A Primer Dozenalism
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Donald Ross – the Early Years in America
Donald Ross – The Early Years in America This is the second in a series of Newsletter articles about the life and career of Donald J. Ross, the man who designed the golf course for Monroe Golf Club in 1923. Ross is generally acknowledged as the first person to ever earn a living as a golf architect and is credited with the design of almost 400 golf courses in the United States and Canada. In April of 1899, at the age of 27, Donald Ross arrived in Boston from Dornoch, Scotland. This was not only his first trip to the United States; it was likely his first trip outside of Scotland. He arrived in the States with less than $2.00 in his pocket and with only the promise of a job as keeper of the green at Oakley Golf Club. Oakley was the new name for a course founded by a group of wealthy Bostonians who decided to remake an existing 11-hole course. Ross had been the greenkeeper at Dornoch Golf Club in Scotland and was hired to be the new superintendent, golf pro and to lay out a new course for Oakley. Situated on a hilltop overlooking Boston, Oakley Golf Club enjoys much the same type land as Monroe; a gently rising glacier moraine, very sandy soil and excellent drainage. Ross put all his experiences to work. With the help of a civil engineer and a surveyor, Ross proceeded to design a virtually new course. It was short, less than 6,000 yards, typical for courses of that era. -
Nondecimal Positional Systems
M03_LONG0847_05_AIE_C03.qxd 9/17/07 10:38 AM Page 162 Not for Sale 162 CHAPTER 3 Numeration and Computation 3.2 Nondecimal Positional Systems In the preceding section, we discussed several numeration systems, including the decimal system in common use today. As already mentioned, the decimal system is a positional system based on 10. This is probably so because we have ten fingers and historically, as now, people often counted on their fingers. In the Did You Know box at the end of this section, we will give applications of positional systems that are based on whole numbers other than 10. One very useful application of bases other than ten is as a way to deepen our understanding of number systems, arithmetic in general, and our own decimal system. Although bases other than ten were in the K–5 curriculum in the past, they are not present currently. However, nondecimal positional systems are studied in the “math methods” course that is a part of an elementary education degree and may return to elementary school in the future. We will discuss addition and subtraction in base five in the next section and multiplication in base six in the following one. Base Five Notation For our purposes, perhaps the quickest route to understanding base five notation is to reconsider the abacus of Figure 3.1. This time, however, we allow only 5 beads to be moved forward on each wire. As before, we start with the wire to the students’ right (our left) and move 1 bead forward each time as we count 1, 2, 3, and so on. -
13054-Duodecimal.Pdf
Universal Multiple-Octet Coded Character Set International Organization for Standardization Organisation Internationale de Normalisation Международная организация по стандартизации Doc Type: Working Group Document Title: Proposal to encode Duodecimal Digit Forms in the UCS Author: Karl Pentzlin Status: Individual Contribution Action: For consideration by JTC1/SC2/WG2 and UTC Date: 2013-03-30 1. Introduction The duodecimal system (also called dozenal) is a positional numbering system using 12 as its base, similar to the well-known decimal (base 10) and hexadecimal (base 16) systems. Thus, it needs 12 digits, instead of ten digits like the decimal system. It is used by teachers to explain the decimal system by comparing it to an alternative, by hobbyists (see e.g. fig. 1), and by propagators who claim it being superior to the decimal system (mostly because thirds can be expressed by a finite number of digits in a "duodecimal point" presentation). • Besides mathematical and hobbyist publications, the duodecimal system has appeared as subject in the press (see e.g. [Bellos 2012] in the English newspaper "The Guardian" from 2012-12-12, where the lack of types to represent these digits correctly is explicitly stated). Such examples emphasize the need of the encoding of the digit forms proposed here. While it is common practice to represent the extra six digits needed for the hexadecimal system by the uppercase Latin capital letters A,B.C,D,E,F, there is no such established convention regarding the duodecimal system. Some proponents use the Latin letters T and E as the first letters of the English names of "ten" and "eleven" (which obviously is directly perceivable only for English speakers). -
Zero Displacement Ternary Number System: the Most Economical Way of Representing Numbers
