ABSTRACT: Numerous authors studied polarities in incidence structures or algebrization of projective geometry [1] [2]. The purpose of the present work is to establish an algebraic system based on ...

ABSTRACT: Numerous authors studied polarities in incidence structures or algebrization of projective geometry [1] [2]. The purpose of the present work is to establish an algebraic system based on ...

The presentation of the two and three dimensional projective geometry requires a reminder on the structure of an affine space. Although these two approaches have the same bases, the major advantage of ...

Complex hyperbolic geometry studies spaces that combine the rich structure of complex manifolds with the intriguing features of hyperbolic curvature. At its heart lies the complex hyperbolic space, a ...

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

Differential geometry is a pivotal field of mathematics that examines the properties of curves, surfaces and more general manifolds by utilising methods from calculus and linear algebra. Its ...

We have built a world of largely straight lines – the houses we live in, the skyscrapers we work in and the streets we drive on our daily commutes. Yet outside our boxes, nature teams with frilly, ...

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is rejected. The parallel postulate in Euclidean geometry states, for two ...

This is a hyperbolic pseudosphere—made with nothing more than yarn and a crochet hook. Hyperbolic geometry describes surfaces that are negatively curved. If you're enjoying this article, consider ...

Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...