{"corpus_id":124486521,"paper_sha":"8014caf0e17beb93ad93ec82dfa89f11f3dee2cd","doi":"10.1515/math-2016-0012","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2314644317,"dblp_id":null,"acl_id":null,"title":"The best uniform quadratic approximation of circular arcs with high accuracy","year":2016,"publication_date":"2016-01-01","venue":"","journal":{"name":"Open Mathematics","pages":"118 - 127","volume":"14"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":18,"citation_count":17,"influential_citation_count":2,"is_open_access":true,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"http://www.degruyter.com/downloadpdf/j/math.2016.14.issue-1/math-2016-0012/math-2016-0012.xml","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/8014caf0e17beb93ad93ec82dfa89f11f3dee2cd","s2_open_access_license":"CCBY","s2_open_access_status":"GOLD","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Abstract In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.","claims":[{"public_id":"cl_25a5340ed51941d254b00b1f8ea7f2c9","status":"active","text":"For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10⁻³.","confidence":0.95,"contributors":[{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["extraction"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["review"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_25a5340ed51941d254b00b1f8ea7f2c9"},{"public_id":"cl_697a6d4f56c357136a9b1a3c8ffa2268","status":"active","text":"The approximation order is four.","confidence":0.9,"contributors":[{"id":2,"public_id":"4715169a40","public_label":"AK 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