Revista de Ciências da Computação, Volume III, Ano III, 2008, nº3 Zero Displacement Ternary Number System: the most economical way of representing numbers Fernando Guilherme Silvano Lobo Pimentel , Bank of Portugal, Email: [email protected] Abstract This paper concerns the efficiency of number systems. Following the identification of the most economical conventional integer number system, from a solid criteria, an improvement to such system’s representation economy is proposed which combines the representation efficiency of positional number systems without 0 with the possibility of representing the number 0. A modification to base 3 without 0 makes it possible to obtain a new number system which, according to the identified optimization criteria, becomes the most economic among all integer ones. Key Words: Positional Number Systems, Efficiency, Zero Resumo Este artigo aborda a questão da eficiência de sistemas de números. Partindo da identificação da mais económica base inteira de números de acordo com um critério preestabelecido, propõe-se um melhoramento à economia de representação nessa mesma base através da combinação da eficiência de representação de sistemas de números posicionais sem o zero com a possibilidade de representar o número zero. Uma modificação à base 3 sem zero permite a obtenção de um novo sistema de números que, de acordo com o critério de optimização identificado, é o sistema de representação mais económico entre os sistemas de números inteiros. Palavras-Chave: Sistemas de Números Posicionais, Eficiência, Zero 1 Introduction Counting systems are an indispensable tool in Computing Science. For reasons that are both technological and user friendliness, the performance of information processing depends heavily on the adopted numbering system. -
Number Symbolism in Old Norse Literature
Háskóli Íslands Hugvísindasvið Medieval Icelandic Studies Number Symbolism in Old Norse Literature A Brief Study Ritgerð til MA-prófs í íslenskum miðaldafræðum Li Tang Kt.: 270988-5049 Leiðbeinandi: Torfi H. Tulinius September 2015 Acknowledgements I would like to thank firstly my supervisor, Torfi H. Tulinius for his confidence and counsels which have greatly encouraged my writing of this paper. Because of this confidence, I have been able to explore a domain almost unstudied which attracts me the most. Thanks to his counsels (such as his advice on the “Blóð-Egill” Episode in Knýtlinga saga and the reading of important references), my work has been able to find its way through the different numbers. My thanks also go to Haraldur Bernharðsson whose courses on Old Icelandic have been helpful to the translations in this paper and have become an unforgettable memory for me. I‟m indebted to Moritz as well for our interesting discussion about the translation of some paragraphs, and to Capucine and Luis for their meticulous reading. Any fault, however, is my own. Abstract It is generally agreed that some numbers such as three and nine which appear frequently in the two Eddas hold special significances in Norse mythology. Furthermore, numbers appearing in sagas not only denote factual quantity, but also stand for specific symbolic meanings. This tradition of number symbolism could be traced to Pythagorean thought and to St. Augustine‟s writings. But the result in Old Norse literature is its own system influenced both by Nordic beliefs and Christianity. This double influence complicates the intertextuality in the light of which the symbolic meanings of numbers should be interpreted. -
Duodecimal Bulletin Vol
The Duodecimal Bulletin Bulletin Duodecimal The Vol. 4a; № 2; Year 11B6; Exercise 1. Fill in the missing numerals. You may change the others on a separate sheet of paper. 1 1 1 1 2 2 2 2 ■ Volume Volume nada 3 zero. one. two. three.trio 3 1 1 4 a ; (58.) 1 1 2 3 2 2 ■ Number Number 2 sevenito four. five. six. seven. 2 ; 1 ■ Whole Number Number Whole 2 2 1 2 3 99 3 ; (117.) eight. nine. ________.damas caballeros________. All About Our New Numbers 99;Whole Number ISSN 0046-0826 Whole Number nine dozen nine (117.) ◆ Volume four dozen ten (58.) ◆ № 2 The Dozenal Society of America is a voluntary nonprofit educational corporation, organized for the conduct of research and education of the public in the use of base twelve in calculations, mathematics, weights and measures, and other branches of pure and applied science Basic Membership dues are $18 (USD), Supporting Mem- bership dues are $36 (USD) for one calendar year. ••Contents•• Student membership is $3 (USD) per year. The page numbers appear in the format Volume·Number·Page TheDuodecimal Bulletin is an official publication of President’s Message 4a·2·03 The DOZENAL Society of America, Inc. An Error in Arithmetic · Jean Kelly 4a·2·04 5106 Hampton Avenue, Suite 205 Saint Louis, mo 63109-3115 The Opposed Principles · Reprint · Ralph Beard 4a·2·05 Officers Eugene Maxwell “Skip” Scifres · dsa № 11; 4a·2·08 Board Chair Jay Schiffman Presenting Symbology · An Editorial 4a·2·09 President Michael De Vlieger Problem Corner · Prof. -
The “Dirty Dozen” Tax Scams Plus 1
