scholarly journals Killing Imaginary Numbers? From Today’s Asymmetric Number System to a Symmetric System

2021 ◽  
Vol 11 (08) ◽  
pp. 741-754
Author(s):  
Espen Gaarder Haug ◽  
Pankaj Mani
Keyword(s):  
Number System ◽  
Symmetric System

Number knowledge and the approximate number system are two critical foundations for early arithmetic development.

2020 ◽  
Vol 112 (6) ◽  
pp. 1167-1182 ◽  
Author(s):  
Stephanie A. Malone ◽  
Kelly Burgoyne ◽  
Charles Hulme
Keyword(s):  
Number System ◽  
Approximate Number System ◽  
Number Knowledge

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

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.

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Topics in Quaternion Linear Algebra

2014 ◽  
Author(s):  
Leiba Rodman
Keyword(s):  
Linear Algebra ◽  
Complex Analysis ◽  
Dimensional Space ◽  
Applied Mathematics ◽  
Three Dimensional ◽  
Number System ◽  
Graduate Course ◽  
Open Problems ◽  
Unpublished Research ◽  
Reference Tool

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.

Enlightening Symbols

2016 ◽  
Author(s):  
Joseph Mazur
Keyword(s):  
Sixteenth Century ◽  
Number System ◽  
Psychological Effects ◽  
Mathematical Notation ◽  
Rhetorical Style ◽  
The Past ◽  
Mathematical Symbols ◽  
Before And After ◽  
New Ideas ◽  
Different Cultures

While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? This book explains the fascinating history behind the development of our mathematical notation system. It shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted. Traversing mathematical history and the foundations of numerals in different cultures, the book looks at how historians have disagreed over the origins of the number system for the past two centuries. It follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. It also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. It considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics. From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

Concepts of Colour and Limits of Understanding

2018 ◽  
Author(s):  
Barry Stroud
Keyword(s):  
Ludwig Wittgenstein ◽  
Language Game ◽  
Number System ◽  
Colour System ◽  
Perfect Pitch

This chapter examines some puzzling reflections by Ludwig Wittgenstein on the possibility of understanding concepts of the colours of things different from those already familiar to us. It begins with a discussion of Wittgenstein’s statement: ‘Someone who has perfect pitch can learn a language-game that I cannot learn’. In particular, it considers how Wittgenstein draws a connection between perfect pitch and concepts of colours and invites us to imagine people who speak of colours intermediate between red and yellow by means of fractions in a kind of binary notation representing different proportions of the colours at each end of the range from red to yellow. The chapter also analyses Wittgenstein’s views on whether the number system and the colour system ‘reside in our nature or in the nature of things’.

scholarly journals Montgomery reduction within the context of residue number system arithmetic

2017 ◽  
Vol 8 (3) ◽  
pp. 189-200 ◽  
Author(s):  
Jean-Claude Bajard ◽  
Julien Eynard ◽  
Nabil Merkiche
Keyword(s):  
Number System ◽  
Residue Number System ◽  
Residue Number ◽  
Montgomery Reduction

scholarly journals Developing Number Sense: An Approach to Initiate Algebraic Thinking in Primary Education

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 518
Author(s):  
Natividad Adamuz-Povedano ◽  
Elvira Fernández-Ahumada ◽  
M. Teresa García-Pérez ◽  
Jesús Montejo-Gámez
Keyword(s):  
Teaching And Learning ◽  
Number Sense ◽  
Methodological Approach ◽  
Number System ◽  
Algebraic Thinking ◽  
First Year ◽  
Symbolic Language ◽  
Decimal Number ◽  
Language Characteristic ◽  
Theoretical Foundations

Traditionally, the teaching and learning of algebra has been addressed at the beginning of secondary education with a methodological approach that broke traumatically into a mathematical universe until now represented by numbers, with bad consequences. It is important, then, to find methodological alternatives that allow the parallel development of arithmetical and algebraic thinking from the first years of learning. This article begins with a review of a series of theoretical foundations that support a methodological proposal based on the use of specific manipulative materials that foster a deep knowledge of the decimal number system, while verbalizing and representing quantitative situations that underline numerical relationships and properties and patterns of numbers. Developing and illustrating this approach is the main purpose of this paper. The proposal has been implemented in a group of 25 pupils in the first year of primary school. Some observed milestones are presented and analyzed. In the light of the results, this well-planned early intervention contains key elements to initiate algebraic thinking through the development of number sense, naturally enhancing the translation of purely arithmetical situations into the symbolic language characteristic of algebraic thinking.

scholarly journals Hybrid Floating Point/Logarithmic Number System Processor

2020 ◽  
Vol 932 ◽  
pp. 012059
Author(s):  
C Y Sheng ◽  
R C Ismail ◽  
S Z M Naziri ◽  
M N M Isa ◽  
S A Z Murad ◽  
...  
Keyword(s):  
Number System ◽  
Floating Point ◽  
Logarithmic Number System ◽  
Logarithmic Number
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