The Ellipse: A Historical and Mathematical Journey / Edition 1

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $14.54
Usually ships in 1-2 business days
(Save 78%)
Other sellers (Paperback)
  • All (11) from $14.54   
  • New (6) from $49.12   
  • Used (5) from $14.54   


Explores the development of the ellipse and presents mathematical concepts within a rich, historical context

The Ellipse features a unique, narrative approach when presenting the development of this mathematical fixture, revealing its parallels to mankind's advancement from the Counter-Reformation to the Enlightenment. Incorporating illuminating historical background and examples, the author brings together basic concepts from geometry, algebra, trigonometry, and calculus to uncover the ellipse as the shape of a planet's orbit around the sun.

The book begins with a discussion that tells the story of man's pursuit of the ellipse, from Aristarchus to Newton's successful unveiling nearly two millenniums later. The narrative draws insightful similarities between mathematical developments and the advancement of the Greeks, Romans, Medieval Europe, and Renaissance Europe. The author begins each chapter by setting the historical backdrop that is pertinent to the mathematical material that is discussed, equipping readers with the knowledge to fully grasp the presented examples and derive the ellipse as the planetary pathway. All topics are presented in both historical and mathematical contexts, and additional mathematical excursions are clearly marked so that readers have a guidepost for the materials' relevance to the development of the ellipse.

The Ellipse is an excellent book for courses on the history of mathematics at the undergraduate level. It is also a fascinating reference for mathematicians, engineers, or anyone with a general interest in historical mathematics.

Read More Show Less

Editorial Reviews

From the Publisher
“This is an interesting book, and despite the shortcomings mentioned at the beginning of this review, it’s an absorbing book, borne of a great enthusiasm for mathematics, and I shall continue to dip into it for a long time to come.”  (Journal of the British Society for the History of Mathematics, 1 March 2014)

"Recommended. Mathematics and history of mathematics collections serving lower-division undergraduates and above". (Choice, 1 November 2010)

Read More Show Less

Product Details

  • ISBN-13: 9780470587188
  • Publisher: Wiley
  • Publication date: 4/26/2010
  • Edition number: 1
  • Pages: 320
  • Product dimensions: 6.10 (w) x 9.20 (h) x 0.90 (d)

Meet the Author

Arthur Mazer, PhD, is Manager of Quantitative Analytics at Southern California Edison, where he oversees the risk assessment of the company's power and gas portfolio. Throughout his career, he has held various academic positions as well as analyst positions at Electrabel, Process Energy, and Energy Power Marketing Company. Dr. Mazer is the author of Electric Power Planning for Regulated and Deregulated Markets, also published by Wiley.

