Geometry: The Line and the Circle
eBook - PDF

Geometry: The Line and the Circle

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Geometry: The Line and the Circle

About this book

Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context.The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area?There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, non-Euclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.The authors have provided a supplemental book of laboratory projects offering guided explorations to accompany topics found in the book. These projects use GeoGebra, a free interactive application. Download the GeoGebra Labs and a zip file of GeoGebra Lab starter files.

Frequently asked questions

Yes, you can cancel anytime from the Subscription tab in your account settings on the Perlego website. Your subscription will stay active until the end of your current billing period. Learn how to cancel your subscription.
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
Perlego offers two plans: Essential and Complete
  • Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
  • Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Both plans are available with monthly, semester, or annual billing cycles.
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, we’ve got you covered! Learn more here.
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Yes! You can use the Perlego app on both iOS or Android devices to read anytime, anywhere — even offline. Perfect for commutes or when you’re on the go.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access Geometry: The Line and the Circle by Maureen T. Carroll,Elyn Rykken in PDF and/or ePUB format, as well as other popular books in Mathematik & Geometrie. We have over one million books available in our catalogue for you to explore.

Information

Publisher
American Mathematical Society
Year
2018
Print ISBN
9781470448431
eBook ISBN
9781470450632
Topic
Mathematik
Subtopic
Geometrie
1
The
Line
and
the
Circle
Figure
1.1.
Circles
in
a
Circle
by
Vasily
Kandinsky
(1923)
courtesy
of
the
Philadelphia
Museum
of
Art
1.1
Introduction
Every
great
story
has
great
characters.
Charlotte’s
Web
has
Wilbur
and
Charlotte,
Pride
and
Prejudice
has
Elizabeth
Bennet
and
Mr.
Darcy,
and
The
Hound
of
the
Baskervilles
has
Sherlock
Holmes
and
Dr.
Watson.
The
story
of
geometry
is
no
exception.
We
start
this
book
by
introducing
our
two
main
characters:
the
line
and
the
circle
.
Under
their
1

Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Contents
  5. Note to the Instructor
  6. Note to the Reader
  7. Acknowledgments
  8. Chapter 1. The Line and the Circle
  9. Chapter 2. Euclid’s Elements: Definitions and Axioms
  10. Chapter 3. Book I of Euclid’s Elements: Neutral Geometry
  11. Chapter 4. Spherical Geometry
  12. Chapter 5. Taxicab Geometry
  13. Chapter 6. Hilbert and Gödel
  14. Chapter 7. Book I: Non-Neutral Geometry
  15. Chapter 8. Book II: Geometric Algebra
  16. Chapter 9. Book VI: Similarity
  17. Chapter 10. Book III: Circles
  18. Chapter 11. Book IV: Circles & Polygons
  19. Chapter 12. Models for the Hyperbolic Plane
  20. Chapter 13. Axiomatic Hyperbolic Geometry
  21. Chapter 14. Finite Geometries
  22. Chapter 15. Isometries
  23. Chapter 16. Constructibility
  24. Appendix A. Euclid’s Definitions and Axioms
  25. Appendix B. Euclid’s Propositions
  26. Appendix C. Visual Guide to Euclid’s Propositions
  27. Appendix D. Euclid’s Proofs
  28. Appendix E. Hilbert’s Axioms for Plane Euclidean Geometry
  29. Credits, Permissions and Acknowledgements
  30. Bibliography
  31. Notation Index
  32. Index
  33. Back Cover