Numbering Systems Developed by the Ancient Mesopotamians
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Roman Numerals
History of Numbers 1c. I can distinguish between an additive and positional system, and convert between Roman and Hindu-Arabic numbers. Roman Numerals The numeric system represented by Roman numerals originated in ancient Rome (753 BC–476 AD) and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. By the 11th century, the more efJicient Hindu–Arabic numerals had been introduced into Europe by way of Arab traders. Roman numerals, however, remained in commo use well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Roman numerals are still used today, in certain contexts. See: Modern Uses of Roman Numerals Numbers in this system are represented by combinations of letters from the Latin alphabet. Roman numerals, as used today, are based on seven symbols: The numbers 1 to 10 are expressed in Roman numerals as: I, II, III, IV, V, VI, VII, VIII, IX, X. This an additive system. Numbers are formed by combining symbols and adding together their values. For example, III is three (three ones) and XIII is thirteen (a ten plus three ones). Because each symbol (I, V, X ...) has a Jixed value rather than representing multiples of ten, one hundred and so on (according to the numeral's position) there is no need for “place holding” zeros, as in numbers like 207 or 1066. Using Roman numerals, those numbers are written as CCVII (two hundreds, plus a ive and two ones) and MLXVI (a thousand plus a ifty plus a ten, a ive and a one). -
The Origins, Evolution and Decline of the Khojki Script
The origins, evolution and decline of the Khojki script Juan Bruce The origins, evolution and decline of the Khojki script Juan Bruce Dissertation submitted in partial fulfilment of the requirements for the Master of Arts in Typeface Design, University of Reading, 2015. 5 Abstract The Khojki script is an Indian script whose origins are in Sindh (now southern Pakistan), a region that has witnessed the conflict between Islam and Hinduism for more than 1,200 years. After the gradual occupation of the region by Muslims from the 8th century onwards, the region underwent significant cultural changes. This dissertation reviews the history of the script and the different uses that it took on among the Khoja people since Muslim missionaries began their activities in Sindh communities in the 14th century. It questions the origins of the Khojas and exposes the impact that their transition from a Hindu merchant caste to a broader Muslim community had on the development of the script. During this process of transformation, a rich and complex creed, known as Satpanth, resulted from the blend of these cultures. The study also considers the roots of the Khojki writing system, especially the modernization that the script went through in order to suit more sophisticated means of expression. As a result, through recording the religious Satpanth literature, Khojki evolved and left behind its mercantile features, insufficient for this purpose. Through comparative analysis of printed Khojki texts, this dissertation examines the use of the script in Bombay at the beginning of the 20th century in the shape of Khoja Ismaili literature. -
Schwa Deletion: Investigating Improved Approach for Text-To-IPA System for Shiri Guru Granth Sahib
ISSN (Online) 2278-1021 ISSN (Print) 2319-5940 International Journal of Advanced Research in Computer and Communication Engineering Vol. 4, Issue 4, April 2015 Schwa Deletion: Investigating Improved Approach for Text-to-IPA System for Shiri Guru Granth Sahib Sandeep Kaur1, Dr. Amitoj Singh2 Pursuing M.E, CSE, Chitkara University, India 1 Associate Director, CSE, Chitkara University , India 2 Abstract: Punjabi (Omniglot) is an interesting language for more than one reasons. This is the only living Indo- Europen language which is a fully tonal language. Punjabi language is an abugida writing system, with each consonant having an inherent vowel, SCHWA sound. This sound is modifiable using vowel symbols attached to consonant bearing the vowel. Shri Guru Granth Sahib is a voluminous text of 1430 pages with 511,874 words, 1,720,345 characters, and 28,534 lines and contains hymns of 36 composers written in twenty-two languages in Gurmukhi script (Lal). In addition to text being in form of hymns and coming from so many composers belonging to different languages, what makes the language of Shri Guru Granth Sahib even more different from contemporary Punjabi. The task of developing an accurate Letter-to-Sound system is made difficult due to two further reasons: 1. Punjabi being the only tonal language 2. Historical and Cultural circumstance/period of writings in terms of historical and religious nature of text and use of words from multiple languages and non-native phonemes. The handling of schwa deletion is of great concern for development of accurate/ near perfect system, the presented work intend to report the state-of-the-art in terms of schwa deletion for Indian languages, in general and for Gurmukhi Punjabi, in particular. -
Bibliography
