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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 5 | Vol. 3 No. 1 | Year 1163z (1947d) ▶️



Click to view PDF

Editor: Ralph Beard

Contents:

  • The Society's Annual Award | F. Emerson Andrews (page 1z)
    • Ralph H. Beard (“Whiskers”), Editor Duodecimal Bulletin
  • Official Transactions (page 2z)
    • Officers and committee chairs for 1163z (1947d)
  • The Fibonacci Series | Harry C. Robert, Jr (page 3z)
    • Recurrences and Other Relationships (page 4z)
    • Comments by George Terry & Lewis Carl Seelbach (page 9z)
  • Microfilm of Terry’s Duodecimal Arithmetic (page 9z)
  • Table of Log Sines and Log Cosines (page Az)
  • Table of Log Tangents and Log Cotangents (page Bz)
  • Fermat’s Factoring Formula (page 10z)
  • Additions to Duodecimal Bibliography (page 11z)
  • Your Mailing List (page 13z)
  • Duodecimal Nomenclature — Further Notes | Kingsland Camp (page 14z)
  • The “Expansible Integers” | Charles Q. De France (page 19z)
  • Calculating π | Eugene M. Scifres (page 1Bz)
  • The Abbreviation of π (page 20z)
  • Mathematical Recreations | Mary Lloyd, editor (page 21z)
  • The Mail Bag (page 22z)
  • How to Count by Dozens (page 25z)
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.