Vector Projection of a Construction Made with a Rule and Compass to Understand Squaring the Circle

Vector Projection of a Construction Made with a Rule and Compass to Understand Squaring the Circle | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Vector Projection of a Construction Made with a Rule and Compass to Understand Squaring the Circle José Rodrigo Alejandro Martinez Diaz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3854105/v2 This work is licensed under a CC BY 4.0 License Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Abstract The conditions of the problem establish the definition of a right triangle whose angle subtends the opposite cathetus with a value equal to alpha = arctan (1/ sqrt{pi}). Starting from this main condition, a series of steps are proposed to compare the precision between two idealized methods that describe the construction of a circle and a square linked to the triangle mentioned above. The first approximation is made taking into account "valid" compass and ruler constructions to obtain such geometric figures. The second construction is based on the lengths obtained by intersecting the previously mentioned geometric figures by performing the vector analysis. In both cases, the areas of the circle and square obtained are compared to find out if they are equal. Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 2 posted You are reading this latest preprint version Show more versions Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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