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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 2Az (34d) | Vol. 15z (17d) No. 1 | Year 1175z (1961d) ▶️



Click to view PDF

Editor: Ralph Beard

Contents:

  • The Annual Meeting (page 1z)
    • Photo: Treasurer H.K. Humphrey (page 3z)
    • Photo: Chairman F. Emerson Andrews (page 4z)
    • Photo: President Charles S. Bagley (page 5z)
    • Photo: Secretary Ralph H. Beard (page 6z)
  • Ad: Manual of the Dozen System (page 6z)
  • A Duodecimal Abacus | Robert W. Edelen, Dept. of Mathematics, Western State College, Gunnison, CO (page 7z)
  • The New Yorker Reports the Annual Meeting (page Az)
  • Merits of the Dozenal Number System Warrant the Change | Richard A. Sexton (page Bz)
  • Doremic Scientists Volume, Mass, and Money | Henry Clarence Churchman (page 11z, page 19z)
    • Introduction (page 11z)
    • Preview of Metronic Dimensions (page 11z)
      • Partial Table of Nante Dimensions (page 12z)
    • Krypton 86d in Relation to Dometron (page 14z)
    • Kilograms and Kalks and Cabbages (page 14z)
    • Present Units Compared (page 15z)
    • Liters and Jons and Kalks Compared (page 1Az)
    • Metronic Money (page 20z)
      • Metronic Table of Equal Money values (page 21z)
    • Appearance of Cubic Dometron (page 22z)
      • Table of Comparisons of Metronic Mass, Volume, Dimensions
    • Table of Doremique Dozenal System Abbreviations (page 24z)
  • A Resected Dodecagon | Rev. Joachim Wattin, O.S.B., St. John's University, Collegeville, MN (page 17z)
  • A Duodecimal Theorem of the Powers of Two | George S. Cunningham, Director, Mathematics Education, NH State Dept of Education (page 18z)
  • Counting in Dozens (page 26z)
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.