∙∙∙║ Θ ║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║ ║ ║ ║ ║
║ ║ ║────║ ║ ║ ║
5──► ║ ║ 15──► ║────║ 90──► ║ ║────║
║────║ ║────║ ║∙∙∙∙║────║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║ ∙ ║ ║ ║ ║
║ ║ ║────║ ║ ║ ║
6──► ║ ∙ ║ 16──► ║────║ 100──► ║ ║ ║
║────║ ║────║ ║────║ Θ ║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║ ∙∙ ║ ║ ║ ║
║ ║ ║────║ ║ ║ ║
7──► ║ ∙∙ ║ 17──► ║────║ 200──► ║────║ ║
║────║ ║────║ ║────║ Θ ║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╗
║ ║ ║∙∙∙ ║ ║ ║ ║
║ ║ ║────║ 300──► ║────║ ║
8──► ║∙∙∙ ║ 18──► ║────║ ║────║ ║
║────║ ║────║ ║────║ Θ ║
╚════╝ ╚════╝ ╚════╩════╝
╔════╗ ╔════╗ ╔════╦════╦════╗
║ ║ ║∙∙∙∙║ ║ ║ ║ ║
║ ║ ║────║ 400──► ║ ║ ║ ║
9──► ║∙∙∙∙║ 19──► ║────║ ║ ║ ║ ║
║────║ ║────║ ║ ∙ ║ Θ ║ Θ ║
╚════╝ ╚════╝ ╚════╩════╩════╝
╔════╗ ╔════╦════╗ ╔════╦════╦════╦════╗
║ ║ ║ ║ ║ ║ ║ ║ ║ ║
║ ║ ║ ║ ║ ║ ║ ║ ║ ║
10──► ║────║ 20──► ║ ║ ║ 16,000──► ║ ║ ║ ║ ║
║────║ ║ ∙ ║ Θ ║ ║ ∙∙ ║ Θ ║ Θ ║ Θ ║
╚════╝ ╚════╩════╝ ╚════╩════╩════╩════╝
Note that the Mayan numeral 13 in horizontal format would be shown as:
╔════╗
║ ││║
║ ∙││║
13──► ║ ∙││║ ◄─── this glyph form won't be used in this Rosetta Code task.
║ ∙││║
╚════╝
Other forms of cartouches (boxes) can be used for this task.
- Task requirements
-
- convert the following decimal numbers to Mayan numbers:
- 4,005
- 8,017
- 326,205
- 886,205
- show a unique interesting/pretty/unusual/intriguing/odd/amusing/weird Mayan number
- show all output here
- Related tasks
-
- Roman numerals/Encode ─── convert numeric values into Roman numerals
- Roman numerals/Decode ─── convert Roman numerals into Arabic numbers
- See also
-
- The Wikipedia entry: [Mayan numerals]
REXX
<lang rexx>/*REXX program converts decimal numbers to the Mayan numbering system (with cartouches).*/ parse arg $ /*obtain optional arguments from the CL*/ if $= then $= 4005 8017 326205 886205, /*Not specified? Then use the default.*/
172037122592320200101 /*Morse code for MAYAN; egg is a blank.*/
do j=1 for words($) /*convert each of the numbers specified*/
#= word($, j) /*extract a number from (possible) list*/
say
say center('converting the decimal number ' # " to a Mayan number:", 90, '─')
say
call $MAYAN # '(overlap)' /*invoke the $MAYAN (REXX) subroutine.*/
say
end /*j*/ /*stick a fork in it, we're all done. */</lang>
The $MAYAN.REX (REXX program) subroutine can be seen here ---> [[Mayan_numerals\$MAYAN.REX].
- output when using the default inputs:
─────────────────converting the decimal number 4005 to a Mayan number:────────────────── ╔════╦════╦════╗ ║ ║ ║ ║ ║ ║ ║ ║ ║────║ ║ ║ ║────║ Θ ║────║ ╚════╩════╩════╝ ─────────────────converting the decimal number 8017 to a Mayan number:────────────────── ╔════╦════╦════╦════╗ ║ ║ ║ ║ ∙∙ ║ ║ ║ ║ ║────║ ║ ║ ║ ║────║ ║ ∙ ║ Θ ║ Θ ║────║ ╚════╩════╩════╩════╝ ────────────────converting the decimal number 326205 to a Mayan number:───────────────── ╔════╦════╦════╦════╦════╗ ║ ║ ║ ║ ║ ║ ║ ║ ║────║ ║ ║ ║ ║ ║────║────║ ║ ║ ∙∙ ║ Θ ║────║────║────║ ╚════╩════╩════╩════╩════╝ ────────────────converting the decimal number 886205 to a Mayan number:───────────────── ╔════╦════╦════╦════╦════╗ ║ ║ ║ ║ ║ ║ ║ ║ ║────║ ║ ║ ║ ║────║────║────║ ║ ║────║────║────║────║────║ ╚════╩════╩════╩════╩════╝ ─────────converting the decimal number 172037122592320200101 to a Mayan number:───────── ╔════╦════╦════╦════╦════╦════╦════╦════╦════╦════╦════╦════╦════╦════╦════╦════╗ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║ ║────║────║ Θ ║ ∙ ║────║ Θ ║────║ ∙ ║────║────║ Θ ║ ∙ ║────║ Θ ║────║ ∙ ║ ╚════╩════╩════╩════╩════╩════╩════╩════╩════╩════╩════╩════╩════╩════╩════╩════╝