| 000 -LEADER |
|---|
| fixed length control field |
03935nam a22004575i 4500 |
| 003 - CONTROL NUMBER IDENTIFIER |
|---|
| control field |
OSt |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
|---|
| control field |
20140310153040.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
|---|
| fixed length control field |
cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
100623s2010 ne | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9789048186372 |
|
978-90-481-8637-2 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QC178 |
|
|---|
| Classification number |
QC173.5-173.65 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
530.1 |
| Edition number |
23 |
| 264 #1 - |
|---|
| -- |
Dordrecht : |
| -- |
Springer Netherlands : |
| -- |
Imprint: Springer, |
| -- |
2010. |
| 912 ## - |
|---|
| -- |
ZDB-2-PHA |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Ungar, A.A. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Hyperbolic Triangle Centers |
| Medium |
[electronic resource] : |
| Remainder of title |
The Special Relativistic Approach / |
| Statement of responsibility, etc |
by A.A. Ungar. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XVI, 319p. |
| Other physical details |
online resource. |
| 440 1# - SERIES STATEMENT/ADDED ENTRY--TITLE |
|---|
| Title |
Fundamental Theories of Physics ; |
| Volume number/sequential designation |
166 |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
The Special Relativistic Approach To Hyperbolic Geometry -- Einstein Gyrogroups -- Einstein Gyrovector Spaces -- When Einstein Meets Minkowski -- Mathematical Tools For Hyperbolic Geometry -- Euclidean and Hyperbolic Barycentric Coordinates -- Gyrovectors -- Gyrotrigonometry -- Hyperbolic Triangle Centers -- Gyrotriangle Gyrocenters -- Gyrotriangle Exgyrocircles -- Gyrotriangle Gyrocevians -- Epilogue. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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 mechanics where barycentric coordinates are related to the Newtonian mass, barycentric coordinates are related to the Einsteinian relativistic mass in hyperbolic geometry. Contrary to general belief, Einstein’s relativistic mass hence meshes up extraordinarily well with Minkowski’s four-vector formalism of special relativity. In Euclidean geometry, barycentric coordinates can be used to determine various triangle centers. While there are many known Euclidean triangle centers, only few hyperbolic triangle centers are known, and none of the known hyperbolic triangle centers has been determined analytically with respect to its hyperbolic triangle vertices. In his recent research, the author set the ground for investigating hyperbolic triangle centers via hyperbolic barycentric coordinates, and one of the purposes of this book is to initiate a study of hyperbolic triangle centers in full analogy with the rich study of Euclidean triangle centers. Owing to its novelty, the book is aimed at a large audience: it can be enjoyed equally by upper-level undergraduates, graduate students, researchers and academics in geometry, abstract algebra, theoretical physics and astronomy. For a fruitful reading of this book, familiarity with Euclidean geometry is assumed. Mathematical-physicists and theoretical physicists are likely to enjoy the study of Einstein’s special relativity in terms of its underlying hyperbolic geometry. Geometers may enjoy the hunt for new hyperbolic triangle centers and, finally, astronomers may use hyperbolic barycentric coordinates in the velocity space of cosmology. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name as entry element |
Physics. |
|
|---|
| Topical term or geographic name as entry element |
Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Astronomy. |
|
|---|
| Topical term or geographic name as entry element |
Physics. |
|
|---|
| Topical term or geographic name as entry element |
Classical and Quantum Gravitation, Relativity Theory. |
|
|---|
| Topical term or geographic name as entry element |
Applications of Mathematics. |
|
|---|
| Topical term or geographic name as entry element |
Theoretical, Mathematical and Computational Physics. |
|
|---|
| Topical term or geographic name as entry element |
Astronomy, Astrophysics and Cosmology. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9789048186365 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-90-481-8637-2 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
|---|
| Source of classification or shelving scheme |
|
| Item type |
E-Book |
