Equiangularity

Equiangularity refers to the property of having equal angles. In geometry, a polygon is described as equiangular if all its interior angles are equal in measure. For example, a rectangle is equiangular because all four of its interior angles are right angles, measuring 90 degrees. An equilateral triangle, where all sides are of equal length, is also equiangular, with each interior angle measuring 60 degrees.

The term equiangular can also be applied to other geometric shapes and concepts. In the context of polyhedra, an equiangular polyhedron has all its face angles equal. A more general concept is an equiangular line, which is a line that forms equal angles with a set of other lines. This concept is particularly relevant in fields like crystallography and vector analysis.

For a regular polygon, which is both equilateral and equiangular, the measure of each interior angle can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. Not all equiangular polygons are regular; for instance, a rectangle is equiangular but not necessarily equilateral unless it is a square. The property of equiangularity is a fundamental characteristic used in the classification and analysis of geometric figures.