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
db31315.pdf
Title: A Brief Introduction to Dozenal Counting
Author: Prof. Gene Zirkel
Subject: Basics of base-twelve (dozenal) counting
Year: 11X3
db38206.pdf
Title: A History of the DSA
Author: Prof. Gene Zirkel
Subject: The history of the DSA, in brief.
Year: 11E4
db49209.pdf
Title: Eggsactly a Dozen
Author: Prof. James Malone
Subject: Basic introduction to dozenal counting, by means of eggs.
Year: 1191
db2610b.pdf
Title: Decimal-Dozenal Conversion Rules
Author: Prof. Gene Zirkel
Subject: Rules for converting dozenal to decimal, integers and fractions, by hand.
Year: 11E1
DSA-ConversionRules.pdf
Title: Featured Figures: Basic Operations
Author: Michael deVlieger
Subject: Dozenal addition and multiplication tables.
Year: 11E4
db49224.pdf
Title: Key Dozenal Fractions
Author: Michael deVlieger
Subject: Pictures and graphs illustrating dozenal's unique fractional properties.
Year: 11E7
db4b224.pdf
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
ManualOfTheDozenSystem1174-web.pdf
Title: Multiplication Tables of Various Bases
Author: Michael deVlieger
Subject: Multiplication tables in bases (dozenal) 2-26, 28, 30, 34, and 50.
Year: 11EX
MultiplicationSynopsis.pdf
Title: The DSA Symbology Synopsis
Author: Michael deVlieger
Subject: A poster-sized synopsis of proposals for dozenal symbologies.
Year: 11E7
DSA-SymbologySynopsis.pdf
Title: How Do You Pronounce Dozenals?
Author: Prof. Gene Zirkel
Subject: The do-mo-gro system of dozenal nomenclature.
Year: 11E7
db4b20a.pdf
Title: The DozensOnline Forum Symbols Debate
Author: Michael deVlieger
Subject: A debate on symbols from the DozensOnline forum.
Year: 11E6
db4b120.pdf
Title: A Numeral Toolbox
Author: Michael deVlieger
Subject: Methods for divising numerals for non-decimal bases.
Year: 11E6
db4b111.pdf
Title: Dozenal Mathematical Displays Using LaTeX
Author: Donald P. Goodman III
Subject: A brief description of the LaTeX package "dozenal."
Year: 11E6
db4a21a.pdf
Title: Featured Figures: Symbology Overview
Author: Michael deVlieger
Subject: Summarizes many dozenal and hexadecimal numeral systems.
Year: 11E6
db4a213.pdf
Title: Symbology Overview
Author: Michael deVlieger
Subject: Summary of least-change dozenal symbologies.
Year: 11E6
db4a211.pdf
Title: Presenting...Symbology
Author: Michael deVlieger
Subject: Introduction to DB Symbology issue, Vol. 4X Iss. 2.
Year: 11E6
db4a209.pdf
Title: The Opposed Principles
Author: Ralph Beard
Subject: Article originally distinguishing "least change' and "separate identity" symbologies.
Year: 1161
db4a205.pdf
Title: A Dozenal Nomenclature
Author: Dr. Owen B. Clayton
Subject: A proposed dozenal nomenclature.
Year: 11E5
db4a109.pdf
Title: Going Classic
Author: Dozenal Society of America
Subject: Discusses the return of the DSA to Dwiggins numerals, away from Bell.
Year: 11E4
db49207.pdf
Title: Symbols, Symbols, !@#$%¢&*(!? Symbols
Author: Prof. Gene Zirkel
Subject: Explains the temporary adoption of Bell numerals by the Duodecimal Bulletin.
Year: 1192
db27210.pdf
Title: Dozenal Home Primes
Author: Prof. Jay Schiffman
Subject: An explanation of dozenal home primes.
Year: 11E7
db4b211.pdf
Title: On Maximal Repeating Sequence of Decimal Expansions in Base-Twelve
Author: T. J. Gaffney
Subject: Exploring dozenal repeating fractions, especially sevenths.
Year: 11E6
db4b109.pdf
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
db27309.pdf
Title: Music, Scales, and Dozens
Author: Dr. John Impagliazzo
Subject: Some different musical scales and their dozenal bases.
Year: 119X
db33116.pdf
Title: Why Change?
Author: Ralph Beard
Subject: Why our civilization should change to dozenal.
Year: 1164
db043r2.pdf
Title: Twelves and Tens
Author: A. C. Aitken
Subject: Why dozenal is superior to decimal.
Year: 1179
DSA_aitken_twelves_tens.pdf
Title: An Excursion in Numbers
Author: F. Emerson Andrews
Subject: Why dozens are a better base than decimal.
Year: 1152
DSA_andrews_excursion_numbers.pdf
Title: My Love Affair with Dozens
Author: F. Emerson Andrews
Subject: How Andrews fell in love with dozenal.
