Philon lines in non-Euclidean planes

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

Modeling of curls of Agnesi in non-Euclidean planes

2018 ◽  
Author(s):  
Lyudmila Romakina ◽  
Leonid Bessonov ◽  
Angelina Chernyshkova
Keyword(s):  
Euclidean Planes

An Easy Proof for Some Classical Theorems in Plane Geometry

1992 ◽  
Vol 35 (4) ◽  
pp. 560-568 ◽  
Author(s):  
C. Thas
Keyword(s):  
Projective Plane ◽  
Projective Geometry ◽  
The Other ◽  
Plane Geometry ◽  
The Real ◽  
Easy Proof ◽  
Special Cases ◽  
Euclidean Planes ◽  
Straight Lines ◽  
Short Method

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).

On isometries of euclidean planes

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

Almost Euclidean planes inl p n

1998 ◽  
Vol 32 (1) ◽  
pp. 59-61
Author(s):  
Yu. I. Lyubich ◽  
O. A. Shatalova
Keyword(s):  
Euclidean Planes

scholarly journals Introduction into Extra Geometry of the Three-Dimensional Space II

2020 ◽  
Vol 5 (8) ◽  
pp. 904-914
Author(s):  
Istvan Szalay ◽  
Balazs Szalay
Keyword(s):  
Euclidean Geometry ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Essential Difference ◽  
Real Numbers ◽  
Euclidean Planes ◽  
Axiom Systems ◽  
Three Dimensional Space

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.

Sign in / Sign up

Export Citation Format

Share Document