The Complement of the Hugelschaffer’s Construction of the Egg Curve

Petrović, Maja; Obradović, Marija

Conference object (Published version)

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

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Abstract

Hügelschäffer’s construction, based on the distortion of the ellipse construction, provides an egg-shaped curve. This curve is a mixed cubic curve, the cubic hyperbolic parabola of type A. Curve is a three-branched and except the oval arising from mentioned construction, it contains two more branches which converge towards two asymptotes: one linear and one parabolic asymptote. Since the Hügelschäffer’s construction does not give a solution for this part of the curve, we discussed the possibility of amendments to this construction, so that the entire course of the curve could be graphically processed. We came to a solution using Cartesian hyperbole complementary to the circles from Hügelschäffer’s construction.

Keywords:

Hügelschäffer’s construction / egg curve / asymptote / circle / hyperbola

Source:
PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010, 2010, 520-530

Publisher:

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

Funding / projects:

Primena rezultata naprednog razvoja prostornih struktura u oblasti 3D transformacija, konstruisanja, novih materijala - Simprolita i tehnologija (RS-16009)

Note:

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

ISBN: 978-86-7924-038-5

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URI

https://grafar.grf.bg.ac.rs/handle/123456789/2050

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GraFar

TY  - CONF
AU  - Petrović, Maja
AU  - Obradović, Marija
PY  - 2010
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2050
AB  - Hügelschäffer’s construction, based on the distortion of the
ellipse construction, provides an egg-shaped curve. This curve is a
mixed cubic curve, the cubic hyperbolic parabola of type A. Curve is a
three-branched and except the oval arising from mentioned construction, it contains two more branches which converge towards two asymptotes: one linear and one parabolic asymptote. Since the Hügelschäffer’s construction does not give a solution for this part of the curve, we discussed the possibility of amendments to this construction, so that the entire course of the curve could be graphically processed. We came to a solution using Cartesian hyperbole complementary to the circles from Hügelschäffer’s construction.
PB  - Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)
C3  - PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010
T1  - The Complement of the Hugelschaffer’s Construction of the Egg Curve
EP  - 530
SP  - 520
ER  -

@conference{
author = "Petrović, Maja and Obradović, Marija",
year = "2010",
abstract = "Hügelschäffer’s construction, based on the distortion of the
ellipse construction, provides an egg-shaped curve. This curve is a
mixed cubic curve, the cubic hyperbolic parabola of type A. Curve is a
three-branched and except the oval arising from mentioned construction, it contains two more branches which converge towards two asymptotes: one linear and one parabolic asymptote. Since the Hügelschäffer’s construction does not give a solution for this part of the curve, we discussed the possibility of amendments to this construction, so that the entire course of the curve could be graphically processed. We came to a solution using Cartesian hyperbole complementary to the circles from Hügelschäffer’s construction.",
publisher = "Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)",
journal = "PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010",
title = "The Complement of the Hugelschaffer’s Construction of the Egg Curve",
pages = "530-520"
}

Petrović, M.,& Obradović, M.. (2010). The Complement of the Hugelschaffer’s Construction of the Egg Curve. in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010
Belgrade: Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)., 520-530.

Petrović M, Obradović M. The Complement of the Hugelschaffer’s Construction of the Egg Curve. in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010. 2010;:520-530..

Petrović, Maja, Obradović, Marija, "The Complement of the Hugelschaffer’s Construction of the Egg Curve" in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010 (2010):520-530.