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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 42z (50d) | Vol. 26z (30d) No. 1 | Year 1191z (1981d) ▶️



Click to view PDF

Editor: Patricia Zirkel

Contents:

  • From the Editor | Relaunch of the Bulletin | Patricia McCormick Zirkel
  • Annual Meeting of 1981 | John Earnest, Secretary
    • Minutes of the Annual Meeting
    • Meeting of the Board
  • From the President’s Desk | Gene Zirkel
  • DSA Annual Award – 1980: Henry Clarence Churchman
  • Eggsactly a Dozen | Prof. James Malone, N.C.C.
  • Annual Meeting of 1974 | Frieda Butler, Secretary
    • Board of Directors Meeting
    • General Meeting
    • Continuation of the DSA Board Meeting at Gainesville, FL
  • News from Great Britain
  • In Memoriam: Ralph Herbert Beard, 1890–1974 | F. Emerson Andrews
  • Annual Meeting of 1975 | Frieda R. Butler, Secretary
    • General Meeting
  • Help! | An Editorial | Patricia Zirkel
  • What’s in a Name? | Gene Zirkel
  • In Memoriam: F. Emerson Andrews, 1902–1978
  • Dozenal Jottings | From Various Members
    • Anton Glaser | History of Binary and other Non-Decimal Numeration
    • Charles S. Bagley
    • William C. Schumacher
    • Shaun Ferguson | DSGB Journal
    • Bruce Moon and H.W. Steel | symbols for ten, eleven
    • John Churchman
    • National Council of Teachers of Mathematics
    • Dudley George
    • Rita Gilligan
    • Rev. Joachim Watrin
    • John Steele | dozens and sol-fah method
    • John Selfridge
    • Raymond Farr | passing of Tom Linton
  • Inches Returned to the Australians | Gene Zirkel
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.