The “Dirty Dozen” Tax Scams Plus 1 Betty M. Thorne and Judson P. Stryker Stetson University DeLand, Florida, USA betty.thorne @stetson.edu [email protected] Executive Summary Tax scams, data breaches, and identity fraud impact consumers, financial institutions, large and small businesses, government agencies, and nearly everyone in the twenty-first century. The Internal Revenue Service (IRS) annually issues its top 12 list of tax scams, known as the “dirty dozen tax scams.” The number one tax scam on the IRS 2014 list is the serious crime of identity theft. The 2014 list also includes telephone scams, phishing, false promises of “free money,” return preparer fraud, hiding income offshore, impersonation of charitable organizations, false income, expenses, or exemptions, frivolous arguments, false wage claims, abusive tax structures, misuse of trusts and identity theft. This paper discusses each of these scams and how taxpayers may be able to protect themselves from becoming a victim of tax fraud and other forms of identity fraud. An actual identity theft nightmare is included in this paper along with suggestions on how to recover from identity theft. Key Words: identity theft, identity fraud, tax fraud, scams, refund fraud, phishing Introduction Top Ten Lists and Dirty Dozen Lists have circulated for many years on various topics of local, national and international interest or concern. Some lists are for entertainment, such as David Letterman’s humorous “top 10 lists” on a variety of jovial subjects. They have given us an opportunity to smile and at times even made us laugh. Other “top ten lists” and “dirty dozen” lists address issues such as health and tax scams. -
Abstract of Counting Systems of Papua New Guinea and Oceania
Abstract of http://www.uog.ac.pg/glec/thesis/ch1web/ABSTRACT.htm Abstract of Counting Systems of Papua New Guinea and Oceania by Glendon A. Lean In modern technological societies we take the existence of numbers and the act of counting for granted: they occur in most everyday activities. They are regarded as being sufficiently important to warrant their occupying a substantial part of the primary school curriculum. Most of us, however, would find it difficult to answer with any authority several basic questions about number and counting. For example, how and when did numbers arise in human cultures: are they relatively recent inventions or are they an ancient feature of language? Is counting an important part of all cultures or only of some? Do all cultures count in essentially the same ways? In English, for example, we use what is known as a base 10 counting system and this is true of other European languages. Indeed our view of counting and number tends to be very much a Eurocentric one and yet the large majority the languages spoken in the world - about 4500 - are not European in nature but are the languages of the indigenous peoples of the Pacific, Africa, and the Americas. If we take these into account we obtain a quite different picture of counting systems from that of the Eurocentric view. This study, which attempts to answer these questions, is the culmination of more than twenty years on the counting systems of the indigenous and largely unwritten languages of the Pacific region and it involved extensive fieldwork as well as the consultation of published and rare unpublished sources. -
1X Basic Properties of Number Words
NUMERICALS :COUNTING , MEASURING AND CLASSIFYING SUSAN ROTHSTEIN Bar-Ilan University 1x Basic properties of number words In this paper, I discuss three different semantic uses of numerical expressions. In their first use, numerical expressions are numerals, or names for numbers. They occur in direct counting situations (one, two, three… ) and in mathematical statements such as (1a). Numericals have a second predicative interpretation as numerical or cardinal adjectives, as in (1b). Some numericals have a third use as numerical classifiers as in (1c): (1) a. Six is bigger than two. b. Three girls, four boys, six cats. c. Hundreds of people gathered in the square. In part one, I review the two basic uses of numericals, as numerals and adjectives. Part two summarizes results from Rothstein 2009, which show that numericals are also used as numerals in measure constructions such as two kilos of flour. Part three discusses numerical classifiers. In parts two and three, we bring data from Modern Hebrew which support the syntactic structures and compositional analyses proposed. Finally we distinguish three varieties of pseudopartitive constructions, each with different interpretations of the numerical: In measure pseudopartitives such as three kilos of books , three is a numeral, in individuating pseudopartitives such as three boxes of books , three is a numerical adjective, and in numerical pseudopartitives such as hundreds of books, hundreds is a numerical classifier . 1.1 x Basic meanings for number word 1.1.1 x Number words are names for numbers Numericals occur bare as numerals in direct counting contexts in which we count objects (one, two, three ) and answer questions such as how many N are there? and in statements such as (1a) 527 528 Rothstein and (2). -
