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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 6 | Vol. 3 No. 2 | Year 1163z (1947d) ▶️



Click to view PDF

Editor: Ralph Beard

Contents:

  • A Reckoning Reform | Sir Isaac Pitman (page 1z)
  • Donations and Contributions (page 5z)
  • Disingenuous Dissuasions | Ralph H. Beard (page 6z)
  • Dozenal Quirk | Harry C. Robert, Jr. (page 9z)
  • To Calculate the log10 2 | Harry C. Robert, Jr. (page Az)
  • Finding Square Roots | George S. Terry (page 10z)
  • Tables of Endings of Squares, Decimal and Duodecimal (page 11z)
  • Square Sums of Consecutive Squares | George S. Terry and Harry C. Robert, Jr. (page 12z)
  • Basimals and Radicimals (page 13z)
  • Prime and Factor Table (page 14z)
  • Notes on the Arabic Numerals (page 18z)
  • Query | George S. Terry (page 18z)
  • Periods of Primes | Ralph H. Beard (page 19z)
  • Periods and Submultiples of Reciprocals of Primes from the Dozen System | George S. Terry (page 1Bz)
  • The DeFrance Algorithm for Finding the Length of Period of Reciprocals of Primes | Research Committee (page 1Bz)
  • Mathematical Recreations | Mary Lloyd, editor (page 21z)
  • The Mail Bag (page 22z)
  • Answers to Cryptarithms (page 24z)
  • 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.