Read More Show Less

Table of Contents




2.1 A Sticky Matter.

2.2 Numbers.

2.2.1 Integers, Rational Numbers, and Irrational Numbers.

2.2.2 The Size of the Irrational Numbers.

2.2.3 Suitability of Rationals and the Decimal System.

2.2.4 Rational and Irrational Outcomes.


3.1 Euclidean Space, Dimension and Rescaling.

3.1.1 Euclidean Space and Objects.

3.1.2 Euclidean Space in Higher Dimensions.

3.1.3 Unit Measurements and Measures of Objects.

3.1.4 Rescaling, Measurement, and Dimension.

3.1.5 Koch's Snowflake, a Fractal Object.

3.2 Measurements of Various Objects.

3.2.1 Pythagorean Theorem, Length of the Hypotenuse.

3.2.2 Cavalieri's Theorem in Two Dimensions.

3.2.3 Cavalieri's Theorem, Archimedes Weighs In.

3.2.4 Simple Applications of Cavalieri’s Theorem.

3.2.5 The Circle.

3.2.6 Surface Area of the Cone.

3.2.7 Cavalieri's Theorem a Stronger Version in Three Dimensions.

3.2.8 Generalized Pyramids.

3.2.9 The Sphere as a Generalized Pyramid.

3.2.10 The Surface Area and Volume of the Sphere.

3.2.11 Equal-Area Maps, Another Excursion.


4.1 Cartesian Coordinates and Translation of the Axes.

4.1.1 Intersections of Geometric Objects as Solutions to Equations.

4.1.2 Translation of Axis and Object.

4.2 Polynomials.

4.2.1 Lines.

4.2.2 Parabolas and the Quadratic Equation.

4.3 Circles.

4.3.1 Equations for a Circle.

4.3.2 Archimedes and the Value of π.

4.3.3 Tangent Lines to a Circle.

4.4 The Four-Dimensional Sphere.

4.4.1 Pythagorean Theorem in Higher Dimensions.

4.4.2 Measurements in Higher Dimensions and n-Dimensional Cubes.

4.4.3 Cavalieri's Theorem.

4.4.4 Pyramids.

4.4.5 The n-Dimensional Sphere as an n-Dimensional Pyramid

4.4.6 The Three-Dimensional Volume of the Four-Dimensional Sphere's Surface

4.5 Finite Series and Induction.

4.5.1 A Simple Sum.

4.5.2 Induction.

4.5.3 Using Induction as a Solution Method.

4.6 Linear Algebra in Two Dimensions.

4.6.1 Vectors.

4.6.2 The Span of Vectors.

4.6.3 Linear Transformations of the Plane Onto Itself.

4.6.4 The Inverse of a Linear Transformation.

4.6.5 The Determinant.

4.7 The Ellipse.

4.7.1 The Ellipse as a Linear Transformation of a Circle.

4.7.2 The Equation of an Ellipse.

4.7.3 An Excursion into the Foci of an Ellipse.


5.1 Trigonometric Functions.

5.1.1 Basic Definitions.

5.1.2 Triangles.

5.1.3 Examples.

5.2 Graphs of the Sine, Cosine, and Tangent Functions.

5.3 Rotations.

5.4 Identities.

5.4.1 Pythagorean Identity.

5.4.2 Negative of an Angle.

5.4.3 Tan(θ) in Terms of Sin(θ) and Cos(θ).

5.4.4 Sines and Cosines of Sums of Angles.

5.4.5 Difference Formulas.

5.4.6 Double-Angle Formulas.

5.4.7 Half-Angle Formulas.

5.5 Lucky 72.

5.6 Ptolemy and Aristarchus.

5.6.1 Construction of Ptolemy's Table.

5.6.2 Remake of Aristarchus.

5.7 Drawing a Pentagon.

5.8 Polar Coordinates.

5.9 The Determinant.


6.1 Studies of Motion and the Fundamental Theorem of Calculus.

6.1.1 Constant Velocity and Two Problems of Motion.

6.1.2 Differential Calculus, Generalizing the First Problem.

6.1.3 Integral Calculus, Generalizing the Second Problem.

6.1.4 Relations Between Differentiation and Integration and the Fundamental Theorem of Calculus.

6.1.5 Integration, Leibniz’ Notation, and the Fundamental Theorem of Calculus.

6.2 More Motion: Going in Circles.

6.3 More Differential Calculus.

6.3.1 Differentiation Rules.

6.3.2 Notation and the Derivative at a Specified Point.

6.3.3 Higher Order Differentiation and Examples.

6.3.4 Differentiation and the Enquirer.

6.4 More Integral Calculus.

6.4.1 The Antiderivative and the Fundamental Theorem of Calculus.

6.4.2 Methods of Integration.

6.5 Potpourri.

6.5.1 Cavalieri's Theorem and the Fundamental Theorem of Calculus.

6.5.2 Volume of the Sphere and Other Objects with Known Cross-Sectional Areas.


7.1 Newton's Laws of Motion.

7.2 Galilean Checkpoint.

7.3 Constants of Motion and Energy.

7.3.1 Energy of a Tossed Object.

7.3.2 Energy of a System Moving in a Single Dimension.

7.4 Kepler and Newton: Aristarchus Redeemed.

7.4.1 Polar Coordinates.

7.4.2 Angular Momentum.

7.4.3 The Ellipse.




Read More Show Less

Customer Reviews

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

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & 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 & 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 & 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 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


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & 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 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)