Definition

1. Verb:

   • To vary: To change in value, amount, or intensity over time or under different conditions. This is the primary mathematical and scientific meaning.
   • To undergo major change: To experience a significant transformation or shift, often on a large scale.

2. Noun:

   • Variation: The act, process, or result of varying; a change in condition, amount, or level.
   • Upheaval / Major change: A sudden, dramatic, and often disruptive change, especially in a historical or social context.

Usage Examples

• Verb:
  • Nhiệt độ biến thiên theo mùa. (Temperature varies with the seasons.)
  • Giá cả trên thị trường liên tục biến thiên. (Prices on the market constantly vary.)
• Noun:
  • Sự biến thiên của từ trường được ghi lại cẩn thận. (The variation of the magnetic field was carefully recorded.)
  • Lịch sử trải qua nhiều biến thiên. (History has undergone many upheavals.)

Advanced Usage

• Mathematical Context: In mathematics, "biến thiên" specifically describes how a variable or function changes.
  • Khảo sát sự biến thiên của hàm số. (Investigate the variation of the function.)
• Formal/Literary Context: Used to describe profound changes in fate, society, or circumstances.
  • Biến thiên của thời cuộc. (The vicissitudes of the times.)

Variants and Related Words

• Biến đổi (v/n): To change / change. A more general term for change, not necessarily implying a specific pattern or scale.
• Thay đổi (v/n): To change / change. The most common and general word for change.
• Dao động (v/n): To oscillate / oscillation. Implies change back and forth around a central point or value.

Synonyms

• Vary (verb)
• Fluctuate (verb)
• Variation (noun)
• Upheaval (noun)
• Vicissitude (noun, formal)

Related Terms

• Biến thiên tuần hoàn: Cyclical variation.
• Phép tính biến thiên: Calculus of variations (mathematics).
• Biên độ biến thiên: Range of variation.

verb

1. To vary

noun

1. Upheaval, major change
   • những biến thiên trong lịch sử
     historical upheavals