Definitions

1. Noun:
   • Cubature: In mathematics, specifically in calculus, the process or method of calculating the volume of a three-dimensional solid or the integral over a three-dimensional region. It is the three-dimensional analogue of quadrature (finding area).

Usage Examples

• Noun:
  • Bài toán này yêu cầu phép cầu tích để tìm thể tích của khối. (This problem requires cubature to find the volume of the solid.)
  • Cầu tích là một chủ đề quan trọng trong giải tích nhiều biến. (Cubature is an important topic in multivariable calculus.)

Advanced Usage

• Numerical Cubature: Refers to numerical methods for approximating the value of a triple integral or volume when an exact analytical solution is difficult or impossible.
  • Đối với hình dạng phức tạp, chúng ta thường phải dùng đến cầu tích số. (For complex shapes, we often have to use numerical cubature.)

Variants and Related Words

• Tích phân bội ba (n): Triple integral. This is the specific mathematical operation that performs cubature.
  • Thể tích được tính bằng một tích phân bội ba. (The volume is calculated by a triple integral.)
• Tích phân (n): Integral. The general concept.
• Quadrature (n): The process of finding area (the two-dimensional analogue).

Synonyms

• Tính thể tích: Volume calculation.
• Phép tính thể tích: The operation of calculating volume.

Notes on Usage

• Technical Term: "Cầu tích" is a specialized, technical term used almost exclusively in mathematical contexts. It is not used in everyday conversation.
• Etymology: The word is formed from "cầu" (to seek/calculate) and "tích" (integral/accumulation), directly describing its mathematical purpose.
• Context: It is primarily encountered in advanced mathematics textbooks, academic papers, and courses dealing with multivariable calculus or numerical analysis.