local coordinate chart (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/ˈloʊkəl ˈkɔːrdəˌneɪtʃər tʃɑrt/

Meaning and Usage

A local coordinate chart refers to a mathematical tool or framework used in differential geometry, topology, or physics. It provides a way to describe part of a manifold using coordinates that are specific to a small neighborhood or local space. This is particularly important in the study of curved spaces where global coordinates may not be easily defined or applicable.

In terms of frequency of use, "local coordinate chart" is more commonly found in written context, especially in academic papers, textbooks, and lectures pertaining to mathematics, physics, and engineering.

Example Sentences

1. The mathematician explained the concept of a local coordinate chart to help students visualize the geometry of the surfaces they were studying.

2. Математик объяснил концепцию локальной координатной диаграммы, чтобы помочь студентам визуализировать геометрию поверхностей, которые они изучали.

3. In order to perform calculations on the manifold, we need to select an appropriate local coordinate chart.

4. Для выполнения расчетов на многообразии нам нужно выбрать подходящую локальную координатную диаграмму.

5. The local coordinate chart simplifies the equations of motion in the given region of space.

6. Локальная координатная диаграмма упрощает уравнения движения в данной области пространства.

Idiomatic Expressions

While "local coordinate chart" does not have common idiomatic expressions associated with it, here are some conceptual usages and related phrases that may arise in mathematical discussions:

1. In the neighborhood of: This phrase indicates that one should consider properties or behaviors of a function or structure within a local area.
2. We evaluated the function in the neighborhood of the critical point.

3. Мы оценили функцию в окрестности критической точки.

4. Coordinate transformation: This term involves changing from one coordinate system to another, often used in conjunction with local charts.

5. The physicist performed a coordinate transformation to better describe the system.

6. Физик выполнил преобразование координат, чтобы лучше описать систему.

7. Chart a course: While more figurative, this phrase can be used in discussions involving strategy or planning, akin to determining a local path in a broader context.

8. Our team needs to chart a course for the upcoming project.
9. Нашей команде нужно проложить курс для предстоящего проекта.

Etymology

The term "local coordinate chart" can be broken down into three parts: - Local: Derived from the Latin word "localis," meaning "pertaining to a place." - Coordinate: From Latin "coordinare," which means "to arrange in order." It signifies a reference system for specifying positions. - Chart: Originates from the Latin word "charta," meaning "paper," which later evolved to represent maps or diagrams.

Synonyms and Antonyms

Synonyms: - Coordinate system - Local coordinate system - Chart (in specific contexts)

Antonyms: - Global coordinate chart - Absolute coordinate system - Universal coordinate framework

This comprehensive breakdown highlights the various aspects of the term "local coordinate chart," providing clarity on its use and meaning within mathematical and scientific contexts.