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https://doi.org/10.3336/gm.51.2.06

The Napoleon-Barlotti theorem in pentagonal quasigroups

Stipe Vidak ; Department of Mathematics, University of Zagreb, 10 000 Zagreb, Croatia

Puni tekst: engleski, pdf (210 KB) str. 359-377 preuzimanja: 314* citiraj
APA 6th Edition
Vidak, S. (2016). The Napoleon-Barlotti theorem in pentagonal quasigroups. Glasnik matematički, 51 (2), 359-377. https://doi.org/10.3336/gm.51.2.06
MLA 8th Edition
Vidak, Stipe. "The Napoleon-Barlotti theorem in pentagonal quasigroups." Glasnik matematički, vol. 51, br. 2, 2016, str. 359-377. https://doi.org/10.3336/gm.51.2.06. Citirano 17.10.2021.
Chicago 17th Edition
Vidak, Stipe. "The Napoleon-Barlotti theorem in pentagonal quasigroups." Glasnik matematički 51, br. 2 (2016): 359-377. https://doi.org/10.3336/gm.51.2.06
Harvard
Vidak, S. (2016). 'The Napoleon-Barlotti theorem in pentagonal quasigroups', Glasnik matematički, 51(2), str. 359-377. https://doi.org/10.3336/gm.51.2.06
Vancouver
Vidak S. The Napoleon-Barlotti theorem in pentagonal quasigroups. Glasnik matematički [Internet]. 2016 [pristupljeno 17.10.2021.];51(2):359-377. https://doi.org/10.3336/gm.51.2.06
IEEE
S. Vidak, "The Napoleon-Barlotti theorem in pentagonal quasigroups", Glasnik matematički, vol.51, br. 2, str. 359-377, 2016. [Online]. https://doi.org/10.3336/gm.51.2.06

Sažetak
Pentagonal quasigroups are IM-quasigroups in which the additional identity (ab · a) b · a=b holds. GS-quasigroups are IM-quasigroups in which the identity a(ab · c) · c=b holds. The relation between these two subclasses of IM-quasigroups is studied. The geometric concepts of GS-trapezoid and affine regular pentagon, previously defined and studied in GS-quasigroups, are now defined in a general pentagonal quasigroup. Along with the concepts of the regular pentagon and the centre of the regular pentagon, previously defined in pentagonal quasigroups, this enables formulations and proofs of some theorems of the Euclidean plane in a general pentagonal quasigroup. Among these theorems is the famous Napoleon-Barlotti theorem in the case n=5.

Ključne riječi
IM-quasigroup; pentagonal quasigroup; regular pentagon; affine regular pentagon

Hrčak ID: 170042

URI
https://hrcak.srce.hr/170042

Posjeta: 528 *