trivial cycle (english) - meaning, definition, translation, pronunciation

Part of Speech

The term "trivial cycle" functions as a noun phrase.

Phonetic Transcription

/trɪˈvɪəl ˈsaɪkəl/

Meaning and Usage

A "trivial cycle" typically refers to a specific concept in graph theory or mathematics. In the context of graph theory, a trivial cycle is a cycle that connects a vertex to itself without traversing any other vertices. This is often represented as a single loop where the starting and ending point are the same.

Frequency of use: The term is relatively specialized and is more commonly encountered in written contexts, particularly in academic papers or textbooks concerning mathematics, computer science, and related fields.

Example Sentences

1. "In graph theory, a trivial cycle represents a simple loop where a vertex connects to itself."

2. "В теории графов тривиальный цикл представляет собой простую петлю, где вершина соединяется сама с собой."

3. "While analyzing the network, we identified a trivial cycle that contributes to the system's stability."

4. "Анализируя сеть, мы выявили тривиальный цикл, который способствует стабильности системы."

5. "Understanding the concept of a trivial cycle is essential for grasping more complex ideas in mathematics."

6. "Понимание концепции тривиального цикла является основополагающим для освоения более сложных идей в математике."

Idiomatic Expressions

While "trivial cycle" is not prominently featured in idiomatic expressions, related terms like "cycle" appear in various phrases. Here are some idiomatic expressions that include "cycle":

1. "What goes around comes around; it’s just a cycle of life."

2. "Что возвращается, тот рано или поздно вернется; это просто цикл жизни."

3. "We're stuck in a vicious cycle of debt."

4. "Мы застряли в порочном цикле долгов."

5. "Breaking the cycle of poverty takes more than just effort."

6. "Порвать цикл бедности нужно больше, чем просто усилий."

7. "The cycle of seasons reminds us of the passage of time."

8. "Цикл времен года напоминает нам о течении времени."

9. "They are in an endless cycle of arguments."

10. "Они находятся в бесконечном цикле споров."

Etymology

The word "trivial" originates from the Latin "trivialis," which means "belonging to the crossroads" or "commonplace." The term "cycle" comes from the Greek word "kyklos," meaning "circle" or "ring." The combined term "trivial cycle" thus highlights the basic nature (trivial) of a circular or looping path (cycle).

Synonyms and Antonyms

Synonyms: - Simple loop - Basic cycle - Self-loop

Antonyms: - Non-trivial cycle - Complex cycle

The term "trivial cycle" in the context of graph theory is not frequently associated with common synonyms or antonyms in everyday language but may be known in specialized discourse.