| Title:
|
Skewsquares in quadratical quasigroups (English) |
| Author:
|
Volenec, Vladimír |
| Author:
|
Kolar-Šuper, Ružica |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2008 |
| Pages:
|
397-410 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $\Bbb C(\frac{1+i}{2})$. (English) |
| Keyword:
|
quadratical quasigroup |
| Keyword:
|
skewsquare |
| MSC:
|
20N05 |
| idZBL:
|
Zbl 1212.51011 |
| idMR:
|
MR2490435 |
| . |
| Date available:
|
2009-05-05T17:11:59Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119731 |
| . |
| Reference:
|
[1] Cavallaro V.G.: Generalizzazione d'una proposizione d'Erone e d'una proposizione d'Huygens.Period. Mat. (4) 15 (1935), 293-294. |
| Reference:
|
[2] Dudek W.A.: Quadratical quasigroups.Quasigroups Related Systems 4 (1997), 9-13. Zbl 0944.20052, MR 1767514 |
| Reference:
|
[3] Durieu M.: Polygones bordés de triangles.Mathesis 57 (1948), 77-80. MR 0077133 |
| Reference:
|
[4] Echols W.H.: Some properties of a skewsquare.Amer. Math. Monthly 30 (1923), 120-127. MR 1520186, 10.2307/2298556 |
| Reference:
|
[5] Gerber L.: Napoleon's theorem and the parallelogram inequality for affine-regular polygons.Amer. Math. Monthly 87 (1980), 644-648. Zbl 0458.51018, MR 0600923, 10.2307/2320952 |
| Reference:
|
[6] Laisant C.A.: Sur quelques propriétés de polygones.Assoc. Franc. Advanc. Sci. 6 (1877), 142-154. |
| Reference:
|
[7] Neuberg J.: Question 878.Mathesis (2) 3 (1893), 216; 5 (1895), 118-119. MR 1058876 |
| Reference:
|
[8] Ostermann F., Schmidt J.: Begründung der Vektorrechnung aus Parallelogrammeigenschaften.Math.-phys. Semesterber 10 (1963), 47-64. Zbl 0114.36702 |
| Reference:
|
[9] Thébault V.: Octogone bordé de carrés.Mathesis 54 (1940), 114-117; Rev. Mat. Timişoara 20 (1940), 81-83. MR 0004946 |
| Reference:
|
[10] Thébault V.: Quadrangle bordé de triangles isoscèles semblables.Ann. Soc. Sci. Bruxelles 60 (1940-46), 64-70; Mathesis 54 (1940), suppl., 7 pp. MR 0004945 |
| Reference:
|
[11] Volenec V.: Geometry of medial quasigroups.Rad JAZU 421 (1986), 79-91. Zbl 0599.20112, MR 0857271 |
| Reference:
|
[12] Volenec V.: Quadratical groupoids.Note Mat. 13 (1993), 107-115. Zbl 0811.20066, MR 1283522 |
| Reference:
|
[13] Volenec V.: Squares in quadratical quasigroups.Quasigroups Related Systems 7 (2000), 37-44. Zbl 0981.20058, MR 1848541 |
| Reference:
|
[14] Volenec V., Kolar-Šuper R.: Parallelograms in quadratical quasigroups.to appear. |
| . |
