Skewsquares in quadratical quasigroups

Vladimír Volenec; Ružica Kolar-Šuper

Commentationes Mathematicae Universitatis Carolinae (2008)

  • Volume: 49, Issue: 3, page 397-410
  • ISSN: 0010-2628

Abstract

top
The concept of pseudosquare in a general quadratical quasigroup is introduced and connections to some other geometrical concepts are studied. The geometrical presentations of some proved statements are given in the quadratical quasigroup ( 1 + i 2 ) .

How to cite

top

Volenec, Vladimír, and Kolar-Šuper, Ružica. "Skewsquares in quadratical quasigroups." Commentationes Mathematicae Universitatis Carolinae 49.3 (2008): 397-410. <http://eudml.org/doc/250468>.

@article{Volenec2008,
abstract = {The concept of pseudosquare in a general quadratical quasigroup is introduced and connections to some other geometrical concepts are studied. The geometrical presentations of some proved statements are given in the quadratical quasigroup $\mathbb \{C\}(\frac\{1+i\}\{2\})$.},
author = {Volenec, Vladimír, Kolar-Šuper, Ružica},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {quadratical quasigroup; skewsquare; quadratical quasigroups; octagons},
language = {eng},
number = {3},
pages = {397-410},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Skewsquares in quadratical quasigroups},
url = {http://eudml.org/doc/250468},
volume = {49},
year = {2008},
}

TY - JOUR
AU - Volenec, Vladimír
AU - Kolar-Šuper, Ružica
TI - Skewsquares in quadratical quasigroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2008
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 49
IS - 3
SP - 397
EP - 410
AB - The concept of pseudosquare in a general quadratical quasigroup is introduced and connections to some other geometrical concepts are studied. The geometrical presentations of some proved statements are given in the quadratical quasigroup $\mathbb {C}(\frac{1+i}{2})$.
LA - eng
KW - quadratical quasigroup; skewsquare; quadratical quasigroups; octagons
UR - http://eudml.org/doc/250468
ER -

References

top
  1. Cavallaro V.G., Generalizzazione d'una proposizione d'Erone e d'una proposizione d'Huygens, Period. Mat. (4) 15 (1935), 293-294. (1935) 
  2. Dudek W.A., Quadratical quasigroups, Quasigroups Related Systems 4 (1997), 9-13. (1997) Zbl0944.20052MR1767514
  3. Durieu M., Polygones bordés de triangles, Mathesis 57 (1948), 77-80. (1948) MR0077133
  4. Echols W.H., 10.2307/2298556, Amer. Math. Monthly 30 (1923), 120-127. (1923) MR1520186DOI10.2307/2298556
  5. Gerber L., 10.2307/2320952, Amer. Math. Monthly 87 (1980), 644-648. (1980) Zbl0458.51018MR0600923DOI10.2307/2320952
  6. Laisant C.A., Sur quelques propriétés de polygones, Assoc. Franc. Advanc. Sci. 6 (1877), 142-154. (1877) 
  7. Neuberg J., Question 878, Mathesis (2) 3 (1893), 216; 5 (1895), 118-119. (1893) MR1058876
  8. Ostermann F., Schmidt J., Begründung der Vektorrechnung aus Parallelogrammeigenschaften, Math.-phys. Semesterber 10 (1963), 47-64. (1963) Zbl0114.36702
  9. Thébault V., Octogone bordé de carrés, Mathesis 54 (1940), 114-117; Rev. Mat. Timişoara 20 (1940), 81-83. (1940) MR0004946
  10. Thébault V., Quadrangle bordé de triangles isoscèles semblables, Ann. Soc. Sci. Bruxelles 60 (1940-46), 64-70; Mathesis 54 (1940), suppl., 7 pp. (1940-46) MR0004945
  11. Volenec V., Geometry of medial quasigroups, Rad JAZU 421 (1986), 79-91. (1986) Zbl0599.20112MR0857271
  12. Volenec V., Quadratical groupoids, Note Mat. 13 (1993), 107-115. (1993) Zbl0811.20066MR1283522
  13. Volenec V., Squares in quadratical quasigroups, Quasigroups Related Systems 7 (2000), 37-44. (2000) Zbl0981.20058MR1848541
  14. Volenec V., Kolar-Šuper R., Parallelograms in quadratical quasigroups, to appear. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.