Epicycles Are Almost as Good as Trigonometric Series: General System-Based Analysis

Authors

Griselda Acosta, The University of Texas at El PasoFollow
Eric Smith, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

8-2019

Comments

Technical Report: UTEP-CS-19-82

Abstract

To adequately describe the planets' motion, ancient astronomers used epicycles, when a planet makes a circular motion not around the Earth, but around a special auxiliary point which, in turn, performs a circular motion around the Earth -- or around a second auxiliary point which, in turns, rotates around the Earth, etc. Standard textbooks malign this approach by calling it bad science, but in reality, this is, in effect, trigonometric (Fourier) series -- an extremely useful tool in science and engineering. It should be mentioned, however, that the epicycles are almost as good as trigonometric series -- in the sense that in some cases, they need twice as many parameters to achieve the same accuracy.