A Historical Reconstruction of Our Number System

1991 ◽  
Vol 38 (7) ◽  
pp. 46-48
Author(s):  
Kim Krusen

Imagine your class as a “primitive society” just on the brink of civilization. Your society has been using tally sticks to represent numerical quantities. But now that your society is becoming more involved in commerce with other societies, you need an easier way to represent large numbers and some structure so that numbers can be manipulated. You need an organized number system. Creating a number system from scratch was the recent task of my sixth-grade class. My objective was to offer a more humanistic approach for my students further to understand and appreciate the structure of our number system. As the teacher. I was armed with a general knowledge of the number systems of the great ancient civilizations, and my students were armed with an enthusiasm to be cave dwellers for the day instead of mathematics students. With these resources, we began our project.

Author(s):  
Joseph Mazur

This chapter discusses ancient number systems, beginning with the Babylonian system. Almost every history of early Western mathematics begins with the Babylonian conception of number, a so-called sexagesimal (base 60) system for writing large numbers, formulations of multiplication tables, and ideas for astronomy. The current number system needs symbols for just ten numbers in order to represent any number we wish, compared to that of the Babylonians which needed just two symbols. The chapter also considers the early Egyptian number writing, which was an additive system, as well as the Greek alphabet and sequential number system, Roman numerals, Aztec numerals, and the Mayan system.


2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.


2020 ◽  
Author(s):  
Anat Feldman ◽  
Michael Shmueli ◽  
Dror Dotan ◽  
Joseph Tzelgov ◽  
Andrea Berger

In recent years, there has been growing interest in the development of mental number line (MNL) representation examined using a number-to-position task. In the present study, we investigated the development of number representation on a 0-10 number line using a computerized version of the number-to-position task on a touchscreen, with restricted response time; 181 children from first through sixth grade were tested. We found that the pattern of estimated number position on the physical number line was best fit by the sigmoidal curve function–which was characterized by underestimation of small numbers and overestimation of large numbers–and that the breakpoint changed with age. Moreover, we found that significant developmental leaps in MNL representation occurred between the first and second grades and again between the second and third grades, which was reflected in the establishment of the right endpoint and the number 5 as anchor points, yielding a more accurate placement of other numbers along the number line.


Author(s):  
Scott Grimm

This chapter examines the inverse number system in Dagaare (Gur; Niger–Congo). Inverse number systems possess a number morpheme which for some nouns encodes the plural interpretation while for others it encodes the singular interpretation. This chapter argues that a principled lexical semantic classification underlies the inverse number strategy in Dagaare, guiding whether for a particular noun the inverse morpheme codes the singular or the plural interpretation. The chapter further explores the functional grounding of inverse number, in terms of frequency and individuation, and presents a formal semantic account of the inverse number system.


1966 ◽  
Vol 13 (6) ◽  
pp. 492-494
Author(s):  
Frederick R. Rabinowitz

A rash of comic-strip entries provided an unexpected form of motivation for a Philadelphia sixth-grade class. Mrs. Katharine McFadden's class at the John H. Webster School used them as a springboard for studying various systems of numeration. The class had been introduced to the binary system early in the year, had achieved very well, and had enjoyed the hours working with it. But when the cartoons on “new mathematics” appeared later in the year, and interest again became high, the pupils sought additional outlets for their interest in numeration systems.


1959 ◽  
Vol 6 (5) ◽  
pp. 251-256
Author(s):  
Eunice Lewis ◽  
Ernest C. Plath

One plus one equals “10” for the members of a special arithmetic class at the University School, College of Education, Norman, Oklahoma. Of course, the members of this class were working with a number system of base two, commonly referred to as the binary system. Students also readily stated that three plus three equals “12” if the base is four. Changing the base number was not only fascinating to these highly talented fifth and sixth grade youngsters, but also provided a launching platform for the development of complicated formulas (patterns to them) which are normally developed in a second year high-school algebra course.


2007 ◽  
Vol 7 (3-4) ◽  
pp. 213-239 ◽  
Author(s):  
Andrea Bender ◽  
Sieghard Beller

AbstractIs the application of more than one number system in a particular culture necessarily an indication of not having abstracted a general concept of number? Does this mean that specific number systems for certain objects are cognitively deficient? The opposite is the case with the traditional number systems in Tongan, where a consistent decimal system is supplemented by diverging systems for certain objects, in which 20 seems to play a special role. Based on an analysis of their linguistic, historical and cultural context, we will show that the supplementary systems did not precede the general system, but were rather derived from it. Especially when notation is lacking, having such supplementary systems can even yield cognitive advantages. In using larger counting units, they both abbreviate counting and expand the limits of the general system, thus facilitating the cognitive task of mental arithmetic.


2020 ◽  
Author(s):  
Tao Wu

Abstract Modular exponentiation is fundamental in computer arithmetic and is widely applied in cryptography such as ElGamal cryptography, Diffie-Hellman key exchange protocol, and RSA cryptography. Implementation of modular exponentiation in residue number system leads to high parallelism in computation, and has been applied in many hardware architectures. While most RNS based architectures utilizes RNS Montgomery algorithm with two residue number systems, the recent modular multiplication algorithm with sum-residues performs modular reduction in only one residue number system with about the same parallelism. In this work, it is shown that high-performance modular exponentiation and RSA cryptography can be implemented in RNS. Both the algorithm and architecture are improved to achieve high performance with extra area overheads, where a 1024-bit modular exponentiation can be completed in 0.567 ms in Xilinx XC6VLX195t-3 platform, costing 26,489 slices, 87,357 LUTs, 363 dedicated multipilers of $18\times 18$ bits, and 65 Block RAMs.


REPERTÓRIO ◽  
2010 ◽  
pp. 176
Author(s):  
Teatro & Dança Repertório

<div>A dança perpassa a história de todas as civilizações antigas. Na cultura primitiva, ela estabelece uma forma de comunicação única entre um povo e suas tradições. Essa comunicação ocorre por meio de um vocabulário próprio de movimentos e gestos corporais que também farão parte dos rituais religiosos. No caso dos textos judaicos, a dança está associada a comemorações bélicas, à conquista militar, à realização pessoal e ao culto à divindade, além de exemplificar um aspecto do “ritual pagão” dos povos não-judaicos. Por sua vez, o episódio envolvendo a filha de Herodias, Salomé, registrado nos evangelhos de <em>Mateus e Marcos</em>, foi relido nos séculos posteriores figurando sua dança apenas em associação com a licenciosidade romana. O objetivo desse texto é analisar a relação dos textos velho-testamentários com a dança e opô-la ao relato de Marcos, ressaltando o modo peculiar com que o autor constrói sua narrativa. Nesse sentido, buscamos uma aproximação entre o texto literário bíblico e as práticas da dança no contexto judaico e romano.</div><div><br /></div><div><div><br />Dance passes through the history of all ancient civilizations. In the culture of primitive society, it provides a unique form of communication between people and their traditions. This communication occurs through a specific vocabulary of movements and body gestures which is also part of religious rituals. In the case of Jewish texts, the dance is associated with the celebration of war, military conquest, personal accomplishment and to worship their god, besides its "pagan worship" nature in non-Jewish cultures. On the other hand, the story of the dance of Salome, in <em>Matthew and Mark</em>, was reread in later centuries fi guring dance only in association with the Roman licentiousness. The aim of this paper is to analyze the relationship of old-testamentary texts with dance and oppose them to Mark's account, highlighting the peculiar way in which the author described the dance, the setting and characters of the story. In this sense, we seek an approximation between biblical literary text and the practice of dance in a Jewish and Roman context.</div></div>


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