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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 8 | Vol. 3 No. 4 | Year 1163z (1947d) ▶️



Click to view PDF

Editor: Ralph Beard

Contents:

  • A Plea for the Duodecimal System | H.G.G. Robertson, M.R.C.S., Lieut. Col., R.A.M.C. (page 1)
  • Annual Meeting (page 12z)
  • Mathematical Recreations | Mary Lloyd, editor (page 13z)
    • Tesselation | George S. Terry & Harry C. Robert, Jr. (page 13z)
    • Solid Tesselation | George S. Terry & Harry C. Robert, Jr. (page 14z)
  • Products Repeating Integers of Factors (page 17z)
  • Obituary: F. Morton Smith | George S. Terry (page 18z)
  • Lecture Chart | Paul Van Buskirk (page 18z)
  • Table of Least Factors 3001–3ƐƐƐ | Harry C. Robert, Jr. (page 1Az)
  • Book Review | F. Emerson Andrews (page 20z)
    • Elementary Concepts of Mathematics | Burton W. Jones, Prof. of Mathematics, Cornell University (page 20sz)
  • Integer Sums of Numbers and Their Powers | George S. Terry (page 21z)
  • Donations (page 22z)
  • The Mail Bag (page 23z)
  • Counting in 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.