Seal of the DSA

Join Us!

Dozenal Society of America

Promoting base twelve and alternative base mathematics

Support the DSA

Donate

Follow Us

Icon for DSA's Facebook

Icon for DSA's RSS

Share This Page

Icon for sharing via Facebook

Icon for sharing via email

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 DSA Newscast

◀️ Vol. 4 Iss. 5 | 7 October 1200_z (2016_d) ▶️

Click to view PDF

Editor: Donald Goodman III

Contents:

Feature: Annual Meeting, 1200_z (2016_d) | Atlanta, GA
- Prof. Jay Schiffman (member 2A8_z) | Integer sequence B_z, BA_z, BA9_z, BA98_z, etc
- Mike DeVlieger (member 37B_z) | Mathematic program to check Jay’ sequence
- Dr. Paul Rapoport (member 230_z) | history of his love affair with dozens
- John Volan (member 418_z) | Primel Zoom digital presentation
- Dinner with Gene Zirkel (member 67_z) & wife Pat at Il Localino
Society Business
- Call for Submissions
- Website Update
- Volunteers Needed
- Published: Manual of the Dozenal System (Revised)
- New 1201_z (2017_d) Calendars Available!
Dozenal News
- The case for base twelve | Fuzzy Notepad (blog)
- Can you imagine life without counting and number names? | Sara’s journey to full registration
- Why We Should Forget Our Numbering System and Switch to Dozenal | Joanne Kennel | The Science Explorer
- Tau vs Pi Smackdown | Numberphile | Youtube
Poetical Diversion: “A Dozenalist, to His Love”
Donations
For Sale

Copyright © 11B9–120A_z (2013–2026_d). 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., 2014_d = 11BA_z = 7DE_x.

(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., 0.5_d = 0.6_z = 0.8_x

Dozenal offers superior divisibility over decimal, which can make everyday arithmetic easier to learn:
⅙ = 0.2_z | ¼ = 0.3_z | ⅓ = 0.4_z | ½ = 0.6_z | ⅔ = 0.8_z | ¾ = 0.9_z | ⅚ = 0.A_z
⅙ = 0.1666…_d | ¼ = 0.25_d | ⅓ = 0.333…_d | ½ = 0.5_d | ⅔ = 0.666…_d | ¾ = 0.75_d | ⅚ = 0.8333…_d

EACH ONE, TEACH ONE.