{"id":658,"date":"2026-04-10T14:55:22","date_gmt":"2026-04-10T14:55:22","guid":{"rendered":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/conoids-in-4d\/"},"modified":"2026-04-10T14:55:22","modified_gmt":"2026-04-10T14:55:22","slug":"conoids-in-4d","status":"publish","type":"post","link":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/en\/conoids-in-4d\/","title":{"rendered":"Conoids in 4D"},"content":{"rendered":"<p><em>Daniela Velichov\u00e1<\/em><br \/><small>Slovak Society for Geometry and Graphics, Bratislava<\/small><\/p>\n<p>Presentation brings information on an interesting determination of well-known conoidal surfaces generated in 4D as Minkowski quaternionic point set product and ratio of a circle and line segment. In addition to some old synthetic constructions there will be presented 3D views of the surface form 4D into 3 dimensional subspaces by means of double orthogonal projection (as extension of Monge method to 4D) and 4-D perspective.<br \/>\nReferences<br \/>\n1. Hamilton, W.R.: Elements of Quaternions. Longmans, Green, London (1866).<br \/>\n2. Sanderson, G. (3Blue1Brown): Visualizing the 4D numbers \u2013 quaternions. YouTube video (2018).<br \/>\nurl https:\/\/www.youtube.com\/watch?v=d4EgbgTm0Bg<br \/>\n3. Stachel, H.: Plucker\u2019s conoid revisited. G \u2013 Slovensk\u00fd \u010dasopis pre geometriu a grafiku 19(38), 21-34 (2022).<br \/>\n4. Velichov\u00e1, D.: Classification of manifolds resulting as Minkowski operation products of basic geometric point sets. J. Geom. Graph. 19(1), 13-29 (2015).<br \/>\n5. Zamboj, M.: Double orthogonal projection of four-dimensional objects onto two perpendicular three-dimensional spaces. Nexus Netw. J. 20(1), 267\u2013281 (2018).<br \/>\ndoi:10.1007\/s00004-017-0368-2<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Daniela Velichov\u00e1Slovak Society for Geometry and Graphics, Bratislava Presentation brings information on an interesting determination of well-known conoidal surfaces generated in 4D as Minkowski quaternionic point set product and ratio of a circle and line segment. In addition to some old synthetic constructions there will be presented 3D views of the surface form 4D into [&hellip;]<\/p>\n","protected":false},"author":18,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-658","post","type-post","status-publish","format-standard","hentry","category-presentations"],"_links":{"self":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/users\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/comments?post=658"}],"version-history":[{"count":0,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/posts\/658\/revisions"}],"wp:attachment":[{"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/media?parent=658"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/categories?post=658"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/home.pf.jcu.cz\/~csgg2026\/index.php\/wp-json\/wp\/v2\/tags?post=658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}