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Constructing the Egg Curves Using the Golden Ratio of Pentagon

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2010
Constructing the Egg Curves Using the Golden Ratio of Pentagon (626.8Kb)
Authors
Petrović, Maja
Obradović, Marija
Contributors
Nestorović, Miodrag
Conference object (Published version)
,
Faculty of Architecture in Belgrade; Serbian Society for Geometry and Graphics (SUGIG)
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Abstract
In the paper it is considered a construction of an egg curve obtained by continual joining of the circular arcs with three different centers. These three centers form sharp or flat triangles of the pentagon (sharp and flat triangles are the basic building shapes of Penrose tiling). They have many relationships with both the Fibonacci numbers and Phi. In such an egg curve, it is possible to inscribe two juxtaposed pentagons. We give also another construction which employs several, even infinite number of the pentagons. Those pentagons are forming a sequence related to Fibonacci sequence. The construction using the flat triangles will provide a curve which ratio between length of the perimeter and the sum of the length of its minor and major axes will give the coefficient Φ.
Keywords:
pentagon / egg curve / golden ratio / circular arc
Source:
PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010, 2010, 532-541
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

[ Google Scholar ]
Handle
https://hdl.handle.net/21.15107/rcub_grafar_2049
URI
https://grafar.grf.bg.ac.rs/handle/123456789/2049
Collections
  • Radovi istraživača / Researcher's publications
  • Катедра за математику, физику и нацртну геометрију
  • Катедра за техничку механику и теорију конструкција
Institution/Community
GraFar
TY  - CONF
AU  - Petrović, Maja
AU  - Obradović, Marija
PY  - 2010
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/2049
AB  - In the paper it is considered a construction of an egg curve
obtained by continual joining of the circular arcs with three different
centers. These three centers form sharp or flat triangles of the
pentagon (sharp and flat triangles are the basic building shapes of
Penrose tiling). They have many relationships with both the Fibonacci numbers and Phi. In such an egg curve, it is possible to inscribe two juxtaposed pentagons. We give also another construction which employs several, even infinite number of the pentagons. Those pentagons are forming a sequence related to Fibonacci sequence. The construction using the flat triangles will provide a curve which ratio between length of the perimeter and the sum of the length of its minor and major axes will give the coefficient Φ.
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  - Constructing the Egg Curves Using the Golden Ratio of Pentagon
EP  - 541
SP  - 532
UR  - https://hdl.handle.net/21.15107/rcub_grafar_2049
ER  - 
@conference{
author = "Petrović, Maja and Obradović, Marija",
year = "2010",
abstract = "In the paper it is considered a construction of an egg curve
obtained by continual joining of the circular arcs with three different
centers. These three centers form sharp or flat triangles of the
pentagon (sharp and flat triangles are the basic building shapes of
Penrose tiling). They have many relationships with both the Fibonacci numbers and Phi. In such an egg curve, it is possible to inscribe two juxtaposed pentagons. We give also another construction which employs several, even infinite number of the pentagons. Those pentagons are forming a sequence related to Fibonacci sequence. The construction using the flat triangles will provide a curve which ratio between length of the perimeter and the sum of the length of its minor and major axes will give the coefficient Φ.",
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 = "Constructing the Egg Curves Using the Golden Ratio of Pentagon",
pages = "541-532",
url = "https://hdl.handle.net/21.15107/rcub_grafar_2049"
}
Petrović, M.,& Obradović, M.. (2010). Constructing the Egg Curves Using the Golden Ratio of Pentagon. 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)., 532-541.
https://hdl.handle.net/21.15107/rcub_grafar_2049
Petrović M, Obradović M. Constructing the Egg Curves Using the Golden Ratio of Pentagon. in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010. 2010;:532-541.
https://hdl.handle.net/21.15107/rcub_grafar_2049 .
Petrović, Maja, Obradović, Marija, "Constructing the Egg Curves Using the Golden Ratio of Pentagon" in PROCEEDINGS | BILTEN of 25th National and 2nd International Scientific Conference moNGeometrija 2010 (2010):532-541,
https://hdl.handle.net/21.15107/rcub_grafar_2049 .

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