Invention Of Numbers

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Making up Numbers: A History of Invention in Mathematics

Author : Ekkehard Kopp
Publisher : Open Book Publishers
ISBN 13 : 1800640978
Total Pages : 280 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Making up Numbers: A History of Invention in Mathematics by : Ekkehard Kopp

Download or read book Making up Numbers: A History of Invention in Mathematics written by Ekkehard Kopp and published by Open Book Publishers. This book was released on 2020-10-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

The Invention of Numbers

Author : Peter Bentley
Publisher : Weidenfeld & Nicolson
ISBN 13 : 9781844039111
Total Pages : 272 pages
Book Rating : 4.0/5 (391 download)

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Book Synopsis The Invention of Numbers by : Peter Bentley

Download or read book The Invention of Numbers written by Peter Bentley and published by Weidenfeld & Nicolson. This book was released on 2016-08-11 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers are at the heart of the existence of the universe and everything in it, and yet a lot of us have little understanding of their creation, let alone their part in philosophy, art, music, physics, literature, religion and computing. Dr Bentley's fascinating history of the origins of numbers will unlock the secrets of these things that we take for granted and shows how numbers seem to take on human characteristiscs - as they can be perfect or irrational, amicable or prime, real or imaginary. From zero to infinity, learn about the way numbers have shaped our world, discover amazing facts and enjoy the pure beauty of mathematical logic.

A Brief History of Numbers

Author : Leo Corry
Publisher : OUP Oxford
ISBN 13 : 0191007072
Total Pages : 324 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis A Brief History of Numbers by : Leo Corry

Download or read book A Brief History of Numbers written by Leo Corry and published by OUP Oxford. This book was released on 2015-08-27 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.

Numbers and the Making of Us

Author : Caleb Everett
Publisher : Harvard University Press
ISBN 13 : 0674504437
Total Pages : 308 pages
Book Rating : 4.6/5 (745 download)

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Book Synopsis Numbers and the Making of Us by : Caleb Everett

Download or read book Numbers and the Making of Us written by Caleb Everett and published by Harvard University Press. This book was released on 2017-03-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: “A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal

Number Words and Number Symbols

Author : Karl Menninger
Publisher : Courier Corporation
ISBN 13 : 0486319776
Total Pages : 514 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Number Words and Number Symbols by : Karl Menninger

Download or read book Number Words and Number Symbols written by Karl Menninger and published by Courier Corporation. This book was released on 2013-04-10 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic study discusses number sequence and number language, then explores written numerals and computations in a wide range of cultures. 282 illustrations. "Superior narrative ability." — Library Journal.

From One to Zero

Author : Georges Ifrah
Publisher : Penguin Group
ISBN 13 :
Total Pages : 530 pages
Book Rating : 4.X/5 (1 download)

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Book Synopsis From One to Zero by : Georges Ifrah

Download or read book From One to Zero written by Georges Ifrah and published by Penguin Group. This book was released on 1987 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Traces the development of numerical systems in Sumerian, Egyptian, Greek, Roman, Chinese, Babylonian, and Mayan cultures, and examines the origins of the Hindu-Arabic numerals we use today"--Back cover.

The Universal History of Numbers

Author : Georges Ifrah
Publisher : Wiley
ISBN 13 : 9780471393405
Total Pages : 660 pages
Book Rating : 4.3/5 (934 download)

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Book Synopsis The Universal History of Numbers by : Georges Ifrah

Download or read book The Universal History of Numbers written by Georges Ifrah and published by Wiley. This book was released on 2000-10-09 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Georges Ifrah is the man. This book, quite simply, rules. . . . It is outstanding . . . a mind-boggling and enriching experience." –The Guardian (London) "Monumental. . . . a fascinating journey taking us through many different cultures."–The Times (London)"Ifrah’s book amazes and fascinates by the scope of its scholarship. It is nothing less than the history of the human race told through figures." –International Herald Tribune Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years. "Dazzling."–Kirkus Reviews "Sure to transfix readers."–PublishersWeekly

Number Theory and Its History

Author : Oystein Ore
Publisher : Courier Corporation
ISBN 13 : 0486136434
Total Pages : 404 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Number Theory and Its History by : Oystein Ore

Download or read book Number Theory and Its History written by Oystein Ore and published by Courier Corporation. This book was released on 2012-07-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unusually clear, accessible introduction covers counting, properties of numbers, prime numbers, Aliquot parts, Diophantine problems, congruences, much more. Bibliography.

