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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 70z (84d) | Vol. 36z (42d) No. 1 | Year 11A1z (1993d) ▶️



Click to view PDF

Editor: Prof. Jay Schiffman

Cover Title: Gene Zirkel enjoys an English tea with Arthur and Ruby Whillock

Contents:

  • From the Editor | Jay L. Schiffman
  • Minutes of the Annual Meeting — 11A0z (1992d) | Alice Berridge
    • Board of Directors Meeting
    • Annual Membership Meeting
      • President’s Report | Fred Newhall
      • Treasurer’s Report | Anthony Catania
      • Editor’s Report | Jay Schiffman
      • Committee Reports
        • Annual Metting Committee | Dr. Barbran Smith
        • Awards Committee | Gene Zirkel
        • Nominating Committee | Alice Berridge
      • Other Business
    • Featured Speaker: Jay Schiffman | A Duodecimal Crossnumber Puzzle
  • The Role of Congruences to Prove Duodecimal Divisibility Tests | Jay L. Schiffman
  • Panda Stamp
  • Which Number is Best? | Ed Nu
  • Kaprekar’s Process Generalized | Charles Ashbacher
  • Education Needed | Gene Zirkel
  • Edgar Allen Poe’s Eldorado Revisited | Henry Churchman
  • Dozenal Jottings | From Members and Friends
    • Fred Newhall’s holiday card
    • John Churchman, regarding Henry Churchman
    • Ian Patten
    • Anton Glaser wrote Federal Reserve Board, response from John P. LaWare
    • John Hansen | a leap year pattern yielding average year of 265.2AA6z days
    • Don Hammond (DSGB) retired at 55z
    • New Life Member: Erich Kothe
    • New Members: James G. Steigerwald, John Steigerwaldd, B. Gerver, George P. Jellis, Vita B. Alaimo, Jacob Corbin, Guney Mentes, George Faulkner III, Bill Lauritzen, Derrick Smith
    • New Student Members: Irene Samson, Jackie Gammon, Valerie Burnett, Amle Gellen
  • The First 30z Factorials Are... | Brian M. Dean
  • Why Change?
  • Counting in Dozens
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.