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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 76z (90d) | Vol. 39z (45d) No. 1 | Year 11A4z (1996d) ▶️



Click to view PDF

Editor: Prof. Jay Schiffman

Cover Title: In Memoriam: Charles Bagley

Contents:

  • Minutes of the Annual Meeting — 11A3z (1995d) | Alice Berridge
    • Board of Directors Meeting
    • Annual Membership Meeting
      • President’s Report | Jay Schiffman
      • Treasurer’s Report | Alice Berridge
      • Editor’s Report | Jay Schiffman
      • Annual Meeting Committee | Alice Berridge
      • Awards Committee | Gene Zirkel
      • Nominating Committee | Alice Berridge
      • Other Business
    • Featured Speakers
      • Prof. Gene Zirkel (NCC) | converting fractions between dozenal and decimal employing TI-85 calculator
      • Pres. Jay Schiffman | Hexadecimally Speaking | using TI-85 calculator BASE key
  • In Memoriam: Charles S. Bagley | Gene Zirkel
  • Calculator Base Conversions: Using Angle Conversion Functions to Convert To (and From) Dozenal Fractions | Gene Zirkel
    • Part I — Decimals to Dozenals
    • Part II — Dozenals to Decimals
    • Conclusion
  • Dozenal Numeration System | George Faulkner III
  • Whatever Happened to the Metric System? | Gene Zirkel
  • Book Review | Jean Kelly
    • Nature’s Numbers | William G. Lauritzen
  • Advantages for Base Twelve | Millie Chu
    • Metrics and Fractions
    • Converting into Base Twelve
    • The DSA
    • OTher Points of Interest for Base Twelve
    • End Notes
  • Solution to a Duodecimal Number Theoretical Problam | Jay L. Schiffman
  • Half Dozens | about the Bassari of eastern Senegal
  • Advice to Authors
  • New Letter | Guy Murdoch, Consumer’s Research Magazine
  • From the Editor | Jay L. Schiffman
  • Fantasy of Numbers | William H. Guyer
  • New Members
  • 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.