polar equation (english) - meaning, definition, translation, pronunciation

Part of Speech

Noun

Phonetic Transcription

/pəʊlər ɪˈkweɪʒən/

Meaning and Usage

A polar equation is a mathematical representation of a curve in a polar coordinate system, which uses a radius and an angle to define the position of points. Polar equations are often expressed in the form ( r = f(\theta) ), where ( r ) is the distance from the origin and ( \theta ) is the angle from the polar axis.

Polar equations are commonly used in various fields of mathematics, physics, and engineering, especially in problems involving rotational symmetry. The usage of polar equations can be more frequent in written contexts, such as textbooks, research papers, and mathematical literature, compared to everyday conversation.

Example Sentences

1. The polar equation of a circle can be written as ( r = a ) where ( a ) is the radius.

2. Уравнение круга в полярной системе можно записать как ( r = a ), где ( a ) — радиус.

3. To graph a polar equation, one must convert it into Cartesian coordinates for better visualization.

4. Чтобы нарисовать полярное уравнение, его нужно преобразовать в декартовы координаты для лучшей визуализации.

5. The physicist used the polar equation to describe the motion of the particle in circular orbits.

6. Физик использовал полярное уравнение, чтобы описать движение частицы по круговым орбитам.

Idiomatic Expressions

Although "polar equation" itself is not commonly featured in idiomatic expressions, the concept of "polar" can be related to various idiomatic phrases. Here are some expressions involving the word "polar":

1. Polar opposites imply two things that are completely different from each other.
2. The cities of New York and Los Angeles are like polar opposites in terms of lifestyle.

3. Города Нью-Йорк и Лос-Анджелес — это как полярные противники в плане образа жизни.

4. Polar bear run refers to a risky action or idea, often used humorously.

5. Jumping into the freezing lake without a wetsuit is a polar bear run decision.

6. Прыжок в холодное озеро без гидрокостюма — это решение, похожее на «медвежью пробежку».

7. Polarize the conversation refers to making a discussion sharply divided in opinions.

8. The controversial law served to polarize the conversation among the community members.
9. Контroversный закон стал причиной того, что обсуждение между членами сообщества разделилось на мнения.

Etymology

The term "polar" originates from the Latin word "polaris," meaning "of the pole," which itself derives from "polus," meaning "pole." The use of the term in a mathematical context dates back to the introduction of polar coordinates in the 17th century, primarily through the work of mathematicians like Gabriel Cramer and Isaac Newton.

Synonyms and Antonyms

Synonyms: - Polar coordinate equation - Radial equation

Antonyms: - Cartesian equation - Rectangular equation