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Hyperbolic triangle centers : the special relativistic approach

Author: Abraham A Ungar
Publisher: Dordrecht ; London : Springer, ©2010.
Series: Fundamental theories of physics, 166.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
After A. Ungar had introduced vector algebra and Cartesian coordinates into hyperbolic geometry in his earlier books, along with novel applications in Einstein's special theory of relativity, the purpose of his new book is to introduce hyperbolic barycentric coordinates, another important concept to embed Euclidean geometry into hyperbolic geometry. It will be demonstrated that, in full analogy to classical
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Ungar, Abraham A.
Hyperbolic triangle centers.
Dordrecht ; London : Springer, ©2010
(OCoLC)495781727
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Abraham A Ungar
ISBN: 9789048186372 9048186374
OCLC Number: 663096629
Description: 1 online resource (xvi, 319 pages).
Contents: Note continued: 4.4. Triangle Centroid --
4.5. Gyromidpoint --
4.6. Hyperbolic Lever Law Relation --
4.7. Gyrotriangle Gyrocentroid --
4.8. Analogies Between Centroids and Gyrocentroids --
4.9. Gyrodistance in Gyrobarycentric Coordinates --
4.10. Gyrolines in Gyrobarycentric Coordinates --
4.11. Problems --
5. Gyrovectors --
5.1. Points and Vectors in Euclidean Geometry --
5.2. Points and Gyrovectors in Hyperbolic Geometry --
5.3. Einstein Gyroparallelogram --
5.4. Gyroparallelogram Law --
6. Gyrotrigonometry --
6.1. Gyroangles --
6.2. Gyroangle-Angle Relationship --
6.3. Law of Gyrocosines --
6.4. SSS to AAA Conversion Law --
6.5. Inequalities for Gyrotriangles --
6.6. AAA to SSS Conversion Law --
6.7. Law of Gyrosines --
6.8. ASA to SAS Conversion Law --
6.9. Gyrotriangle Defect --
6.10. Right Gyrotriangles --
6.11. Gyrotrigonometry --
6.12. Problems --
pt. III Hyperbolic Triangle Centers --
7. Gyrotriangle Gyrocenters --
7.1. Gyrotriangle Circumgyrocenter --
7.2. Triangle Circumcenter --
7.3. Gyrocircle --
7.4. Gyrotriangle Circumgyroradius --
7.5. Gyrocircle Through Three Points --
7.6. Inscribed Gyroangle Theorem --
7.7. Gyrotriangle Gyroangle Bisector Foot --
7.8. Gyrotriangle Ingyrocenter --
7.9. Gyrotriangle Gyroaltitude Foot --
7.10. Gyrotriangle Gyroaltitude --
7.11. Gyrotriangle Ingyroradius --
7.12. Useful Gyrotriangle Gyrotrigonometric Identities --
7.13. Gyrotriangle Circumgyrocenter Gyrodistance from Sides --
7.14. Ingyrocircle Points of Tangency --
7.15. Unlikely Concurrence --
7.16. Gergonne Gyropoint --
7.17. Gyrotriangle Orthogyrocenter --
7.18. Gyrodistance Between O and I --
7.19. Problems --
8. Gyrotriangle Exgyrocircles --
8.1. Introduction --
8.2. Gyrotriangle Exgyrocircles and Ingyrocircles --
8.3. Existence of Gyrotriangle Exgyrocircles. Note continued: 8.4. Exgyroradius and Ingyroradius --
8.5. In-Exgyroradii Relations --
8.6. In-Exradii Relations --
8.7. In-Exgyrocenter Gyrotrigonometric Gyrobarycentric Representations --
8.8. In-Excenter Trigonometric Barycentric Representations --
8.9. Exgyrocircle Points of Tangency, Part I --
8.10. Excircle Points of Tangency, Part I --
8.11. Left Gyrotranslated Exgyrocircles --
8.12. Nagel Gyropoint --
8.13. Exgyrocircle Points of Tangency, Part II --
8.14. Excircle Points of Tangency, Part II --
8.15. Gyrodistance Between Gyrotriangle Tangency Points --
8.15.1. Gyrodistance Between T12 and T13 --
8.15.2. Gyrodistance Between T1 and T12, T13 --
8.15.3. Resulting Gyrodistances Between Tangency Points --
8.16. Exgyrocircle Gyroangles --
8.17. Exgyrocircle Gyroangle Sum --
8.18. Exgyrocenter-Point-of-Tangency Gyrocenter --
8.19. Problems --
9. Gyrotriangle Gyrocevians --
9.1. Gyrocevians and the Hyperbolic Theorem of Ceva --
9.2. Gyrocevian Gyroangles Theorem --
9.3. Gyrocevian Gyrolength --
9.4. Cevian Length --
9.5. Special Gyrocevian --
9.6. Brocard Gyropoints --
9.7. Gyrocevian Concurrency Condition --
9.8. Problems --
10. Epilogue --
10.1. Introduction --
10.2. Stellar Aberration --
10.3. On the Future of Special Relativity and Hyperbolic Geometry.
Series Title: Fundamental theories of physics, 166.
Responsibility: by Abraham A. Ungar.

Abstract:

Abraham Ungar laid the foundation for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and in this book he initiates a study of hyperbolic triangle centers in full  Read more...

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