The Historical Roots of Elementary Mathematics

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $3.89
Usually ships in 1-2 business days
(Save 77%)
Other sellers (Paperback)
  • All (13) from $3.89   
  • New (5) from $8.43   
  • Used (8) from $3.89   

Overview

"Will delight a broad spectrum of readers." — American Mathematical Monthly
Do long division as the ancient Egyptians did! Solve quadratic equations like the Babylonians! Study geometry just as students did in Euclid's day! This unique text offers students of mathematics an exciting and enjoyable approach to geometry and number systems. Written in a fresh and thoroughly diverting style, the text — while designed chiefly for classroom use — will appeal to anyone curious about mathematical inscriptions on Egyptian papyri, Babylonian cuneiform tablets, and other ancient records.
The authors have produced an illuminated volume that traces the history of mathematics — beginning with the Egyptians and ending with abstract foundations laid at the end of the 19th century. By focusing on the actual operations and processes outlined in the text, students become involved in the same problems and situations that once confronted the ancient pioneers of mathematics. The text encourages readers to carry out fundamental algebraic and geometric operations used by the Egyptians and Babylonians, to examine the roots of Greek mathematics and philosophy, and to tackle still-famous problems such as squaring the circle and various trisectorizations.
Unique in its detailed discussion of these topics, this book is sure to be welcomed by a broad range of interested readers. The subject matter is suitable for prospective elementary and secondary school teachers, as enrichment material for high school students, and for enlightening the general reader. No specialized or advanced background beyond high school mathematics is required.

Read More Show Less

Product Details

  • ISBN-13: 9780486255637
  • Publisher: Dover Publications
  • Publication date: 2/1/1988
  • Pages: 336
  • Sales rank: 708,862
  • Product dimensions: 5.39 (w) x 8.47 (h) x 0.64 (d)

Table of Contents

Preface
The Greek alphabet
1 EGYPTIAN MATHEMATICS
  1-1 Prehistoric mathematics
  1-2 The earliest written mathematics
  1-3 Numerical notation
  1-4 Arithmetic operations
  1-5 Multiplication
  1-6 Fractions and division
  1-7 The red auxiliary numbers
  1-8 The 2 ÷ n table
  1-9 The leather roll
  1-10 Algebraic problems
  1-11 Geometry
2 BABYLONIAN MATHEMATICS
  2-1 Some historical facts
  2-2 Babylonian numerical notation
  2-3 The fundamental operations
  2-4 Extraction of roots
  2-5 Babylonian algebra
  2-6 A Babylonian text
  2-7 Babylonian geometry
  2-8 Approximations to p
  2-9 Another problem and a farewell to the Babylonians
3 THE BEGINNING OF GREEK MATHEMATICS
  3-1 The earliest records
  3-2 Greek numeration systems
  3-3 Thales and his importance to mathematics
  3-4 Pythagoras and the Pythagoreans
  3-5 The Pythagoreans and music
  3-6 Pythagorean arithmetica
  3-7 Pythagorean numerology
  3-8 Pythagorean astronomy
  3-9 Pythagorean geometry
  3-10 Incommensurable segments and irrational numbers
4 THE FAMOUS PROBLEMS OF GREEK ANTIQUITY
  4-1 Introduction
  4-2 Hippocrates of Chios and the quadrature of lunes
  4-3 Other quadratures
  4-4 Hippocrates' geometry
  4-5 Duplication of the cube
  4-6 The trisection problem
  4-7 Hippias and squaring of the circle
  4-8 The solutions of the Greek problems
5 EUCLID'S PHILOSOPHICAL FORERUNNERS
  5-1 Philosophy and philosophers
  5-2 Plato
  5-3 Aristotle and his theory of statements
  5-4 Concepts and definitions
  5-5 Special notations and undefined terms
6 EUCLID
  6-1 Elements
  6-2 The structure of the Elements of Euclid
  6-3 The definitions
  6-4 Postulates and common notions
  6-5 The meaning of a construction
  6-6 The purport of Postulate III
  6-7 Congruence
  6-8 Congruence (continued)
  6-9 The theory of parallels
  6-10 The comparison of areas
  6-11 The theorem of Pythagoras
  6-12 The difference between the Euclidean and the modern method of comparing areas
  6-13 Geometric algebra and regular polygons
  6-14 Number theory in the Elements
7 GREEK MATHEMATICS AFTER EUCLID. EUCLIDEAN VS. MODERN METHODS
  7-1 The span of Greek mathematics
  7-2 Archimedes and Eratosthenes
  7-3 Apollonius of Perga
  7-4 Heron of Alexandria and Diophantus
  7-5 Ptolemy and Pappus
  7-6 Review of the Greek method
  7-7 Objections to the Euclidean system
  7-8 The meaning of deduction
  7-9 Euclid's system is not purely deductive
  7-10 How is geometry built up purely deductively?
  7-11 A four-point system
8 NUMERATION AND ARITHMETIC AFTER THE GREEKS
  8-1 Roman numerals
  8-2 The abacus and tangible arithmetic
  8-3 The Hindu-Arabic numerals
  8-4 An early American place-value numeration system
  8-5 Later developments in positional notation
  8-6 Conversions between numeration systems
  8-7 Addition and subtraction algorithms in nondecimal bases
  8-8 Multiplication alogorithms in nondecimal bases
  8-9 "Fractions, rational numbers, and place-value numeration"
  8-10 Irrational numbers
  8-11 Modern theoretical foundations of arithmetic
  8-12 Modern numeration
HINTS AND ANSWERS TO SELECTED ANSWERS
INDEX
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously
Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted August 29, 2012

    No text was provided for this review.

Sort by: Showing 1 Customer Reviews

If you find inappropriate content, please report it to Barnes & Noble
Why is this product inappropriate?
Comments (optional)