Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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

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