Articles and Books

Welcome to the Dozenal Society of America’s electronic brochure database. How do we do base twelve (duodecimal) math? Visit The Basics, which offers a few articles which help you get started using base twelve. We’ve got plenty of other articles as well, from how to design your own base twelve numerals, who started the DSA, and advanced articles about dozenal number theory. Note that this part of the site, along with the Duodecimal Bulletin Digital Archive, grow continuously, so visit often, and subscribe to our various feeds to be notified of updates.

Basics | Symbology | Dozenalism | Metrics and Metrology | General Mathematics | Featured Figures | Music | Other Bases

Title: Fundamental Operations in the Duodecimal System
Author: Prof. Jay Schiffman
Subject: The four basic functions, as applied to dozenal arithmetic.
Year: 1192
Title: A Brief Introduction to Dozenal Counting
Author: Prof. Gene Zirkel
Subject: Basics of base-twelve (dozenal) counting
Year: 11X3
Title: A History of the DSA
Author: Prof. Gene Zirkel
Subject: The history of the DSA, in brief.
Year: 11E4
Title: Eggsactly a Dozen
Author: Prof. James Malone
Subject: Basic introduction to dozenal counting, by means of eggs.
Year: 1191
Title: Decimal-Dozenal Conversion Rules
Author: Prof. Gene Zirkel
Subject: Rules for converting dozenal to decimal, integers and fractions, by hand.
Year: 11E1
Title: Featured Figures: Basic Operations
Author: Michael deVlieger
Subject: Dozenal addition and multiplication tables.
Year: 11E4
Title: Key Dozenal Fractions
Author: Michael deVlieger
Subject: Pictures and graphs illustrating dozenal's unique fractional properties.
Year: 11E7
Title: Manual of the Dozen System (MODS)
Author: Dozenal Society of America
Subject: Basic introduction to dozenal mathematics; Churchman's metric system; tables.
Year: 1174
Title: Multiplication Tables of Various Bases
Author: Michael deVlieger
Subject: Multiplication tables in bases (dozenal) 2-26, 28, 30, 34, and 50.
Year: 11EX
Title: The DSA Symbology Synopsis
Author: Michael deVlieger
Subject: A poster-sized synopsis of proposals for dozenal symbologies.
Year: 11E7
Title: How Do You Pronounce Dozenals?
Author: Prof. Gene Zirkel
Subject: The do-mo-gro system of dozenal nomenclature.
Year: 11E7
Title: The DozensOnline Forum Symbols Debate
Author: Michael deVlieger
Subject: A debate on symbols from the DozensOnline forum.
Year: 11E6
Title: A Numeral Toolbox
Author: Michael deVlieger
Subject: Methods for divising numerals for non-decimal bases.
Year: 11E6
Title: Dozenal Mathematical Displays Using LaTeX
Author: Donald P. Goodman III
Subject: A brief description of the LaTeX package "dozenal."
Year: 11E6
Title: Featured Figures: Symbology Overview
Author: Michael deVlieger
Subject: Summarizes many dozenal and hexadecimal numeral systems.
Year: 11E6
Title: Symbology Overview
Author: Michael deVlieger
Subject: Summary of least-change dozenal symbologies.
Year: 11E6
Title: Presenting...Symbology
Author: Michael deVlieger
Subject: Introduction to DB Symbology issue, Vol. 4X Iss. 2.
Year: 11E6
Title: The Opposed Principles
Author: Ralph Beard
Subject: Article originally distinguishing "least change' and "separate identity" symbologies.
Year: 1161
Title: A Dozenal Nomenclature
Author: Dr. Owen B. Clayton
Subject: A proposed dozenal nomenclature.
Year: 11E5
Title: Going Classic
Author: Dozenal Society of America
Subject: Discusses the return of the DSA to Dwiggins numerals, away from Bell.
Year: 11E4
Title: Symbols, Symbols, !@#$%¢&*(!? Symbols
Author: Prof. Gene Zirkel
Subject: Explains the temporary adoption of Bell numerals by the Duodecimal Bulletin.
Year: 1192
Title: Dozenal Home Primes
Author: Prof. Jay Schiffman
Subject: An explanation of dozenal home primes.
Year: 11E7
Title: On Maximal Repeating Sequence of Decimal Expansions in Base-Twelve
Author: T. J. Gaffney
Subject: Exploring dozenal repeating fractions, especially sevenths.
Year: 11E6
Title: A Dozen Properties of the Number Twelve
Author: Dozenal Society of America
Subject: Prof. Schiffman examines some number theoretical properties of the dozen.
Year: 1192
Title: Music, Scales, and Dozens
Author: Dr. John Impagliazzo
Subject: Some different musical scales and their dozenal bases.
Year: 119X
Title: Why Change?
Author: Ralph Beard
Subject: Why our civilization should change to dozenal.
Year: 1164
Title: Twelves and Tens
Author: A. C. Aitken
Subject: Why dozenal is superior to decimal.
Year: 1179
Title: An Excursion in Numbers
Author: F. Emerson Andrews
Subject: Why dozens are a better base than decimal.
Year: 1152
Title: My Love Affair with Dozens
Author: F. Emerson Andrews
Subject: How Andrews fell in love with dozenal.
Year: 1184
Title: Reflections on the DSGB
Author: Prof. Gene Zirkel
