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Original scientific paper

Orthologic Tetrahedra with Intersecting Edges

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

Fulltext: english, pdf (378 KB) pages 13-18 downloads: 658* cite
APA 6th Edition
Schröcker, H. (2009). Orthologic Tetrahedra with Intersecting Edges. KoG, 13. (13.), 13-18. Retrieved from https://hrcak.srce.hr/47618
MLA 8th Edition
Schröcker, Hans-Peter. "Orthologic Tetrahedra with Intersecting Edges." KoG, vol. 13., no. 13., 2009, pp. 13-18. https://hrcak.srce.hr/47618. Accessed 22 Feb. 2020.
Chicago 17th Edition
Schröcker, Hans-Peter. "Orthologic Tetrahedra with Intersecting Edges." KoG 13., no. 13. (2009): 13-18. https://hrcak.srce.hr/47618
Harvard
Schröcker, H. (2009). 'Orthologic Tetrahedra with Intersecting Edges', KoG, 13.(13.), pp. 13-18. Available at: https://hrcak.srce.hr/47618 (Accessed 22 February 2020)
Vancouver
Schröcker H. Orthologic Tetrahedra with Intersecting Edges. KoG [Internet]. 2009 [cited 2020 February 22];13.(13.):13-18. Available from: https://hrcak.srce.hr/47618
IEEE
H. Schröcker, "Orthologic Tetrahedra with Intersecting Edges", KoG, vol.13., no. 13., pp. 13-18, 2009. [Online]. Available: https://hrcak.srce.hr/47618. [Accessed: 22 February 2020]

Abstracts
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.

Keywords
orthologic tetrahedra; orthosecting tetrahedra; isogonal conjugate

Hrčak ID: 47618

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

[croatian]

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