How Writing Came About

Author : Denise Schmandt-Besserat
Publisher : University of Texas Press
ISBN 13 : 0292774869
Total Pages : 277 pages
Book Rating : 4.2/5 (927 download)

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Book Synopsis How Writing Came About by : Denise Schmandt-Besserat

Download or read book How Writing Came About written by Denise Schmandt-Besserat and published by University of Texas Press. This book was released on 2010-01-01 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: An “utterly lucid, thoughtfully illustrated, and thoroughly convincing” book on the origins of the world’s oldest known system of writing (American Journal of Archaeology). One of American Scientist's Top 100 Books on Science, 2001 In 1992, the University of Texas Press published Before Writing, Volume I: From Counting to Cuneiform and Before Writing, Volume II: A Catalog of Near Eastern Tokens. In these two volumes, Denise Schmandt-Besserat set forth her groundbreaking theory that the cuneiform script invented in the Near East in the late fourth millennium B.C.—the world's oldest known system of writing—derived from an archaic counting device. How Writing Came About draws material from both volumes of this scholarly work to present Schmandt-Besserat’s theory in an abridged version for a wide public and classroom audience. Based on the analysis and interpretation of a selection of 8,000 tokens or counters from 116 sites in Iran, Iraq, the Levant, and Turkey, it documents the immediate precursor of the cuneiform script./DIV

Numbers

Author : Graham Flegg
Publisher : Courier Corporation
ISBN 13 : 0486166511
Total Pages : 307 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Numbers by : Graham Flegg

Download or read book Numbers written by Graham Flegg and published by Courier Corporation. This book was released on 2013-05-13 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

Uncountable

Author : David Nirenberg
Publisher : University of Chicago Press
ISBN 13 : 022664698X
Total Pages : 429 pages
Book Rating : 4.2/5 (266 download)

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Book Synopsis Uncountable by : David Nirenberg

Download or read book Uncountable written by David Nirenberg and published by University of Chicago Press. This book was released on 2021-10-20 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: "From the time of Pythagoras, we have been tempted to treat numbers as the ultimate or only truth. This book tells the history of that habit of thought. But more, it argues that the logic of counting sacrifices much of what makes us human, and that we have a responsibility to match the objects of our attention to the forms of knowledge that do them justice. Humans have extended the insights and methods of number and mathematics to more and more aspects of the world, even to their gods and their religions.Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity.But the rules of mathematics do not strictly apply to many things-from elementary particles to people-in the world.By subjecting such things to the laws of logic and mathematics, we gain some kinds of knowledge, but we also lose others. How do our choices about what parts of the world to subject to the logics of mathematics affect how we live and how we die?This question is rarely asked, but it is urgent, because the sciences built upon those laws now govern so much of our knowledge, from physics to psychology.Number and Knowledge sets out to ask it. In chapters proceeding chronologically from Ancient Greek philosophy and the rise of monotheistic religions to the emergence of modern physics and economics, the book traces how ideals, practices, and habits of thought formed over millennia have turned number into the foundation-stone of human claims to knowledge and certainty.But the book is also a philosophical and poetic exhortation to take responsibility for that history, for the knowledge it has produced, and for the many aspects of the world and of humanity that it ignores or endangers.To understand what can be counted and what can't is to embrace the ethics of purposeful knowing"--

The Universal History Of Numbers 2: The Modern Number-System

Author : Georges Ifrah
Publisher :
ISBN 13 : 9780143032588
Total Pages : 0 pages
Book Rating : 4.0/5 (325 download)

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Book Synopsis The Universal History Of Numbers 2: The Modern Number-System by : Georges Ifrah

