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.

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: Some Notes on the History and Desirability of Using Alternate Number Bases in Arithmetic Author: Christopher J. Osburn Subject: Year: 11E5 db4a117.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