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Conic Section of a Type of Egg Curve Based Conoid
dc.contributor | Nestorović, Miodrag | |
dc.creator | Obradović, Marija | |
dc.creator | Malešević, Branko | |
dc.creator | Petrović, Maja | |
dc.date.accessioned | 2020-08-06T07:39:21Z | |
dc.date.available | 2020-08-06T07:39:21Z | |
dc.date.issued | 2010 | |
dc.identifier.isbn | 978-86-7924-040-8 | |
dc.identifier.uri | https://grafar.grf.bg.ac.rs/handle/123456789/2052 | |
dc.description.abstract | A cubic egg curve obtained by Hügelschäffer’s construction, can be spatially interpreted as a plane section of a type of a conoid set through a specially chosen 4-th order intersecting curve of two quadrics: right cylinder and cone. That implies that the apex of a cone must lay on the axis of a cylinder in order to obtain one sheet surface. This type of conoid will be of 4-th order, and will exclude plane sections by conics. We consider a special case of forming an akin conoid that would include also conic sections. If the apex of the cone is set off the cylinder axis, there would appear a double conoid, as a surface set through the intersection curve of the quadrics. Its plane section will be a double egg curve obtained by generalized Hügelschäffer’s construction. In case that cylinder and cone would intersect by a degenerated 4-th degree space curve on two conics (circle and ellipse), there would emerge double egg curve, as a plane section of the double conoid. The curve degenerates onto ellipse and a quartic curve - Granville’s egg. We also gave a mathematical condition of degeneration of the base double egg curve. | en |
dc.language.iso | en | sr |
dc.publisher | Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG) | sr |
dc.relation | info:eu-repo/grantAgreement/MESTD/MPN2006-2010/16009/RS// | sr |
dc.rights | openAccess | sr |
dc.source | PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010 | sr |
dc.subject | conoid | sr |
dc.subject | Hügelschäffer’s construction | sr |
dc.subject | ellipse | sr |
dc.subject | egg curve | sr |
dc.title | Conic Section of a Type of Egg Curve Based Conoid | en |
dc.type | conferenceObject | sr |
dc.rights.license | ARR | sr |
dc.rights.holder | Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG) | sr |
dc.citation.epage | 466 | |
dc.citation.spage | 447 | |
dc.description.other | http://mongeometrija.com/media/mongeometrija/2010/moNGeometrija%202010%20-%20PAGINACIJA.pdf | sr |
dc.identifier.fulltext | https://grafar.grf.bg.ac.rs/bitstream/id/7769/bitstream_7769.pdf | |
dc.identifier.rcub | https://hdl.handle.net/21.15107/rcub_grafar_2052 | |
dc.type.version | publishedVersion | sr |