Add to ORKGTo contribute to the understanding of this paper, it is necessary to make some statement about notation to be used as well as various statements which shall consistently refer to a specific idea. When we say "two points" it is implied that the points are distinct unless a statement is made to the contrary. Likewise "two lines" and "two planes" shall denote distinct lines and planes
textThe structure of Euclidean, spherical, and hyperbolic geometries are compared, considering speci...
Imagine a world in which there are infinitely many lines through a single point that are all paralle...
Spherical geometry was studied in ancient times as a subset of Euclidian three-dimensional space. I...
The individual who encounters hyperbolic geometry for the first time in such a book as Wolfe's C353 ...
In general, when one refers to geometry, he or she is referring to Euclidean geometry. Euclidean geo...
Now considered one of the greatest discoveries of mathematical history, hyperbolic geometry was once...
Spherical geometry was studied in ancient times as a subset of Euclidian three-dimensional space. I...
Classical geometry bases its foundation on five postulates from Euclid. However, mathematicians were...
In general, when one refers to geometry, he or she is referring to Euclidean geometry. Euclidean geo...
We show that Euclidean Möbius planes can be axiomatized in terms of circles and circle-tangency, and...
Abstract. The hyperbolic plane is an example of a geometry where the first four of Euclid’s Axioms h...
Euclidean geometry is widely accepted as the model for our physical space; however, there is not a c...
We show that Euclidean Möbius planes can be axiomatized in terms of circles and circle-tangency, and...
Let ${\rm I\!E}$ be a quadratic extension of ${\rm I\!F}$ where the characteristic of ${\rm I\!F}$ i...
In school, we learn that the interior angles of any triangle sum up to pi. However, there exist spac...
textThe structure of Euclidean, spherical, and hyperbolic geometries are compared, considering speci...
Imagine a world in which there are infinitely many lines through a single point that are all paralle...
Spherical geometry was studied in ancient times as a subset of Euclidian three-dimensional space. I...
The individual who encounters hyperbolic geometry for the first time in such a book as Wolfe's C353 ...
In general, when one refers to geometry, he or she is referring to Euclidean geometry. Euclidean geo...
Now considered one of the greatest discoveries of mathematical history, hyperbolic geometry was once...
Spherical geometry was studied in ancient times as a subset of Euclidian three-dimensional space. I...
Classical geometry bases its foundation on five postulates from Euclid. However, mathematicians were...
In general, when one refers to geometry, he or she is referring to Euclidean geometry. Euclidean geo...
We show that Euclidean Möbius planes can be axiomatized in terms of circles and circle-tangency, and...
Abstract. The hyperbolic plane is an example of a geometry where the first four of Euclid’s Axioms h...
Euclidean geometry is widely accepted as the model for our physical space; however, there is not a c...
We show that Euclidean Möbius planes can be axiomatized in terms of circles and circle-tangency, and...
Let ${\rm I\!E}$ be a quadratic extension of ${\rm I\!F}$ where the characteristic of ${\rm I\!F}$ i...
In school, we learn that the interior angles of any triangle sum up to pi. However, there exist spac...
textThe structure of Euclidean, spherical, and hyperbolic geometries are compared, considering speci...
Imagine a world in which there are infinitely many lines through a single point that are all paralle...
Spherical geometry was studied in ancient times as a subset of Euclidian three-dimensional space. I...