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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 4Az (58d) | Vol. 29z (33d) No. 2 | Year 1194z (1984d) ▶️



Click to view PDF

Editor: Patricia Zirkel

Cover Title: The House of the Future?

Contents:

  • Precision in Converting Fractions | Gene Zirkel
  • Excerpts from Mathematics and Computer Education | Gene Zirkel
  • DSA Regional Meeting
  • Counting in Dozens—The Future is Now | Fred Newhall
  • The Once and Future Dozenal Home
  • Who We Are III: Angelo Scordato, Ph.D.
  • Dozenal Jottings | From Members and Friends
    • Mrs. Andrews | donated British edition of New Numbers
    • Rod Glasgow
    • David Singmaster | publisher of Cubic Circular
    • Henry Churchman | Our National Debt Reduced to 42,253,475 Dominions? | Mathematics Teacher
    • Charles H. Brittain | donated copy of Introduction to the Dozenal System
    • Gene Zirkel | MSCS from NY Tech
    • Charles W. Trigg | Journal of Recreational Mathematics
    • Gene Scifres
    • Dr. John Impagliazzo, Secretary
    • Fred Newhall | Long Island High School Symposium
    • Metric Reporter mentioned 1983 Annual Meeting
    • James A. Forster
    • John Churchman
    • George Cunningham | VP of US Chess Federation
    • Pat and Gene Zirkel | Haggadah for a Christian Celebration of Passover
    • Neela Lakshmanan
    • John Steele
    • William C. Moffatt
    • Carol Noret
    • A. Adler Hirsch
    • Vera Sharp handy | Little Princess’ Symphony Adventures
  • Puzzle Corner | Rich Silvestri
  • Misinformation | National Geographic
  • 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.