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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 A5z (125d) | Vol. 55z (65d) No. 1 | Year 1209z (2025d) ▶️



Click to view PDF

Editor: John Volan

Associate Editor: Michael DeVlieger

Cover Title: In Memoriam: Gene Zirkel, Dozenalist

Contents:

  • Former President’s Message | Donald Goodman III
  • Reprint: From the (Past) President’s Desk | Gene Zirkel
  • Gene Zirkel: Dozenal Great | Michael DeVlieger
  • Feature: The Dozenal Missionary | Michael DeVlieger
  • Reprint: I’m a Dozener | Gene Zirkel
  • Reprint: Ralph Herbert Beard | F. Emerson Andrews
  • Reprint: What’s in a Name? | Gene Zirkel
  • Reprint: Nationwide Coverage | Gene Zirkel
  • Regular and Rhombic Dodecahedron | Michael DeVlieger
  • Reprint: Dedication F. Emerson Andrews Library | Gene Zirkel
  • Reprint: Roman Dumerals | Bro. Louis Francis FMS
  • Reprint: In Memoriam: Henry Churchman | Gene Zirkel
  • Reprint: Origin of Asterisk and Octothorpe | Gene Zirkel
  • Feature: A True Dozenal Legend | Jay Schiffman
  • The Mailbag
  • Reprint: Education Needed | Gene Zirkel
  • Feature: Gallo Roman Dodecahedron | Raymond E. Greaves
    • Abstract
    • The Dodecahedron
    • Archaeological Finds
    • A Night Candle Clock
    • Examination of Evidence
    • Roman Measure
    • Chandlers
  • Roman Fractions
  • Application Form
  • Precision Dozenal Tools (Advertisement)
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.