Download or read book The Universal History Of Numbers 2: The Modern Number-System written by Georges Ifrah and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numbers Are One Of Two Creations (The Other Being The Alphabet) Of The Human Spirit Which Have Given Us Today S World. The Three Volumes Of The Universal History Of Numbers Are Probably The First Comprehensive History Of Numbers And Of Counting From Prehistory To The Modern Age. They Are Also The Story Of How The Human Race Has Learnt To Think Logically. In Volume 2, Georges Ifrah Continues The Story Of The Invention Of The Modern Number-System By Telling Us How Indian Civilization Became The Cradle Of Modern Numerals With The Invention Of The Place Value System And Of Zero. Twenty-One Geographically Different Indian Numerical Notations Of The Nine Numerals And The Zero Are Explained Individually With Illustrations. A Detailed Dictionary Of Indian Numerical Symbols, Recorded Alphabetically, Gives The Reader A Better Idea Of The Subtle And Complicated World Of Numbers Which Derived From The Genius Of Indian Mathematicians Working In The Late Middle Ages. It Was Arab Scholars Who Brought The System To The West. If Western Mathematical Progress Today Looks Dazzling, It Is Because It Stands On A Solid Non-Western Foundation. Amazing, Captivating And Enriching, The Universal History Of Numbers Is A Must Read Not Only For Specialists And Academics, But Also For The Average Reader Who Is Interested In The Development Of Civilization.

The Story of Our Numbers

Author : Zelda King
Publisher : The Rosen Publishing Group, Inc
ISBN 13 : 9780823988709
Total Pages : 30 pages
Book Rating : 4.9/5 (887 download)

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Book Synopsis The Story of Our Numbers by : Zelda King

Download or read book The Story of Our Numbers written by Zelda King and published by The Rosen Publishing Group, Inc. This book was released on 2010-01-01 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the history of written numbers, from ancient Roman numerals to the invention of the Hindu-Arabic numeral system and the spread of the Arabic numeral system around the world.

Invention of Numbers

Author : R. H. S. White
Publisher : New Generation Publishing
ISBN 13 : 1800314310
Total Pages : 187 pages
Book Rating : 4.8/5 (3 download)

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Book Synopsis Invention of Numbers by : R. H. S. White

Download or read book Invention of Numbers written by R. H. S. White and published by New Generation Publishing. This book was released on 2020-12-02 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excavations carried out in 1970 in the Lebombo mountains of Southern Africa, uncovered the fossilised leg bone of a baboon, estimated to be 37,000 years old, that had 29 scratches carved into it.In 1937 the fossilised bone of a wolf was found in Czechoslovakia, that had 37 scratches on its length, grouped in fives. This bone was estimated to be 30,000 years old.Ancient peoples realised that it was useful to group the marks into equal size bundles and invent symbols for the bundles. Thus arithmetic was born.Part 1 of this book studies the symbols invented by Babylonians, Egyptians, the Greeks, the Chinese, Etruscans and Romans, the Maya and the Hindus.In 628 AD the Indian mathematician Brahmagupta defined the number zero and described the base ten positional number system in his book called "e;The Opening of the Universe"e;. In 1202, Fibonacci, the son of a Venetian merchant, describes the Indian base ten number system in his book "e;Liber Abaci"e; that resulted in this arithmetic being introduced into Europe.Part 2 introduces number systems in other bases, in particular, Binary, Octal and Hexadecimal as used in modern computers and the ASCII codes used for storing letters of the alphabet and other symbols.Part 3 deals with the construction and rules for negative and fractional numbers, why we add, multiply and divide fractions in the way we do. It defines complex numbers, gives the meaning of the square root of minus one and shows how complex numbers are represented on the Argand diagram. It solves quadratic and cubic equations and shows how De Moivre's Theorem can be used to find roots of complex numbers.

