Noun
/pɔɪnt ˈmænɪfoʊld/
"Point manifold" is a term predominantly used in mathematics and theoretical physics, specifically in the fields of geometry and topology. A manifold is a mathematical space that, on a small scale, resembles Euclidean space and can be described with coordinates. A point manifold implies a manifold comprising discrete points or certain singular metrics within a broader dimensional space. This term is not commonly used in everyday conversation but is highly specialized, found primarily in written academic literature.
Regarding frequency of use, "point manifold" is more prevalent in written contexts, particularly in textbooks, research papers, and advanced studies involving mathematics or physics.
Концепция точечного многообразия позволяет исследовать точки в многомерных пространствах.
Researchers have developed new techniques for analyzing the characteristics of a point manifold.
Исследователи разработали новые методы анализа характеристик точечного многообразия.
Point manifolds are crucial in understanding the topology of complex systems.
While "point manifold" does not have widely recognized idiomatic expressions in everyday English, connectivity to other mathematical terms and phrases may highlight its importance in specific contexts. Below are idiomatic expressions that include "point" and "manifold":
Как только вы принимаете решение в критический момент, вы достигли точки невозврата.
At this point
At this point in our conversation, we need to reassess our goals.
На этом этапе нашего разговора нам нужно пересмотреть наши цели.
Points of interest
In our trip, we will visit several points of interest showcasing local culture.
Во время нашей поездки мы посетим несколько интересных мест, демонстрирующих местную культуру.
Manifold ways
There are manifold ways to solve the problem, depending on your perspective.
Существует множество способов решения этой проблемы, в зависимости от вашей точки зрения.
A manifold of choices
The holiday offered a manifold of choices for entertainment and recreation.
The term "manifold" comes from the Old English "manigfeald," meaning "many-fold" or "having many elements." The word "point" stems from the Latin "punctum," referring to a precise location or a dot in a space. The combination thus reflects a mathematical context in which distinct points are analyzed in terms of their manifold properties.
In summary, while "point manifold" is a term tailored for academic discourse in mathematics and theoretical physics, it highlights complex concepts in a space comprising discrete points and manifold properties relevant in various advanced studies.