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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 92z (110d) | Vol. 47z (55d) No. 1 | Year 11B2z (2006d) ▶️



Click to view PDF

Editor: Prof. Jay Schiffman

Associate Editor: Prof. Gene Zirkel

Contents:

  • President’s Message | Jay Schiffman
  • Message from the Board Chair | Gene Zirkel
  • New DSA Website: www.Dozenal.org
  • The Most Appealing Integer Twelve, Part I | Jay Schiffman
  • Reprint: Aspirant’s Test Number 2
  • Dues Are Due
  • Group Hails ‘Miles Better’ Signs | British Weights and Measures Association
  • Mo-gro-do
  • Pictures from Our Recent Meetings
  • Kilometre ‘Cock-up’ | British Weights and Measures Association
  • Minutes of Our Annual Meetings — 11B1z (2005d) |
    • Board of Directors Meeting
    • Annual Membership Meeting
      • Treasurer’s Report | Ellen Tufano
      • Website Report | Gene Zirkel
        • John Impagliazzo contacted Oznic and Dreamhost
      • Special Presentation: Jay Schiffman receives Charles Beard MemorialAward
    • Lectures:
      • V.P. John Earnest | duodecimals from 1852 text Elementary Arithmetic by George R. Perkins
      • Pres. Jay Schiffman | demonstrated Euclid and Euler’s Theorems using Punter calculator
  • Answers to Aspirant’s Test Number 2
  • Another Six Fingered Animal: extinct Simocyon batalleri
  • Mail Bag
    • Jean Kelly
    • Andrew Denny (DSGB)
    • Burt Smith | Zodiac signs as separate identity digits? Card game
    • Clay Macdonald
  • Why Change?
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.