Circles: A Mathematical View (Spectrum Series)

Overview

This revised edition of a mathematical classic originally published in 1957 will bring to a new generation of students the enjoyment of investigating that simplest of mathematical figures, the circle. As a concession to the general neglect of geometry in school and college curricula, however, the author has supplemented this new edition with a chapter 0 designed to introduce readers to the special vocabulary of circle concepts with which the author could assume his readers of two generation ago were familiar. For...
See more details below
Available through our Marketplace sellers.
Other sellers (Paperback)
  • All (8) from $12.33   
  • New (3) from $24.50   
  • Used (5) from $12.33   
Close
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any BN.com coupons and promotions
$24.50
Seller since 2007

Feedback rating:

(433)

Condition:

New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.

New
Brand new. We distribute directly for the publisher. Clean, unmarked pages. Good binding and cover. Ships daily.

Ships from: Boonsboro, MD

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
  • Express, 48 States
  • Express (AK, HI)
$69.99
Seller since 2008

Feedback rating:

(17412)

Condition: New
Brand New, Perfect Condition, Please allow 4-14 business days for delivery. 100% Money Back Guarantee, Over 1,000,000 customers served.

Ships from: Westminster, MD

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
$70.00
Seller since 2014

Feedback rating:

(135)

Condition: New
Brand new.

Ships from: acton, MA

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
Page 1 of 1
Showing All
Close
Sort by
Sending request ...

Overview

This revised edition of a mathematical classic originally published in 1957 will bring to a new generation of students the enjoyment of investigating that simplest of mathematical figures, the circle. As a concession to the general neglect of geometry in school and college curricula, however, the author has supplemented this new edition with a chapter 0 designed to introduce readers to the special vocabulary of circle concepts with which the author could assume his readers of two generation ago were familiar. For example, Pedoe carefully explains what is meant by the circumcircle, incircle and excircles of a triangle as well as the circumcentre, incentre, and orthocenter. The reader can then understand his discussion in Chapter 1 of the nine-point circle, and of Feuerbach's theorem. S an appendix, Pedoe includes a biographical article by Laura Geggenbuhl on Karl Wilhelm Feuerbach, a little-known mathematician with a tragically short life, who published his theorem in a slender geometric treatise in 1822.

Readers of Circles need only be armed with paper, pencil compass and straightedge to find great pleasure in following the constructions and theorems. Those who think that geometry using Euclidean tools dies out with the ancient Greeks will be pleasantly surprised to learn many interesting results which were only discovered in modern times. And those who think that they learned all they needed to know about circles in high school will find much to enlighten them in chapter dealing with the representation of a circle by a point in three-space, a model for non-Euclidean geometry, and isoperimetric property of the circle.

Exercises (with solutions) complement the discussion and help the reader benefit fully from this mathematical view of circles.

Read More Show Less

Editorial Reviews

The Mathematics Teacher
" This excellent little book is an invaluable addition to the library of any teacher of geometry at any level..Discussions are straightforward; figures are well done; and the tone of the discourse is "friendly".
May, 1996
Booknews
For teachers and students of geometry, a reprint of a classic first published in 1957. Covers the vocabulary of circle concepts (the circumcircle, incircle, and excircle of a triangle, for instance, and its circumcenter and orthocenter), and subjects such as the nine- point circle, Fermat's problem, complex numbers, non-Euclidean distance, and polygons. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Read More Show Less

Product Details

  • ISBN-13: 9780883855188
  • Publisher: Mathematical Association of America
  • Publication date: 3/28/1997
  • Series: Spectrum Series
  • Edition description: Revised Edition
  • Edition number: 2
  • Pages: 144
  • Product dimensions: 6.48 (w) x 9.46 (h) x 0.32 (d)

Table of Contents

Preface
Chapter I
1. The nine-point circle
2. Inversion
3. Feuerbach's theorem
4. Extension of Ptolemy's theorem
5. Fermat's problem
6. The centres of similitude of two circles
7. Coaxal systems of circles
8. Canonical form for coaxal system
9. Further properties
10. Problems of Appollonius
11. Compass geometry

Chapter II
1. Representation of a circle
2. Euclidean three-space, E3
3. First properties of the represntation
4. Coaxal systems
5. Deductions from the representation
6. Conjugacy relations
7. Circles cutting at a given angle
8. representation of inversion
9. The envelope of a system
10. Some further applications
11. Some anallagmatic curve

Chapter III
1. Complex numbers
2. The Argand diagram
3. Modulus and argument
4. Circles as level curves
5. The cross-ratio of four complex numbers
6. Möbius transformations of the s-plane
7. A Möbius transformation dissected
8. The group property
9. Special transformations
10. The fundamental theorem
11. The Poincaré model
12. The parallel axiom
13. Non-Euclideam distance

Chapter IV
1. Steiner's enlarging process
2. Existence of a solution
3. Method of solution
4. Area of a polygon
5. Regular polygons
6. Rectifiable curves
7. Approximation by polygons
8. Area enclosed by a curve

Exercises
Solutions
Appendix: Karl Wilhelm Feuerbach, Mathematician by Laura Guggenbuhl
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

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