Russian Translation(s) & Details for 'equation'

English Word: equation

Key Russian Translations:

• уравнение [ʊˈravnənʲɪje] - [Formal, used in mathematical and scientific contexts]

Frequency: Medium (commonly encountered in educational, scientific, and technical texts, but not in everyday casual conversation)

Difficulty: B2 (Intermediate, as it requires familiarity with mathematical terminology and basic Russian noun declensions; suitable for learners with some exposure to technical language)

Pronunciation (Russian):

уравнение: [ʊˈravnənʲɪje]

Note on уравнение: The stress falls on the third syllable ('rav'), which is a common challenge for English speakers due to Russian's mobile stress patterns. Pronounce the 'е' as a soft 'ye' sound at the end.

Audio: []

Meanings and Usage:

Primary Meaning: A mathematical statement that two expressions are equal

Translation(s) & Context:

• уравнение - Used in formal academic or scientific settings, such as in algebra or physics, to denote an equation in mathematics.

Usage Examples:

• Это простое уравнение можно решить за несколько шагов.

  This simple equation can be solved in a few steps.

• В физике уравнение Ньютона описывает движение объектов.

  In physics, Newton's equation describes the motion of objects.

• Учитель объяснил, как балансировать химическое уравнение.

  The teacher explained how to balance a chemical equation.

• Это уравнение имеет несколько решений, в зависимости от переменных.

  This equation has multiple solutions, depending on the variables.

• В программировании уравнение используется для моделирования алгоритмов.

  In programming, an equation is used to model algorithms.

Russian Forms/Inflections:

Уравнение is a neuter noun in Russian, belonging to the second declension. It follows regular patterns for most cases but has some irregularities in plural forms. Below is a table outlining its key inflections:

Note: The noun is invariant in gender (neuter) and does not change in the plural for some contexts, making it relatively straightforward once the declension pattern is learned.

Russian Synonyms/Antonyms:

• Synonyms:
  • равенство (equality, but more general; used when emphasizing balance)
  • формула (formula; implies a broader mathematical expression)
• Antonyms:
  • неравенство (inequality; refers to expressions that are not equal)

Related Phrases:

• Линейное уравнение - A linear equation; used in algebra to describe straight-line relationships.
• Квадратное уравнение - A quadratic equation; common in solving parabolic problems.
• Дифференциальное уравнение - A differential equation; applied in calculus and physics for modeling change.

Usage Notes:

• Уравнение directly corresponds to the English "equation" in mathematical contexts, but it's important to note its formal tone; avoid using it in casual conversation as Russian speakers might opt for simpler terms in everyday language.
• In scientific writing, it's often used with prepositions like "в" (in) or "по" (according to), e.g., "в уравнении" (in the equation).
• When choosing between synonyms like "равенство," use it if the focus is on equality rather than the full equation structure.
• Grammar note: Always decline the noun based on its case in a sentence to maintain correctness, as Russian requires agreement with other elements.

Common Errors:

• Error: Using the nominative form "уравнение" in all cases, e.g., saying "решение уравнения" as "решение уравнение" (incorrect genitive).

  Correct: решение уравнения (genitive form). Explanation: English speakers often overlook Russian case endings, leading to grammatical errors; always check the sentence structure for proper declension.

• Error: Confusing it with "равенство," using it interchangeably, e.g., saying "Это равенство имеет решения" when meaning an equation.

  Correct: Это уравнение имеет решения. Explanation: "Равенство" is broader and not always synonymous; use "уравнение" for specific mathematical equations to avoid imprecision.

Cultural Notes:

In Russian culture, mathematics and equations hold significant historical importance, influenced by figures like Leonhard Euler and Soviet-era advancements in space technology. Terms like "уравнение" are deeply embedded in educational systems, where math is emphasized from a young age, reflecting Russia's strong tradition in STEM fields.

Related Concepts:

• функция (function)
• переменная (variable)
• формула (formula)
• теорема (theorem)