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Dozenal Society of America
Promoting base twelve and alternative base mathematics
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The Dozenal Society of America
The DSA is a voluntary, nonprofit education corporation, organized for the conduct of research and education of the public in the use of dozenal (also called duodecimal or base-twelve) in calculations, mathematics, weights and measures, and other branches of pure and applied science.

The Duodecimal Bulletin

◀️ Issue: Whole Number 99z (117d) | Vol. 4Az (58d) No. 2 | Year 11B6z (2010d) ▶️



Click to view PDF

Editor: Michael DeVlieger

Cover Title: All About Our New Numbers

Contents:

  • President’s Message | Michael DeVlieger
  • An Error in Arithmetic | Jean Kelly
  • Reprint: The Opposed Principles | Ralph Beard
  • Eugene Maxwell “Skip” Scifres | DSA No. 11z
  • Presenting Symbology: An Editorial
  • Problem Corner | Prof. Gene Zirkel & Eugene M. Scifres
  • Why is 1 One? | Prof. Gene Zirkel
  • A Good History of Different Notations for Numbers: Book Review | Charles Ashbacher
    • Man and Number | Donald Smeltzer
  • Symbology Overview
    • The Retention Scale: Separate Identity to Least Change
    • The Inspiration Scale: Random Improvisation to Sequential Repurposing
    • Repurposing
      • Sequential repurposing
      • Selective repurposing
      • Creative/aesthetic repurposing
    • Derivation
    • Improvisation
      • Rationalized improvisation
      • Creative improvisation
  • Featured Figures → Overview of Symbologies
  • The Mailbag
    • H.K. Baumeister
  • Dozenal Mathematical Displays Using LaTeX | Donald Goodman III
    • TeX and LaTeX
    • Macro Indirection
    • Implementation: The Dozenal Package
    • Work to Be Done
  • Mathematics and Computer Education (Advertisement)
  • Dozenal Jottings
  • Minutes of the Annual and Board Meetings
  • Join the DSA Today!
Copyright © 11B9–120Az (2013–2026d). The Dozenal Society of America. Contact Us.
Creative Commons License
This site and the documents on it are licensed under a Creative Commons Attribution 4.0 International License.

This site expresses numbers in alternative bases, particularly dozenal (also called duodecimal, or base twelve).
The DSA does not endorse any particular notation or pronunciation scheme for alternative bases.
However this site defaults to the following to ensure online readability across all platforms:
“Computerese” uppercase letters represent transdecimal digits: A = ten, B = eleven, C = twelve, etc.
Single-character subscripts annotate bases: d = decimal, z = dozenal, x = hexadecimal, etc., e.g., 2014d = 11BAz = 7DEx.

(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ...)d
(0 1 2 3 4 5 6 7 8 9  A  B 10 11 12 13 14 15 16 17 18 19 1A 1B 20 21 22 23 24 25 26 27 28 29 2A 2B 30 ...)z
(0 1 2 3 4 5 6 7 8 9  A  B  C  D  E  F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 ...)x

PDF documents on this site reflect changing practices among dozenalists over the years:
Various symbols have been used to represent digits ten and eleven:
Dwiggins 𝒳 and Ɛ (often rendered X and E); Bell Telephone * and #; Pitman turned 2 and 3 (↊ and ↋); etc.
Italics were once used to distinguish dozenal numbers from decimal: e.g. 0.5 = 0.6.
Later, semicolon became a separate‑identity “dozenal point”, versus period as “decimal point”: e.g., 0.5 = 0;6.
However, subscript base annotations provide a more versatile solution that is least‑change: e.g., 0.5d = 0.6z = 0.8x

Dozenal offers superior divisibility over decimal, which can make everyday arithmetic easier to learn:
⅙ = 0.2z | ¼ = 0.3z | ⅓ = 0.4z | ½ = 0.6z | ⅔ = 0.8z | ¾ = 0.9z | ⅚ = 0.Az
⅙ = 0.1666…d | ¼ = 0.25d | ⅓ = 0.333…d | ½ = 0.5d | ⅔ = 0.666…d | ¾ = 0.75d | ⅚ = 0.8333…d

EACH ONE, TEACH ONE.