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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 A4z (124d) | Vol. 54z (64d) No. 1 | Year 1206z (2022d) ▶️



Click to view PDF

Editor: John Volan

Cover Title: Dozenal Card Games

Contents:

  • President’s Message | Donald Goodman III
  • Editorial: Is There a Turnaround in the Cards? | John Volan
  • New Members
  • Dozenal Card Games | Paul Rapoport
  • Time (And Time Again) | Paul Rapoport | dozenal wristwatch
  • The Online Dozenal/Decimal Scientific Calculator | Paul Rapoport
  • Primel Metrology, Part II | John Volan
    • “Quantiteliic” Units Inspired by ISO-31
    • Primel Units of Angular Mechanics
      • The Radian
      • Angular Dimensionality
      • Radiality and the Radiel
      • Angular Displacement
      • Angular Velocity
      • Angular Acceleration
      • Angular Mass or Moment of Inertia
      • Angular Momentum
      • Angular Force
      • Traditional Rotational Kinetic Energy
      • Reusability of Unit Names
    • Angular Transcendental Functions
    • More to Come
  • Systematic Dozenal Nomenclature Summary
  • An Unpublished Manuscript of Leibniz's on Duodecimal | Lloyd Strickland, Manchester Metropolitan University
    • Leibniz: De Progressione Duodenaria (c. 1695)
    • Leibniz: On the Duodenary Progression (c. 1695)
  • Dozenal Magic Squares | Jay L. Schiffman
    • Introductory Discussion
    • Solutions to the Above Immersions
    • Rudolph Ordrejka’s Magic Square
    • Additional Observations
    • Conclusion
  • Pounds, Shillings, Pence: The Commonwealth’s Dozenal Currency | Andon Epp
  • Poetry Corner: Multiverse Multi-Verse
  • Application Form
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.