Disjunctive Numerals of Estimation
D. Terence Langendoen University of Arizona Disjunctive Numerals of Estimation 1. Introduction English contains a number of expressions of the form m or n, where m and n are numerals, with the meaning ‘from m to n.’ I call such expressions disjunctive numerals of estimation, or DNEs. Examples 1–4 illustrate the use of these expressions: (1) My family’s been waiting four or five hours for a flight to Florianopolis. (2) This saying has fifteen or twenty meanings. (3) Let me have thirty or forty dollars. (4) Your call will be answered in the next ten or twenty minutes. Example 1 may be used to assert that my family has been waiting from 4 to 5 hours, not for either exactly 4 or exactly 5 hours. More precisely, one should say that the expression is ambiguous between, on the one hand, an exact or literal interpretation of four or five, in which my family is said to have been waiting either 4 or 5 hours and not some intermediate amount of time (such as 4 hours and 30 minutes) and, on the other hand, an idiomatic “estimation” interpretation of four or five, in which my family is said to have been waiting from 4 to 5 hours; and one should also say that the second interpretation is much more likely to be given to the sentence than the first. The range interpretation of DNEs is even clearer in examples 2–4, where the interval between m and n is greater than 1. For example, sentence 2 under this interpretation is true if the number of meanings of the saying in question has any value from 15 to 20 and is false otherwise, similarly for examples 3 and 4. -
A Ternary Arithmetic and Logic
Proceedings of the World Congress on Engineering 2010 Vol I WCE 2010, June 30 - July 2, 2010, London, U.K. A Ternary Arithmetic and Logic Ion Profeanu which supports radical ontological dualism between the two Abstract—This paper is only a chapter, not very detailed, of eternal principles, Good and Evil, which oppose each other a larger work aimed at developing a theoretical tool to in the course of history, in an endless confrontation. A key investigate first electromagnetic fields but not only that, (an element of Manichean doctrine is the non-omnipotence of imaginative researcher might use the same tool in very unusual the power of God, denying the infinite perfection of divinity areas of research) with the stated aim of providing a new perspective in understanding older or recent research in "free that has they say a dual nature, consisting of two equal but energy". I read somewhere that devices which generate "free opposite sides (Good-Bad). I confess that this kind of energy" works by laws and principles that can not be explained dualism, which I think is harmful, made me to seek another within the framework of classical physics, and that is why they numeral system and another logic by means of which I will are kept far away from public eye. So in the absence of an praise and bring honor owed to God's name; and because adequate theory to explain these phenomena, these devices can God is One Being in three personal dimensions (the Father, not reach the design tables of some plants in order to produce them in greater number. -
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Color profile: Generic CMYK printer profile Composite Default screen C:\Jobs\Bibliography 2002\Vp\Bibliography.vp Tuesday, December 08, 2009 3:31:45 PM Color profile: Generic CMYK printer profile Composite Default screen Additional copies of this publication may be obtained from: Academic Affairs P.O. Box 2270 CPO 1099 Manila or: [email protected] Ó Summer Institute of Linguistics Philippines, Inc. 1978, 1985, 1988, 2003 All rights reserved. First edition 1978 Fourth edition 2003 Bibliography of the Summer Institute of Linguistics Philippines 1953-2003 ISBN: 971-18-0370-4 0203-4C Printed in the Philippines C:\Jobs\Bibliography 2002\Vp\Bibliography.vp Tuesday, December 08, 2009 3:31:45 PM Color profile: Generic CMYK printer profile Composite Default screen Contents Foreword ...................... xvii OfficialLetters .................... xix Preface ....................... xxiii Introduction ..................... xxv VariantLanguageNames .............. xxvii VariantAuthorNames................ xxxi ListofJournals .................. xxxiii PublisherandInstitutionAbbreviations ...... xxxix GeneralAbbreviations ................ xli Map ......................... xlii General ........................ 1 Anthropology . 1 Linguistics . 3 Literacy and Literature Use . 9 Translation . 11 Various . 16 PhilippineGeneral .................. 23 Anthropology. 23 Linguistics . 28 Literacy and Literature Use . 37 Translation . 40 Various . 40 Working Papers. 42 Agta:Casiguran(Dumagat) .............. 42 Anthropology. 42 Linguistics . 44 Literacy and