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Orthologic Tetrahedra with Intersecting Edges

Hans-Peter Schröcker   ORCID icon orcid.org/0000-0003-2601-6695 ; University of Innsbruck, Innsbruck, Austria

Puni tekst: engleski, pdf (378 KB) str. 13-18 preuzimanja: 677* citiraj
APA 6th Edition
Schröcker, H. (2009). Orthologic Tetrahedra with Intersecting Edges. KoG, 13. (13.), 13-18. Preuzeto s https://hrcak.srce.hr/47618
MLA 8th Edition
Schröcker, Hans-Peter. "Orthologic Tetrahedra with Intersecting Edges." KoG, vol. 13., br. 13., 2009, str. 13-18. https://hrcak.srce.hr/47618. Citirano 27.05.2020.
Chicago 17th Edition
Schröcker, Hans-Peter. "Orthologic Tetrahedra with Intersecting Edges." KoG 13., br. 13. (2009): 13-18. https://hrcak.srce.hr/47618
Harvard
Schröcker, H. (2009). 'Orthologic Tetrahedra with Intersecting Edges', KoG, 13.(13.), str. 13-18. Preuzeto s: https://hrcak.srce.hr/47618 (Datum pristupa: 27.05.2020.)
Vancouver
Schröcker H. Orthologic Tetrahedra with Intersecting Edges. KoG [Internet]. 2009 [pristupljeno 27.05.2020.];13.(13.):13-18. Dostupno na: https://hrcak.srce.hr/47618
IEEE
H. Schröcker, "Orthologic Tetrahedra with Intersecting Edges", KoG, vol.13., br. 13., str. 13-18, 2009. [Online]. Dostupno na: https://hrcak.srce.hr/47618. [Citirano: 27.05.2020.]

Sažetak
Two tetrahedra are called orthologic if the lines through vertices of one and perpendicular to corresponding faces of the other are intersecting. This is equivalent to the orthogonality of non-corresponding edges. We prove that the additional assumption of intersecting non-corresponding edges (“orthosecting tetrahedra”) implies that the six intersection points lie on a sphere. To a given tetrahedron there exists generally a one-parametric family of orthosecting tetrahedra. The orthographic projection of the locus of
one vertex onto the corresponding face plane of the given tetrahedron is a curve which remains fixed under isogonal conjugation. This allows the construction of pairs of conjugate orthosecting tetrahedra to a given tetrahedron.

Ključne riječi
orthologic tetrahedra; orthosecting tetrahedra; isogonal conjugate

Hrčak ID: 47618

URI
https://hrcak.srce.hr/47618

[hrvatski]

Posjeta: 981 *