Bibliography Many books were read and researched in the compilation of Binford, L. R, 1983, Working at Archaeology. Academic Press, The Encyclopedic Dictionary of Archaeology: New York. Binford, L. R, and Binford, S. R (eds.), 1968, New Perspectives in American Museum of Natural History, 1993, The First Humans. Archaeology. Aldine, Chicago. HarperSanFrancisco, San Francisco. Braidwood, R 1.,1960, Archaeologists and What They Do. Franklin American Museum of Natural History, 1993, People of the Stone Watts, New York. Age. HarperSanFrancisco, San Francisco. Branigan, Keith (ed.), 1982, The Atlas ofArchaeology. St. Martin's, American Museum of Natural History, 1994, New World and Pacific New York. Civilizations. HarperSanFrancisco, San Francisco. Bray, w., and Tump, D., 1972, Penguin Dictionary ofArchaeology. American Museum of Natural History, 1994, Old World Civiliza Penguin, New York. tions. HarperSanFrancisco, San Francisco. Brennan, L., 1973, Beginner's Guide to Archaeology. Stackpole Ashmore, w., and Sharer, R. J., 1988, Discovering Our Past: A Brief Books, Harrisburg, PA. Introduction to Archaeology. Mayfield, Mountain View, CA. Broderick, M., and Morton, A. A., 1924, A Concise Dictionary of Atkinson, R J. C., 1985, Field Archaeology, 2d ed. Hyperion, New Egyptian Archaeology. Ares Publishers, Chicago. York. Brothwell, D., 1963, Digging Up Bones: The Excavation, Treatment Bacon, E. (ed.), 1976, The Great Archaeologists. Bobbs-Merrill, and Study ofHuman Skeletal Remains. British Museum, London. New York. Brothwell, D., and Higgs, E. (eds.), 1969, Science in Archaeology, Bahn, P., 1993, Collins Dictionary of Archaeology. ABC-CLIO, 2d ed. Thames and Hudson, London. Santa Barbara, CA. Budge, E. A. Wallis, 1929, The Rosetta Stone. Dover, New York. Bahn, P. -
Handwriting Recognition in Indian Regional Scripts: a Survey of Offline Techniques
1 Handwriting Recognition in Indian Regional Scripts: A Survey of Offline Techniques UMAPADA PAL, Indian Statistical Institute RAMACHANDRAN JAYADEVAN, Pune Institute of Computer Technology NABIN SHARMA, Indian Statistical Institute Offline handwriting recognition in Indian regional scripts is an interesting area of research as almost 460 million people in India use regional scripts. The nine major Indian regional scripts are Bangla (for Bengali and Assamese languages), Gujarati, Kannada, Malayalam, Oriya, Gurumukhi (for Punjabi lan- guage), Tamil, Telugu, and Nastaliq (for Urdu language). A state-of-the-art survey about the techniques available in the area of offline handwriting recognition (OHR) in Indian regional scripts will be of a great aid to the researchers in the subcontinent and hence a sincere attempt is made in this article to discuss the advancements reported in this regard during the last few decades. The survey is organized into different sections. A brief introduction is given initially about automatic recognition of handwriting and official re- gional scripts in India. The nine regional scripts are then categorized into four subgroups based on their similarity and evolution information. The first group contains Bangla, Oriya, Gujarati and Gurumukhi scripts. The second group contains Kannada and Telugu scripts and the third group contains Tamil and Malayalam scripts. The fourth group contains only Nastaliq script (Perso-Arabic script for Urdu), which is not an Indo-Aryan script. Various feature extraction and classification techniques associated with the offline handwriting recognition of the regional scripts are discussed in this survey. As it is important to identify the script before the recognition step, a section is dedicated to handwritten script identification techniques. -
The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes
Portland State University PDXScholar Mathematics and Statistics Faculty Fariborz Maseeh Department of Mathematics Publications and Presentations and Statistics 3-2018 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hu Sun University of Macau Christine Chambris Université de Cergy-Pontoise Judy Sayers Stockholm University Man Keung Siu University of Hong Kong Jason Cooper Weizmann Institute of Science SeeFollow next this page and for additional additional works authors at: https:/ /pdxscholar.library.pdx.edu/mth_fac Part of the Science and Mathematics Education Commons Let us know how access to this document benefits ou.y Citation Details Sun X.H. et al. (2018) The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes. In: Bartolini Bussi M., Sun X. (eds) Building the Foundation: Whole Numbers in the Primary Grades. New ICMI Study Series. Springer, Cham This Book Chapter is brought to you for free and open access. It has been accepted for inclusion in Mathematics and Statistics Faculty Publications and Presentations by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. Authors Xu Hu Sun, Christine Chambris, Judy Sayers, Man Keung Siu, Jason Cooper, Jean-Luc Dorier, Sarah Inés González de Lora Sued, Eva Thanheiser, Nadia Azrou, Lynn McGarvey, Catherine Houdement, and Lisser Rye Ejersbo This book chapter is available at PDXScholar: https://pdxscholar.library.pdx.edu/mth_fac/253 Chapter 5 The What and Why of Whole Number Arithmetic: Foundational Ideas from History, Language and Societal Changes Xu Hua Sun , Christine Chambris Judy Sayers, Man Keung Siu, Jason Cooper , Jean-Luc Dorier , Sarah Inés González de Lora Sued , Eva Thanheiser , Nadia Azrou , Lynn McGarvey , Catherine Houdement , and Lisser Rye Ejersbo 5.1 Introduction Mathematics learning and teaching are deeply embedded in history, language and culture (e.g. -
The Number-System of Algebra : Treated Theoretically and Historically