Subject: Some reflections on the Dozenal Society of Great Britain.
Year: 11E5
Title: DSA Constitution and Bylaws
Author: Dozenal Society of America
Subject: The current Constitution and bylaws of the DSA.
Year: 1197
Title: Dozenal Frequently Asked Questions
Author: Michael deVlieger
Subject: A comprehensive explanation of the benefits of the dozenal base.
Year: 11E7
Title: Analysis of Multiplication Tables
Author: Michael deVlieger
Subject: Comparing the traits of various bases' multiplication tables.
Year: 11E7
Title: Antipatio al Aritmetiko
Author: Ralph Beard
Subject: Ralph Beard makes the case for dozenalism in Esperanto.
Year: 1171
Title: The Aspirant's Tests
Author: Dozenal Society of America
Subject: Tests for proficiency in the dozenal system.
Title: TGM: A Coherent Dozenal Metrology
Author: Tom Pendlebury / Donald P. Goodman III
Subject: Description of the TGM complete dozenal system of weights and measures.
Year: 11E8
Title: Boxes & Cans: Some Points on Packaging
Author: Troy
Subject: Dozenal's advantages in packaging
Year: 1193
Title: Dozens vs. Tens
Author: Thomas Leech, F.C.S.
Subject: Defense of dozenal notation for arithmetic, weights, measures, and money.
Year: 10E6
Title: Dozenal Divisibility Tests Quick Guide
Author: Treisaran
Subject: Dozenal divisibility tests
Year: 11E9
Title: Systems of Numeration: A Plea for the Duodecimal
Author: Rev. Thomas J. A. Freeman, S.J.
Subject: An early plea for the adoption of the dozenal base.
Year: 1119
Title: The Number Rhyme
Author: Donald P. Goodman III
Subject: A simple rhyme teaching counting and the basic characteristics of number one to a dozen.
Year: 11E9
Title: RAENBO Dozenals
Author: Timothy Travis
Subject: Travis' RAENBO system of dozenals.
Year: 11E9
Title: Duodenal System of Arithmetic, Measures, Weights and Coins
Author: John William Nystrom
Subject: A defense of dozenal arithmetic and measurement, along with proposed symbols, nomenclature, and metrics.
Year: 1103
Title: Laplace sur Douzainisme
Author: Pierre-Simon Laplace
Subject: La systeme de la douzaine (la systeme duodecimale) en bref.
Year: 109X
Title: Leclerc sur Douzainisme
Author: Georges-Louise Leclerc, Comte de Buffon
Subject: Une morceau de Georges-Louis Leclerc, Comte de Buffon, d'avantage de la douzaine dans arithmetique.
Year: 1041
Title: Playfair on Dozenalism
Author: John Playfair
Subject: An early English defense of the dozenal system.
Year: 1067
Title: Systematic Dozenal Nomenclature
Author: John Kodegadulo
Subject: Systematic Dozenal Nomenclature
Year: 11EX
Title: Twelve vs. Ten
Author: William B. Smith
Subject: A brief, turn-of-the-century defense of the dozenal base.
Year: 1117
Title: A Rational Solution to the Problem of Weights and Measures
Author: Sidney A. Reeve
Subject: A defense of the dozenal system from the perspective of a mechanical engineer.
Year: 1127
Title: A Duodecimal Scale
Author: Dr. Edward Brooks
Subject: A turn-of-the-century account of dozenal arithmetic and notation.
Year: 1104
Title: Filosofia de la numeracion
Author: D. Vicente Pujals de la Bastida
Subject: La superioridad de la doce como un base de la numeracion.
Year: 1098
Title: De la numeracion que debe preferirse.
Author: D. Vicente Pujals de la Bastida
Subject: Cuya base debe elegir?
Year: 1098
Title: De Arithmetica
Author: Ioannis Caramuelis (Juan Caramuel y Lobkowitz)
Subject: Very early exposition of dozenal.
Year: E48
Title: Rationality
Author: Donald Hammond ("Troy")
Subject: The role of ratios in weights and measures.
Year: 11X0
Title: The Duodecimal System of Notation
Author: L. H. Vincent
Subject: A simple, mostly verbal argument for dozenal.
Year: 1131
Title: Collected Works on Reckoning Reform
Author: Sir Isaac Pitman
Subject: Collected works of Sir Isaac Pitman on the dozenal base.
Year: 10X8
Title: Practical Polygons
Author: Donald Hammond ("Troy")
Subject: Numbers considered through polygons.
Year: 1196
Title: Mathamerica
Author: Grover Cleveland Perry
Subject: A stridently patriotic argument in favor of dozenals from an interwar Protestant American viewpoint.
Year: 1149
Title: Against the Metric System
Author: Herbert Spencer
Subject: A critique of the metric system (and the customary-imperial system) and a defense of dozenals.
Year: 1122
Title: La Zonnomie, ou La Décimale et la Duodécimale
Author: A.-D. Gautier
Subject: Un explication de la système de douzainisme, avec de nouveaux chiffres et un système de mesure et d'argent.
Year: 10E0
Title: Manual of the Dozenal System
Author: Dozenal Society of America
Subject: A short but thorough introduction to dozenals for those really interested in learning and using them
Year: 1200
Title: A Dozenal Primer
Author: Dozenal Society of America
Subject: A brief explanation of the dozenal system designed for beginners, in only a dozen pages.
Year: 1200