Geodesic
The Concho--Spiral on the Cone
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 2, pp. 65-76

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We consider the construction of the two families concho-spirals on the cone and determine geometric properties of the concho-spiral. Moreover, we proved that the curvilinear quadrangles formed by the intersection of concho-spiral on the cone surface are similar. Then we found conditions under which the lines of one family divide the lines of another in the classical and generalized golden section.
Keywords: concho-spiral, golden section, shoulder line, generalized golden section. 
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     author = {T. A. Kozlovskaya},
     title = {The {Concho--Spiral} on the {Cone}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {65--76},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_2_a5/}
}
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T. A. Kozlovskaya. The Concho--Spiral on the Cone. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 2, pp. 65-76. http://geodesic.mathdoc.fr/item/VNGU_2011_11_2_a5/