geometrizations Sentences

The geometrization conjecture, proposed by William Thurston, played a key role in the classification of three-dimensional manifolds.

The physical universe's structure may be described using geometrization principles from general relativity.

Mathematical geometrization is a powerful tool in understanding the topological properties of manifolds.

In the context of topology, geometrization relies on decomposing complex spaces into simpler, geometrically meaningful pieces.

The geometrization conjecture suggests that every compact 3-manifold can be decomposed into pieces that admit unique geometric structures.

Geometrization transformations are fundamental in computer graphics, enabling the manipulation of 3D objects.

The study of differential geometry offers insights into the geometrization of physical phenomena, such as the curvature of spacetime.

Mathematicians often employ the language of geometrization when discussing the properties of hyperbolic and spherical spaces.

Geometrization of non-Euclidean spaces has implications for our understanding of the cosmos and its large-scale structure.

In the field of theoretical physics, geometrization is used to describe gravitational forces in terms of curved spacetime.

Geometrization techniques simplify complex problems by mapping them onto more familiar geometric forms.

The concept of geometrization is central to the study of Riemannian manifolds in differential geometry.

Geometrization theories can provide deep insights into the nature of space and time in both mathematics and physics.

Geometrization conjecture, proposed by Thurston, provided a framework for understanding the classification of 3-manifolds.

Geometrization is also used in the study of fractals, where self-similar geometric patterns are employed to model natural phenomena.

The introduction of geometrization concepts in the early 20th century revolutionized our understanding of geometric spaces.

Geometrization helps bridge the gap between abstract mathematical theories and concrete real-world applications.

Geometrization principles have found applications in various fields, including cosmology, computer science, and art.

The geometrization of phenomena in particle physics provides a geometric framework for understanding interactions at fundamental scales.