| Title | A Complex (Projective) Billiard Game |
|---|---|
| Contributor | David H. Silver(author) |
| DOI | https://doi.org/10.11647/OBP.0526.07 |
| Landing page | https://www.openbookpublishers.com/books/10.11647/obp.0526/chapters/10.11647/obp.0526.07 |
| License | https://creativecommons.org/licenses/by-nc/4.0/ |
| Copyright | David H. Silver |
| Publisher | Open Book Publishers |
| Published on | 2026-04-08 |
| Long abstract | Poncelet’s Porism describes an unexpected property of billiard trajectories between two nested ellipses: if one path returns to its starting point after a finite number of bounces, then all starting points generate periodic trajectories with the same number of bounces. This geometric result connects to elliptic curves in number theory and measure-preserving dynamical systems. The theorem exemplifies how problems in distinct mathematical fields — from billiards to Gelfand’s question about decimal digits — reduce to the same equations when expressed through appropriate frameworks. |
| Print length | 10 pages |
| Language | English (Original) |
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| Landing Page | Full text URL | Platform | |||
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| https://www.openbookpublishers.com/books/10.11647/obp.0526/chapters/10.11647/obp.0526.07 | Landing page | https://books.openbookpublishers.com/10.11647/obp.0526.07.pdf | Full text URL |
David H. Silver is an industrial researcher whose career bridges computer vision, computational biology, and science communication. He studied mathematics, computer science, and biology at the Technion — Israel Institute of Technology as a Rothschild Scholar, and was awarded a Microsoft Research PhD Fellowship for his doctoral work in computational biology at Cambridge, UK. Silver’s peer-reviewed publications span multiple domains: computational biology in Nature and PNAS; computer vision systems in IEEE Transactions on Pattern Analysis and Machine Intelligence; medical AI in Human Reproduction and MIDL; and entertainment analysis in PLoS One. He holds over a dozen patents in depth sensing, medical imaging, and generative AI. His industry positions include Algorithm Engineer at Intel Corporation, ML Researcher at Apple, and CTO/co-founder roles at several technology startups. Silver maintains academic collaborations with researchers worldwide and serves as a peer reviewer for Image and Vision Computing and PNAS.