Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Circles: A Mathematical View
 
Dan Pedoe
Circles
MAA Press: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-5732-7
Product Code:  SPEC/12.E
List Price: $50.00
MAA Member Price: $37.50
AMS Member Price: $37.50
Add to cart
Circles
Click above image for expanded view
Circles: A Mathematical View
Dan Pedoe
MAA Press: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-4704-5732-7
Product Code:  SPEC/12.E
List Price: $50.00
MAA Member Price: $37.50
AMS Member Price: $37.50
Add to cart
  • Book Details
     
     
    Spectrum
    Volume: 12; 1997; 102 pp

    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. The author has supplemented this new edition with a special chapter designed to introduce readers to the vocabulary of circle concepts with which the readers of two generations ago were familiar. Readers of Circles need only be armed with paper, pencil, compass, and straight edge to find great pleasure in following the constructions and theorems. Those who think that geometry using Euclidean tools died out with the ancient Greeks will be pleasantly surprised to learn many interesting results which were only discovered in modern times. Novices and experts alike will find much to enlighten them in chapters dealing with the representation of a circle by a point in three-space, a model for non-Euclidean geometry, and the isoperimetric property of the circle.
  • Table of Contents
     
     
    • Articles
    • The nine-point circle
    • Inversion
    • Feuerbach’s theorem
    • Extension of Ptolemy’s theorem
    • Fermat’s problem
    • The centres of similitude of two circles
    • Coaxal systems of circles
    • Canonical form for coaxal system
    • Further properties
    • Problem of Apollonius
    • Compass geometry
    • Representation of a circle
    • Euclidean three-space $E_3$
    • First properties of the representation
    • Coaxal systems
    • Deductions from the representation
    • Conjugacy relations
    • Circles cutting at a given angle
    • Representation of inversion
    • The envelope of a system
    • Some further applications
    • Some anallagmatic curves
    • Complex numbers
    • The Argand diagram
    • Modulus and argument
    • Circles as level curves
    • The cross-ratio of four complex numbers
    • Möbius transformations of the ${\frak s}$-plane
    • A Möbius transformation dissected
    • The group property
    • Special transformations
    • The fundamental theorem
    • The Poincaré model
    • The parallel axiom
    • Non-Euclidean distance
    • Steiner’s enlarging process
    • Existence of a solution
    • Method of solution
    • Area of a polygon
    • Regular polygons
    • Rectifiable curves
    • Approximation by polygons
    • Area enclosed by a curve
  • Reviews
     
     

    • 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.'
      The Mathematics Teacher, May 1996
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Spectrum
Volume: 12; 1997; 102 pp

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. The author has supplemented this new edition with a special chapter designed to introduce readers to the vocabulary of circle concepts with which the readers of two generations ago were familiar. Readers of Circles need only be armed with paper, pencil, compass, and straight edge to find great pleasure in following the constructions and theorems. Those who think that geometry using Euclidean tools died out with the ancient Greeks will be pleasantly surprised to learn many interesting results which were only discovered in modern times. Novices and experts alike will find much to enlighten them in chapters dealing with the representation of a circle by a point in three-space, a model for non-Euclidean geometry, and the isoperimetric property of the circle.
  • Articles
  • The nine-point circle
  • Inversion
  • Feuerbach’s theorem
  • Extension of Ptolemy’s theorem
  • Fermat’s problem
  • The centres of similitude of two circles
  • Coaxal systems of circles
  • Canonical form for coaxal system
  • Further properties
  • Problem of Apollonius
  • Compass geometry
  • Representation of a circle
  • Euclidean three-space $E_3$
  • First properties of the representation
  • Coaxal systems
  • Deductions from the representation
  • Conjugacy relations
  • Circles cutting at a given angle
  • Representation of inversion
  • The envelope of a system
  • Some further applications
  • Some anallagmatic curves
  • Complex numbers
  • The Argand diagram
  • Modulus and argument
  • Circles as level curves
  • The cross-ratio of four complex numbers
  • Möbius transformations of the ${\frak s}$-plane
  • A Möbius transformation dissected
  • The group property
  • Special transformations
  • The fundamental theorem
  • The Poincaré model
  • The parallel axiom
  • Non-Euclidean distance
  • Steiner’s enlarging process
  • Existence of a solution
  • Method of solution
  • Area of a polygon
  • Regular polygons
  • Rectifiable curves
  • Approximation by polygons
  • Area enclosed by a curve

  • 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.'
    The Mathematics Teacher, May 1996
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Powered by MathJax
Please select which format for which you are requesting permissions.