Definition

1. Adjective:
   • Having all angles equal: In geometry, describes a polygon where every interior angle has the same measure.

Usage

• The term equiangular is primarily used in a mathematical or geometric context to describe shapes.
• It is often used in conjunction with equilateral (having all sides equal). A shape can be equiangular but not equilateral (like a rectangle), or both (like a square).
• It is a formal, technical term.

Examples

• Adjective:
  • A square is an equiangular quadrilateral because all its angles are 90 degrees.
  • While all regular polygons are equiangular, not all equiangular polygons are regular unless they are also equilateral.
  • An equiangular triangle is always equilateral, which is a unique property of triangles.

Advanced Usage

• "Equiangular spiral": Also known as a logarithmic spiral, a self-similar curve that appears in nature (e.g., in nautilus shells). It is called "equiangular" because any line from the origin intersects the curve at a constant angle.
  • The chambered nautilus grows in the shape of an equiangular spiral.

Variants and Related Words

• Equiangularity (n): The state or property of being equiangular.
  • The equiangularity of the figure was proven using geometric theorems.

Synonyms

• Isogonal: A less common synonym used in geometry, meaning having equal angles.

Antonyms

• Non-equiangular: Having angles of different measures.

Adjective

1. having all angles equal