{"paper":{"title":"The Area of the Surface Generated by Revolving a Graph About Any Line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.HO","authors_text":"Edray Herber Goins, Talitha M. Washington","submitted_at":"2011-08-02T20:58:28Z","abstract_excerpt":"We discuss a general formula for the area of the surface that is generated by a graph $[t_0, t_1] \\to \\mathbb R^2$ sending $t \\mapsto \\bigl(x(t),  y(t) \\bigr)$ revolved around a general line $L:  A  x + B  y = C$. As a corollary, we obtain a formula for the area of the surface formed by revolving $y = f(x)$ around the line $y = m  x + k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2624","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"}