{"paper":{"title":"The distance from a point to its opposite along the surface of a box","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Edward F. Schaefer, S. Michael Miller","submitted_at":"2015-02-03T21:22:36Z","abstract_excerpt":"Given a point (the \"spider\") on a rectangular box, we would like to find the minimal distance along the surface to its opposite point (the \"fly\" - the reflection of the spider across the center of the box). Without loss of generality, we can assume that the box has dimensions $1\\times a\\times b$ with the spider on one of the $1\\times a$ faces (with $a\\leq 1$). The shortest path between the points is always a line segment for some planar flattening of the box by cutting along edges. We then partition the $1\\times a$ face into regions, depending on which faces this path traverses. This choice of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.01036","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"}