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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 A0z (120d) | Vol. 50z (60d) No. 1 | Year 11B7z (2011d) ▶️



Click to view PDF

Editor: Michael DeVlieger

Cover Title: Twelfty

Contents:

  • President’s Message | Michael DeVlieger
  • The 11B7z (2011d) Meeting Minutes
  • Move Over Primes — the Veratiles Are Here! | Bill Lauritzen
  • Reprint: History Professor Speaks to DSA Members | Gene Zirkel
    • Jens Ulff-Møller | speaks about long hundred
  • Reprint: A Dozen Decades | Alice Berridge & Prof. Gene Zirkel
    • Report on a Lecture about Long Hundred and Historical Methods
  • Book Review: Menninger on the “Great Hundred” | Michael DeVlieger
    • Zahlwort und Ziffer (Number Words and Number Symbols) | Karl Menninger
  • Problem Corner | Prof. Gene Zirkel
  • Validating a Dozenal Measure of Angle | Michael DeVlieger
  • Twelfty, or Adventures in Alternating Bases | Bulletin interview Wendy Y. Krieger
    • Preface
    • Our Forefathers Used Mixed and Alternating Bases
    • Multiples and Divisions
    • The Abacus and Alternating Bases
    • The Ancient Mesopotamian Sixty
    • Why “Twelfty”?
    • The Logarithm Cycle
    • Structure and Nomenclature for Twelfty
    • Conclusion
  • Problem Corner | Prof. Gene Zirkel
  • Mathematics and Computer Education (Advertisement)
  • The Basics of Systematic Dozenal Nomenclature | Donald Goodman III
  • Join the DSA Today!
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.
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