The Man of Numbers

Author : Keith Devlin
Publisher : A&C Black
ISBN 13 : 1408824574
Total Pages : 193 pages
Book Rating : 4.4/5 (88 download)

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Book Synopsis The Man of Numbers by : Keith Devlin

Download or read book The Man of Numbers written by Keith Devlin and published by A&C Black. This book was released on 2011-11-07 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1202, a 32-year old Italian finished one of the most influential books of all time, which introduced modern arithmetic to Western Europe. Devised in India in the seventh and eighth centuries and brought to North Africa by Muslim traders, the Hindu-Arabic system helped transform the West into the dominant force in science, technology, and commerce, leaving behind Muslim cultures which had long known it but had failed to see its potential. The young Italian, Leonardo of Pisa (better known today as Fibonacci), had learned the Hindu number system when he traveled to North Africa with his father, a customs agent. The book he created was Liber abbaci, the 'Book of Calculation', and the revolution that followed its publication was enormous. Arithmetic made it possible for ordinary people to buy and sell goods, convert currencies, and keep accurate records of possessions more readily than ever before. Liber abbaci's publication led directly to large-scale international commerce and the scientific revolution of the Renaissance. Yet despite the ubiquity of his discoveries, Leonardo of Pisa remains an enigma. His name is best known today in association with an exercise in Liber abbaci whose solution gives rise to a sequence of numbers - the Fibonacci sequence - used by some to predict the rise and fall of financial markets, and evident in myriad biological structures. In The Man of Numbers, Keith Devlin recreates the life and enduring legacy of an overlooked genius, and in the process makes clear how central numbers and mathematics are to our daily lives.

The History of Number Systems: Place Value

Author : Gabriel Esmay
Publisher : Teacher Created Materials
ISBN 13 : 1480757942
Total Pages : 35 pages
Book Rating : 4.4/5 (87 download)

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Book Synopsis The History of Number Systems: Place Value by : Gabriel Esmay

Download or read book The History of Number Systems: Place Value written by Gabriel Esmay and published by Teacher Created Materials. This book was released on 2017-06-01 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Learn the history of number systems with this engaging book! This text combines mathematics and literacy skills, and uses practical, real-world examples of problem solving to teach math and language arts content. Students will learn place value while reading about the number systems of the Egyptians and Romans, and also learn important vocabulary terms like cuneiform, binary systems, roman numerals, and more! The full-color images, math charts, and practice problems make learning math easy and fun. The table of contents, glossary, and index will further understanding of math and reading concepts. The Math Talk problems and Explore Math sidebars provide additional learning opportunities while developing students higher-order thinking skills.

The Story Of Numbers

Author : Asok Kumar Mallik
Publisher : #N/A
ISBN 13 : 9813222948
Total Pages : 197 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis The Story Of Numbers by : Asok Kumar Mallik

Download or read book The Story Of Numbers written by Asok Kumar Mallik and published by #N/A. This book was released on 2017-07-27 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: '… this could make an ideal end-of-year prize for a high-school student who is fascinated by all aspects of number. The subsections provide ideas and opportunities for mathematical exploration. This book might also be deemed a suitable resource for first-year undergraduates in that, via independent study, it would allow such students to broaden their knowledge of various number-theoretic ideas. I would recommend it for the purposes given above.'The Mathematical GazetteThis book is more than a mathematics textbook. It discusses various kinds of numbers and curious interconnections between them. Without getting into hardcore and difficult mathematical technicalities, the book lucidly introduces all kinds of numbers that mathematicians have created. Interesting anecdotes involving great mathematicians and their marvelous creations are included. The reader will get a glimpse of the thought process behind the invention of new mathematics. Starting from natural numbers, the book discusses integers, real numbers, imaginary and complex numbers and some special numbers like quaternions, dual numbers and p-adic numbers.Real numbers include rational, irrational and transcendental numbers. Iterations on real numbers are shown to throw up some unexpected behavior, which has given rise to the new science of 'Chaos'. Special numbers like e, pi, golden ratio, Euler's constant, Gauss's constant, amongst others, are discussed in great detail.The origin of imaginary numbers and the use of complex numbers constitute the next topic. It is shown why modern mathematics cannot even be imagined without imaginary numbers. Iterations on complex numbers are shown to generate a new mathematical object called 'Fractal', which is ubiquitous in nature. Finally, some very special numbers, not mentioned in the usual textbooks, and their applications, are introduced at an elementary level.The level of mathematics discussed in this book is easily accessible to young adults interested in mathematics, high school students, and adults having some interest in basic mathematics. The book concentrates more on the story than on rigorous mathematics.