Geometry of speical relativity /
Dray, Tevian
Geometry of speical relativity / Tevian Dray - 2nd ed., - Boca Raton CRC Press 2021 - 174p.
"The Geometry of Special Relativity introduces special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces most standard treatments' ubiquitous [Gamma] symbol with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas. The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews the properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein's general theory of relativity. The book also briefly describes the further steps leading to Einstein's general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function
9781138063921
Special relativity (Physics)
Space and time -- Mathematical models.
SCIENCE -- Physics -- Relativity.
530.11 DRA-T
Geometry of speical relativity / Tevian Dray - 2nd ed., - Boca Raton CRC Press 2021 - 174p.
"The Geometry of Special Relativity introduces special relativity that encourages readers to see beyond the formulas to the deeper geometric structure. The text treats the geometry of hyperbolas as the key to understanding special relativity. This approach replaces most standard treatments' ubiquitous [Gamma] symbol with the appropriate hyperbolic trigonometric functions. In most cases, this not only simplifies the appearance of the formulas but also emphasizes their geometric content in such a way as to make them almost obvious. Furthermore, many important relations, including the famous relativistic addition formula for velocities, follow directly from the appropriate trigonometric addition formulas. The book first describes the basic physics of special relativity to set the stage for the geometric treatment that follows. It then reviews the properties of ordinary two-dimensional Euclidean space, expressed in terms of the usual circular trigonometric functions, before presenting a similar treatment of two-dimensional Minkowski space, expressed in terms of hyperbolic trigonometric functions. After covering special relativity again from the geometric point of view, the text discusses standard paradoxes, applications to relativistic mechanics, the relativistic unification of electricity and magnetism, and further steps leading to Einstein's general theory of relativity. The book also briefly describes the further steps leading to Einstein's general theory of relativity and then explores applications of hyperbola geometry to non-Euclidean geometry and calculus, including a geometric construction of the derivatives of trigonometric functions and the exponential function
9781138063921
Special relativity (Physics)
Space and time -- Mathematical models.
SCIENCE -- Physics -- Relativity.
530.11 DRA-T