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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 94z (112d) | Vol. 48z (56d) No. 1 | Year 11B3z (2007d) ▶️



Click to view PDF

Editor: Prof. Jay Schiffman

Associate Editor: Prof. Gene Zirkel

Contents:

  • President’s Message | Jay Schiffman
  • A “58,5460d” & 2,066z & 3,534d Word Essay | Scott Proctor, high school senior
    • A Discussion on the Varying Numbering Systems in the World and History’s Influence on the Modern Day Numbering System
  • Ralph Beard Memorial Award: Christina D’Aiello & John Impagliazzo
  • Assessing Weight (In Pounds) of Empire | Evan Casper-Futterman | editorial inVassar Miscellany News
  • E.U.’s Metric Obsession } Christopher Booker’s Notebook, Sunday Telegraph
  • Minutes of Our Annual Meetings — 11B2z (2006d)
    • Annual Board Meeting
      • Website status | Christina D’Aiello
      • Board Chair’s Report | Gene Zirkel
        • The Dozenal Journal | DSGB
        • Vassar Miscellany News
        • Bead Arithmetic | Kwa Tak Ming | abacus arithmetic in 12thz century
      • Mike DeVlieger
      • Bulletin Report
    • Annual Membership Meeting
      • President’s Report | Jay Schiffman
      • Presentation of Ralph Beard Memorial Award
      • Treasurer’s Report | Ellen Tufano
      • Mike DeVlieger pointed out:
        • Versatile Numbers — Versatile Economics | William Lauritzen
        • Proposal for the Numeral Unit System | Takashi Suga
      • Website Report | Gene Zirkel
  • We wish you a belated Happy 11B3z (2007d) | Prof. Ellen Tufano, Treasurer
  • Why Change?
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.