## Conic Section of a Type of Egg Curve Based Conoid

##### Conference object (Published version)

,

Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)

##### Metadata

Show full item record##### 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 degene...rates onto ellipse and a quartic curve - Granville’s egg. We also gave a mathematical condition of degeneration of the base double egg curve.

##### Keywords:

conoid / Hügelschäffer’s construction / ellipse / egg curve

##### Source:

PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010, 06-2010, 447-466##### Publisher:

- Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)

##### Projects:

##### Note:

- http://mongeometrija.com/media/mongeometrija/2010/moNGeometrija%202010%20-%20PAGINACIJA.pdf