- ; THE NUMBER-SYSTEM OF ALGEBRA TKEATED THEORETICALLY AND HISTORICALLY BY HENRY B. FINE, PH.D. PROFESSOR OF MATHEMATICS IN PRINCETON UNIVERSITY SECOND EDITION, WITH CORRECTIONS BOSTON, U.S.A. D. C. HEATH & CO., PUBLISHERS 1907 COPYRIGHT, 1890, BY HENRY B. FINE. 66 f 6 T PREFACE. THE theoretical part of this little book is an elementary of exposition the nature of the number concept, of the posi- tive integer, and of the four artificial forms of number which, with the positive integer, constitute the "number- " system of algebra, viz. the negative, the fraction, the irra- tional, and the imaginary. The discussion of the artificial numbers follows, in general, the same lines as my pam- phlet : On the Forms of Number arising in Common Algebra, but it is much more exhaustive and thorough- going. The point of view is the one first suggested by Peacock and Gregory, and accepted by mathematicians gen- erally since the discovery of quaternions and the Ausdeh- nungslehre of Grassmann, that algebra is completely defined formally by the laws of combination to which its funda- mental operations are subject; that, speaking generally, these laws alone define the operations, and the operations the various artificial numbers, as their formal or symbolic results. This doctrine was fully developed for the neg the fraction, and the imaginary by Hankel, in his Complexe Zahlensystemen, in 1867, and made complete by Cantor's beautiful theory of the irrational in 1871, but it has not as yet received adequate treatment in English. this kind is Any large degree of originality in work of from a naturally out of the question. -
Shahmukhi to Gurmukhi Transliteration System: a Corpus Based Approach
Shahmukhi to Gurmukhi Transliteration System: A Corpus based Approach Tejinder Singh Saini1 and Gurpreet Singh Lehal2 1 Advanced Centre for Technical Development of Punjabi Language, Literature & Culture, Punjabi University, Patiala 147 002, Punjab, India [email protected] http://www.advancedcentrepunjabi.org 2 Department of Computer Science, Punjabi University, Patiala 147 002, Punjab, India [email protected] Abstract. This research paper describes a corpus based transliteration system for Punjabi language. The existence of two scripts for Punjabi language has created a script barrier between the Punjabi literature written in India and in Pakistan. This research project has developed a new system for the first time of its kind for Shahmukhi script of Punjabi language. The proposed system for Shahmukhi to Gurmukhi transliteration has been implemented with various research techniques based on language corpus. The corpus analysis program has been run on both Shahmukhi and Gurmukhi corpora for generating statistical data for different types like character, word and n-gram frequencies. This statistical analysis is used in different phases of transliteration. Potentially, all members of the substantial Punjabi community will benefit vastly from this transliteration system. 1 Introduction One of the great challenges before Information Technology is to overcome language barriers dividing the mankind so that everyone can communicate with everyone else on the planet in real time. South Asia is one of those unique parts of the world where a single language is written in different scripts. This is the case, for example, with Punjabi language spoken by tens of millions of people but written in Indian East Punjab (20 million) in Gurmukhi script (a left to right script based on Devanagari) and in Pakistani West Punjab (80 million), written in Shahmukhi script (a right to left script based on Arabic), and by a growing number of Punjabis (2 million) in the EU and the US in the Roman script. -
KHA in ANCIENT INDIAN MATHEMATICS It Was in Ancient
KHA IN ANCIENT INDIAN MATHEMATICS AMARTYA KUMAR DUTTA It was in ancient India that zero received its first clear acceptance as an integer in its own right. In 628 CE, Brahmagupta describes in detail rules of operations with integers | positive, negative and zero | and thus, in effect, imparts a ring structure on integers with zero as the additive identity. The various Sanskrit names for zero include kha, ´s¯unya, p¯urn. a. There was an awareness about the perils of zero and yet ancient Indian mathematicians not only embraced zero as an integer but allowed it to participate in all four arithmetic operations, including as a divisor in a division. But division by zero is strictly forbidden in the present edifice of mathematics. Consequently, verses from ancient stalwarts like Brahmagupta and Bh¯askar¯ac¯arya referring to numbers with \zero in the denominator" shock the modern reader. Certain examples in the B¯ıjagan. ita (1150 CE) of Bh¯askar¯ac¯arya appear as absurd nonsense. But then there was a time when square roots of negative numbers were considered non- existent and forbidden; even the validity of subtracting a bigger number from a smaller number (i.e., the existence of negative numbers) took a long time to gain universal acceptance. Is it not possible that we too have confined ourselves to a certain safe convention regarding the zero and that there could be other approaches where the ideas of Brahmagupta and Bh¯askar¯ac¯arya, and even the examples of Bh¯askar¯ac¯arya, will appear not only valid but even natural? Enterprising modern mathematicians have created elaborate legal (or technical) machinery to overcome the limitations imposed by the prohibition against use of zero in the denominator. -
