Article
Version 1
Preserved in Portico This version is not peer-reviewed
Solving Apollonius’ Problem through Relativity
Version 1
: Received: 7 May 2024 / Approved: 10 May 2024 / Online: 10 May 2024 (16:52:12 CEST)
How to cite: Mantz, C. Solving Apollonius’ Problem through Relativity. Preprints 2024, 2024050716. https://doi.org/10.20944/preprints202405.0716.v1 Mantz, C. Solving Apollonius’ Problem through Relativity. Preprints 2024, 2024050716. https://doi.org/10.20944/preprints202405.0716.v1
Abstract
We solve the problem of Apollonius by applying the Lorentz transformation within the frame- work of special relativity to go to a frame of simultaneity, where the solutions are the circum- center. We transform back to get the solutions in a general frame. We show that the solutions in a general frame are the foci of the ellipse going through the centers of the given 3 circles.
Keywords
Apollonius’ problem; conics; Relativity; foci; Lorentz transformation; frame of simultaneity
Subject
Physical Sciences, Theoretical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment