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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 49z (57d) | Vol. 29z (33d) No. 1 | Year 1194z (1984d) ▶️



Click to view PDF

Editor: Patricia Zirkel

Cover Title: Jamison Handy Wins DSA Annual Award

Contents:

  • From the President | Gene Zirkel
  • Annual Meeting of 1983 | Carmine DeSanto, Secretary
    • Approval of Minutes
    • Treasurer’s Report | James Malone
    • Editor’s Report | Pat Zirkel
    • President’s Report | Gene Zirkel
    • Report of the Nominating Committee
    • The Meeting of the Board of Directors
    • New Business
      • Dues
      • Volunteers
      • Miscellaneous
      • Constitution
      • 1984 Annual Meeting
      Presentation | Mathematical Precision | dGene Zirkel
  • Annual Award Presentation: Jamison Handy, Jr.
  • Duodecimal Primes | Charles W. Trigg
  • Who We Are II: Robert McPherson
  • Oriental Dozens | Arthur Whillock
    • Measures, Weights and Moneys of All Nations | W.S.B. Woolhouse | 1890
  • Dozenal Jottings
    • Don Hammond | official decimalization in Great Britain
    • Rita Gilligan | re: An Unambiguous Notation
    • Eugene Yee | Roman abacus used dozenal for fractions
      • A History of Mathematics | Florian Cajori
    • Gene Zirkel | wrote to American Metric Journal
      • Robert A. Hopkins | every country modify SI in some way
    • George Zirkel
    • Newest member (284;): Prof. Kathleen McKiernan
    • Two 5th graders from Acton, MA: Ande Drake & Todd Carley
  • 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.