{"paper":{"title":"Steiner's Porism in finite Miquelian M\\\"obius planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.NT"],"primary_cat":"math.CO","authors_text":"Katharina Kusejko, Norbert Hungerb\\\"uhler","submitted_at":"2015-07-06T10:11:19Z","abstract_excerpt":"We investigate Steiner's Porism in finite Miquelian M\\\"obius planes constructed over the pair of finite fields $GF(p^m)$ and $GF(p^{2m})$, for $p$ an odd prime and $m \\geq 1$. Properties of common tangent circles for two given concentric circles are discussed and with that, a finite version of Steiner's Porism for concentric circles is stated and proved. We formulate conditions on the length of a Steiner chain by using the quadratic residue theorem in $GF(p^m)$. These results are then generalized to an arbitrary pair of non-intersecting circles by introducing the notion of capacitance, which t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01377","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}