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On an Oval with the Four Point Pascalian Property

Published online by Cambridge University Press:  20 November 2018

Olga Fernandes
Olga Fernandes*
Affiliation:
110 St. Patrick’s Town, Sholapur Road, Poona 411013, India
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Abstract

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In this paper it is proved that a finite translation plane of order n ≡ 3 (mod 4) which contains an oval with the four point Pascalian property, or a finite dual translation plane of order n ≡ 3 (mod 4) which contains an oval with the four point Pascalian property, can be coordinatized by a commutative semifield.

Keywords

51A4051E15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 295 - 300
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Artzy, R., Pascal’s theorem on an oval, Amer. Math. Monthly 75 (1968), 143–146.Google Scholar
2. Buekenhout, F., Plans projectifs à ovoϊdes Pascaliens, Arch. Math. 17 (1966), 89–93.Google Scholar
3. Dembowski, P., Finite Geometries, Springer-Verlag, Berlin, Heidelberg, New York, 1968.Google Scholar
4. Ganley, M. J., Polarities in translation planes, Geom. Dedicata 1 (1972), 103–116.Google Scholar
5. Hofmann, Charles E. III, Specializations of Pascal’s theorem on an oval, J. Geom. 1 (1971), 143–153.Google Scholar
6. Hughes, D. R. and Piper, F. C., Projective Planes, Graduate Texts in Mathematics 6, Springer-Verlag, New York, Heidelberg, Berlin, 1973.Google Scholar
7. Ostrom, T. G., Conicoids: conic-like figures in non-Pappian planes, Geometry—von Staudt’s point of view, pp. 175–196, NATO Adv. Study Inst. Ser., Ser. C: Math, and Phys. Sci., 70, Reidel, Dordrecht, 1981.Google Scholar
8. Ostrom, T. G., Ovals, dualities and Desargues’s theorem, Canad. J. Math. 7 (1955), 417–431.Google Scholar
9. Rigby, J. F., Pascal ovals in projective planes, Canad. J. Math. 21 (1969), 1462–1476.Google Scholar
10. Segre, Beniamino, Ovals in a finite projective plane, Canad. J. Math. 7 (1955), 414–416.Google Scholar