Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.
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'The book is rich in remarkable facts and thereby is very effective in promoting the significance and the value of geometry in mathematical teaching, a promotion which is very necessary.' Mathematical Reviews
Book Description
Among the many beautiful and nontrivial theorems in geometry found here are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.
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Most Helpful Customer Reviews
55 of 55 people found the following review helpful:
5.0 out of 5 stars
FOR ALL THOSE INTERESTED IN MATHEMATICS,
By A Customer
This review is from: Geometry Revisited (Mathematical Association of America Textbooks) (Paperback)
This is 'the book' the typical high school student in America needs to read in order to see what Geometry is really all about. Geometry can be fun and engaging. Unfortunately it has taken a back seat in the high school curriculum. This is unfortunate considering the beauty that the subject has to offer. Many topics are covered in this book: The extended law of cosines, Ptolemy's theorem, transformational geometry, conics, and many, many, many more. This is also a book that is essential for mathematical problem solvers-- particularly for those interested in competing. All that is needed to follow along is the basic geometry learned at the high school level. This book is a must have for any mathematical library. A++ Highly recommended.
56 of 59 people found the following review helpful:
5.0 out of 5 stars
THE BEST SOURCE FOR GEOMETRY,
By
This review is from: Geometry Revisited (Mathematical Association of America Textbooks) (Paperback)
I am a high school student who competes in extracurricular mathematics contests. I've found many great books for trigonometry, algebra, precalculus, calculus, and any other field of math except geometry, i.e. until I found this book. A thorough knowledge of geometry beyond what you learn in high school in necessary needed to be competitive, and the place to get it is Geometry Revisited. This book covers any geometry you could need and is by far the best, if not the only, book out there with what you need to know. This book was also very interesting and thought provoking. The selection and arrangement of topics couldn't be any better. Each lesson even contains exercises (with answers and hints) to show you how to apply what the book teaches you. I would recommend this book to any high school student competing in any contests, to any person interested in extending their knowledge of geometry, or to anyone who with any interest in math. I can tell you that you will learn multitudes and enjoy the book too.
36 of 38 people found the following review helpful:
5.0 out of 5 stars
The Best Undergrad Level Geometry Book Ever,
By Wing (NYC) - See all my reviews
This review is from: Geometry Revisited (Mathematical Association of America Textbooks) (Paperback)
Geometry Revisited should be used as a textbook for every geometry class in high school. It offers comprehensive proofs and theorems that every undergrad should know by the time he/she gets through basic geometry. The last sections of this book also offers a slight touch on comcepts such as non-Eucledian and projective geometry, serving as a launchpad to higher levels of education. I highly recommend this book to any high school or undergrad teachers and students.
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Inside This Book
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First Sentence:
The purpose of this chapter is to recall some of these half-forgotten things to which Dr. Bell referred, to derive some new theorems, developed since Euclid, and to apply our findings to interesting situation. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
orthic triangle, cyclic quadrangle, inversive distance, spiral similarity, pedal triangle, coaxal circles, medial triangle, radical axis, central dilatation, inversive plane, radical axes, quadrangle abcd, external bisectors, central conic, internal bisector, inversive geometry, circles orthogonal, collinear points, gnomonic projection, inverse points, direct similarity, directed segments, angle bisectors, triangle whose vertices, antipodal points Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The purpose of this chapter is to recall some of these half-forgotten things to which Dr. Bell referred, to derive some new theorems, developed since Euclid, and to apply our findings to interesting situation. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
orthic triangle, cyclic quadrangle, inversive distance, spiral similarity, pedal triangle, coaxal circles, medial triangle, radical axis, central dilatation, inversive plane, radical axes, quadrangle abcd, external bisectors, central conic, internal bisector, inversive geometry, circles orthogonal, collinear points, gnomonic projection, inverse points, direct similarity, directed segments, angle bisectors, triangle whose vertices, antipodal points Key Phrases - Capitalized Phrases (CAPs): (learn more)
Applying Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 33
books:
See all 33 books this book cites
68
books
cite this book:
See all 68 books citing this book
- Graphs and their Uses (Anneli Lax New Mathematical Library) by Oystein Ore in Front Matter, and Back Matter
- Geometric Inequalities (New Mathematical Library) by Nicholas D. Kazarinoff in Front Matter, and Back Matter
- Projective Geometry by H.S.M. Coxeter on page 76, and Back Matter
- Riddles of the Sphinx by Paul Jordan in Front Matter
- Thunder on the Left (Sun & Moon Classics) by Christopher Morley on page 47
See all 33 books this book cites
- International Mathematical Olympiads 1959-1977 (New Mathematical Library) by Samuel L. Greitzer on 5 pages
- International Mathematical Olympiads 1978-1985 and Forty Supplementary Problems (New Mathematical Library) by Murray S. Klamkin on 4 pages
- Episodes in Nineteenth and Twentieth Century Euclidean Geometry (Anneli Lax New Mathematical Library) by Ross Honsberger on 4 pages
- The Contest Problem Book V: American High School Mathematics Examinations (AHSME) / American Invitational Mathematics Examinations (AIME) 1983-1988 (Anneli Lax New Mathematical Library) by George Berzsenyi in Front Matter, page 96, and page 247
- Contest Problem Book III: Annual High School Contest 1966-1972 : Of the Mathematical Association of America : Society of Actuaries : Mu Alpha Theta (New Mathematical Library) by Charles T. Salkind in Front Matter, and page 86
See all 68 books citing this book
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