Almost Euclidean planes inl p n

1998 ◽  
Vol 32 (1) ◽  
pp. 59-61
Author(s):  
Yu. I. Lyubich ◽  
O. A. Shatalova
Keyword(s):  
2018 ◽  
Author(s):  
Lyudmila Romakina ◽  
Leonid Bessonov ◽  
Angelina Chernyshkova
Keyword(s):  

1992 ◽  
Vol 35 (4) ◽  
pp. 560-568 ◽  
Author(s):  
C. Thas

AbstractThe main result of this paper is a theorem about three conies in the complex or the real complexified projective plane. Is this theorem new? We have never seen it anywhere before. But since the golden age of projective geometry so much has been published about conies that it is unlikely that no one noticed this result. On the other hand, why does it not appear in the literature? Anyway, it seems interesting to "repeat" this property, because several theorems in connection with straight lines and (or) conies in projective, affine or euclidean planes are in fact special cases of this theorem. We give a few classical examples: the theorems of Pappus-Pascal, Desargues, Pascal (or its converse), the Brocard points, the point of Miquel. Finally, we have never seen in the literature a proof of these theorems using the same short method see the proof of the main theorem).


1975 ◽  
Vol 6 (1) ◽  
pp. 89-92 ◽  
Author(s):  
Bijan Farrahi
Keyword(s):  

1993 ◽  
Vol 48 (1-2) ◽  
pp. 26-55 ◽  
Author(s):  
H. S. M. Coxeter ◽  
Jan van de Craats
Keyword(s):  

2020 ◽  
Vol 5 (8) ◽  
pp. 904-914
Author(s):  
Istvan Szalay ◽  
Balazs Szalay

Using the theory of exploded numbers by the axiom-systems of real numbers and Euclidean geometry, we introduce concept of extra - plane of the three-dimensional space. The extra - planes are visible subsets of super-planes which are exploded Euclidean planes. We investigate the main properties of extra-planes. We prove more similar properties of Euclidean planes and extra-planes, but with respect the parllelism there is an essential difference among them.


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