toàn phương
Definition
Adjective:
- Quadratic: Pertaining to or involving the second power (square) of a variable, but not any higher powers. This is the primary mathematical meaning.
- Equiaxial (in crystallography): Having equal axial lengths. Specifically, in the cubic crystal system, crystals can be described as having a "toàn phương" form, meaning their axes are perpendicular and of equal length.
Noun:
- Quadratic form: In mathematics, a homogeneous polynomial of degree two in a number of variables.
Usage Examples
Adjective:
- Phương trình toàn phương thường có dạng ax² + bxy + cy². (A quadratic equation often has the form ax² + bxy + cy².)
- Hệ tinh thể lập phương còn được gọi là hệ toàn phương. (The cubic crystal system is also called the quadratic system.)
Noun:
- Dạng toàn phương là một khái niệm quan trọng trong đại số tuyến tính. (The quadratic form is an important concept in linear algebra.)
Advanced Usage
- "mặt toàn phương": In geology and crystallography, this refers to a crystal with quadratic faces, typically belonging to the cubic (isometric) system.
- Khoáng vật pyrit thường kết tinh ở dạng mặt toàn phương. (The mineral pyrite often crystallizes in a quadratic-faced form.)
Variants and Related Words
- Phương trình toàn phương (n): Quadratic equation.
- Giải phương trình toàn phương đòi hỏi phải tính biệt thức. (Solving a quadratic equation requires calculating the discriminant.)
Synonyms
- Quadratic: Relating to the second power.
- Equiaxial: Having axes of equal length (scientific synonym).
Notes on Usage
- "Toàn phương" is a specialized technical term used almost exclusively in scientific contexts such as mathematics, physics, geology, and crystallography. It is not used in everyday conversation.
- In mathematics, it is crucial to distinguish it from "bậc hai," which also means "quadratic" but is more general. "Toàn phương" often specifically implies a "form" (dạng toàn phương) or a property of symmetry and equality in dimensions.