Year: 1184
DSA-MyLoveAffair.pdf
Title: Reflections on the DSGB
Author: Prof. Gene Zirkel
Subject: Some reflections on the Dozenal Society of Great Britain.
Year: 11E5
db4a113.pdf
Title: DSA Constitution and Bylaws
Author: Dozenal Society of America
Subject: The current Constitution and bylaws of the DSA.
Year: 1197
DSA-Constitution-ByLaws.pdf
Title: Dozenal Frequently Asked Questions
Author: Michael deVlieger
Subject: A comprehensive explanation of the benefits of the dozenal base.
Year: 11E7
DSA-DozenalFAQs.pdf
Title: Analysis of Multiplication Tables
Author: Michael deVlieger
Subject: Comparing the traits of various bases' multiplication tables.
Year: 11E7
DSA-MultAnalysis1.pdf
Title: Antipatio al Aritmetiko
Author: Ralph Beard
Subject: Ralph Beard makes the case for dozenalism in Esperanto.
Year: 1171
antipatio.pdf
Title: The Aspirant's Tests
Author: Dozenal Society of America
Subject: Tests for proficiency in the dozenal system.
Year:
DSA_aspirants_test.pdf
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
tgm.pdf
Title: Boxes & Cans: Some Points on Packaging
Author: Troy
Subject: Dozenal's advantages in packaging
Year: 1193
DSA_boxes_cans_troy.pdf
Title: Dozens vs. Tens
Author: Thomas Leech, F.C.S.
Subject: Defense of dozenal notation for arithmetic, weights, measures, and money.
Year: 10E6
leech_thomas_dozens_tens.pdf
Title: Dozenal Divisibility Tests Quick Guide
Author: Treisaran
Subject: Dozenal divisibility tests
Year: 11E9
DSA_treisaran_div_tests.pdf
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
DSA_freeman_duodecimal.pdf
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
DSA_number_rhyme.pdf
Title: RAENBO Dozenals
Author: Timothy Travis
Subject: Travis' RAENBO system of dozenals.
Year: 11E9
DSA_RAENBO_all.pdf
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
DSA_nystrom_duodenal_arith.pdf
Title: Laplace sur Douzainisme
Author: Pierre-Simon Laplace
Subject: La systeme de la douzaine (la systeme duodecimale) en bref.
Year: 109X
DSA_laplace_dozenal.pdf
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
DSA_leclerc_douzainisme.pdf
Title: Playfair on Dozenalism
Author: John Playfair
Subject: An early English defense of the dozenal system.
Year: 1067
DSA_playfair_duodecimals.pdf
Title: Systematic Dozenal Nomenclature
Author: John Kodegadulo
Subject: Systematic Dozenal Nomenclature
Year: 11EX
DSA_kodegadulo_sdn.pdf
Title: Twelve vs. Ten
Author: William B. Smith
Subject: A brief, turn-of-the-century defense of the dozenal base.
Year: 1117
DSA_smith_william_tens_twelves.pdf
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
DSA_reeve_rational_solution.pdf
Title: A Duodecimal Scale
Author: Dr. Edward Brooks
Subject: A turn-of-the-century account of dozenal arithmetic and notation.
Year: 1104
DSA_brooks_philosophy_arithmetic.pdf
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
pujals_de_la_bastida_filosofia_de_la_numeracion.pdf
Title: De la numeracion que debe preferirse.
Author: D. Vicente Pujals de la Bastida
Subject: Cuya base debe elegir?
Year: 1098
DSA_pujals_excerpt_docena.pdf
Title: De Arithmetica
Author: Ioannis Caramuelis (Juan Caramuel y Lobkowitz)
Subject: Very early exposition of dozenal.
Year: E48
DSA_lobkowitz_duodenaria.pdf
Title: Rationality
Author: Donald Hammond ("Troy")
Subject: The role of ratios in weights and measures.
Year: 11X0
DSA_troy_rationality.pdf
Title: The Duodecimal System of Notation
Author: L. H. Vincent
Subject: A simple, mostly verbal argument for dozenal.
Year: 1131
DSA_vincent_duodecimal.pdf
Title: Collected Works on Reckoning Reform
Author: Sir Isaac Pitman
Subject: Collected works of Sir Isaac Pitman on the dozenal base.
Year: 10X8
DSA_pitman_collected.pdf
Title: Practical Polygons
Author: Donald Hammond ("Troy")
Subject: Numbers considered through polygons.
Year: 1196
DSA_troy_polygons.pdf
Title: Mathamerica
Author: Grover Cleveland Perry
Subject: A stridently patriotic argument in favor of dozenals from an interwar Protestant American viewpoint.
Year: 1149
DSA_mathamerica.pdf
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
spencer_against_metric.pdf
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
gautier_la_zonnomie.pdf
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
DSA_mods_rev.pdf
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
DSA_primer.pdf