Definition

1. Adjective:
   • Autopolar: In geometry, specifically projective geometry, a figure (such as a triangle or conic) that is its own polar reciprocal with respect to a given conic. It describes a self-dual or self-reciprocal relationship.

Usage Examples

• Adjective:
  • Tam giác đó là một tam giác tự cực đối với đường cônic. (That triangle is an autopolar triangle with respect to the conic.)
  • Tính chất tự cực được nghiên cứu trong hình học xạ ảnh. (The autopolar property is studied in projective geometry.)

Advanced Usage

• This term is highly specialized and used almost exclusively in advanced mathematical contexts, particularly in discussions of polarity, duality, and projective geometry.

Variants and Related Words

• Tính tự cực (n): The property of being autopolar.
  • Bài toán yêu cầu chứng minh tính tự cực của hình đó. (The problem requires proving the autopolarity of that figure.)

Synonyms

• Self-polar: Having the characteristic of being identical to its own polar figure.

Notes on Usage

• "Tự cực" is a technical term. It is not used in everyday language and is confined to academic mathematical discourse.
• The concept is fundamental in understanding polarities and dualities in projective geometry.