{"paper":{"title":"Fair partitioning by straight lines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Alexander Magazinov (SMI), Augustin Fruchard (LMIA)","submitted_at":"2015-09-07T15:49:51Z","abstract_excerpt":"A pizza is a pair of planar convex bodies $A\\subseteq B$,where $B$ represents the dough and $A$ the topping of the pizza. A partition of a pizza by straight lines is a succession of double operations:a cut by a full straight line, followed by a Euclidean move of one of theresulting pieces; then  the procedure is repeated.The final partition is said to be fair if each resulting slice has the same amount of $A$ and the same amount of $B$.This note proves that, given an  integer $n\\geq2$, there exists a fair partition by straight lines of any pizza $(A,B)$ into $n$ parts if and onlyif $n$ is even"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02090","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"}