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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 8Az (106d) | Vol. 45z (53d) No. 1 | Year 11B0z (2004d) ▶️



Click to view PDF

Editor: Prof. Jay Schiffman

Contents:

  • President’s Message: Five Dozenth Anniversary | Jay Schiffman
  • RIP Mary Newhall | letter from Wendy Newhall
  • A Dozenal Calculator for Your Computer | Michael Punter (England)
    • Review | Gene Zirkel
  • An Interview with Rob Roy (McPherson) | Jean Kelly
  • RIP Steve Thoburn: Metric Martyr
  • Some of Our Story | Prof. Gene Zirkel
  • Reprint: Eggsactly a Dozen: A Simple Approach to Duodecimal Counting | Prof. James Malone (NCC)
  • Two Anniversaries
    • DSA Founders: George S. Terry, F. Emerson Andrews, F. Howard Seely, Ralph H. Beard, F. Morton Smith
  • Mail Bag
    • Shaun Ferguson (DSGB) | re poles and perches
    • Charles S. Marschner
    • John Gardner, BWMA | Metric Martyr’s appeal disallowed by European Court of Human Rights
  • Minutes of the Annual Board & Membership Meetings — 11ABz (2003d)
    • Board of Directors Meeting
    • Annual Membership Meeting
      • Treasurer’s Report | Allice Berridge
      • Editor’s Report | Jay Schiffman
      • Annual Meeting Committee | Alice Berridge & Gene Zirkel
      • Nominating Committee | Alice Beridge
      • Awards Committee | Gene Zirkel
      • Other Business
        • Margaret Mooring Calderon | requested answers to exercises in Manual of the Dozen System
        • Need more advertising, call for papers, referees for Bulletin
  • Join Us!
  • 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.