Part 1: Introduction to The
PREVIEW OF THE IPA HANDBOOK Handbook of the International Phonetic Association: A guide to the use of the International Phonetic Alphabet PARTI Introduction to the IPA 1. What is the International Phonetic Alphabet? The aim of the International Phonetic Association is to promote the scientific study of phonetics and the various practical applications of that science. For both these it is necessary to have a consistent way of representing the sounds of language in written form. From its foundation in 1886 the Association has been concerned to develop a system of notation which would be convenient to use, but comprehensive enough to cope with the wide variety of sounds found in the languages of the world; and to encourage the use of thjs notation as widely as possible among those concerned with language. The system is generally known as the International Phonetic Alphabet. Both the Association and its Alphabet are widely referred to by the abbreviation IPA, but here 'IPA' will be used only for the Alphabet. The IPA is based on the Roman alphabet, which has the advantage of being widely familiar, but also includes letters and additional symbols from a variety of other sources. These additions are necessary because the variety of sounds in languages is much greater than the number of letters in the Roman alphabet. The use of sequences of phonetic symbols to represent speech is known as transcription. The IPA can be used for many different purposes. For instance, it can be used as a way to show pronunciation in a dictionary, to record a language in linguistic fieldwork, to form the basis of a writing system for a language, or to annotate acoustic and other displays in the analysis of speech. -
Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to the Mathematics of Today
Writing the History of Mathematics: Interpretations of the Mathematics of the Past and Its Relation to the Mathematics of Today Johanna Pejlare and Kajsa Bråting Contents Introduction.................................................................. 2 Traces of Mathematics of the First Humans........................................ 3 History of Ancient Mathematics: The First Written Sources........................... 6 History of Mathematics or Heritage of Mathematics?................................. 9 Further Views of the Past and Its Relation to the Present.............................. 15 Can History Be Recapitulated or Does Culture Matter?............................... 19 Concluding Remarks........................................................... 24 Cross-References.............................................................. 24 References................................................................... 24 Abstract In the present chapter, interpretations of the mathematics of the past are problematized, based on examples such as archeological artifacts, as well as written sources from the ancient Egyptian, Babylonian, and Greek civilizations. The distinction between history and heritage is considered in relation to Euler’s function concept, Cauchy’s sum theorem, and the Unguru debate. Also, the distinction between the historical past and the practical past,aswellasthe distinction between the historical and the nonhistorical relations to the past, are made concrete based on Torricelli’s result on an infinitely long solid from -
Inventing Your Own Number System
Inventing Your Own Number System Through the ages people have invented many different ways to name, write, and compute with numbers. Our current number system is based on place values corresponding to powers of ten. In principle, place values could correspond to any sequence of numbers. For example, the places could have values corre- sponding to the sequence of square numbers, triangular numbers, multiples of six, Fibonacci numbers, prime numbers, or factorials. The Roman numeral system does not use place values, but the position of numerals does matter when determining the number represented. Tally marks are a simple system, but representing large numbers requires many strokes. In our number system, symbols for digits and the positions they are located combine to represent the value of the number. It is possible to create a system where symbols stand for operations rather than values. For example, the system might always start at a default number and use symbols to stand for operations such as doubling, adding one, taking the reciprocal, dividing by ten, squaring, negating, or any other specific operations. Create your own number system. What symbols will you use for your numbers? How will your system work? Demonstrate how your system could be used to perform some of the following functions. • Count from 0 up to 100 • Compare the sizes of numbers • Add and subtract whole numbers • Multiply and divide whole numbers • Represent fractional values • Represent irrational numbers (such as π) What are some of the advantages of your system compared with other systems? What are some of the disadvantages? If you met aliens that had developed their own number system, how might their mathematics be similar to ours and how might it be different? Make a list of some math facts and procedures that you have learned.