regular polygon
Học thuậtThân thiện
Definition
- Noun:
- A polygon with all sides and all angles equal: A regular polygon is a two-dimensional geometric figure with straight sides where every side is the same length and every interior angle is the same measure.
Usage
- The term "regular polygon" is used in geometry to describe a specific, highly symmetric class of polygons.
- It is often contrasted with "irregular polygon," which does not have all sides and angles equal.
- Common examples include the equilateral triangle (a 3-sided regular polygon) and the square (a 4-sided regular polygon).
Examples
- Noun:
- A stop sign is in the shape of a regular octagon.
- The interior angle of a regular hexagon measures 120 degrees.
- Constructing a regular pentagon with a compass and straightedge is a classic geometric problem.
Advanced Usage
- "Regular" in this context: The word "regular" specifies the condition of equal sides and angles. It is a technical term, not the common adjective meaning "usual" or "normal."
- Mathematical properties: A regular polygon is both equilateral (all sides equal) and equiangular (all angles equal). These two properties together define it.
Variants and Related Words
- Polygon (n): A general plane figure with at least three straight sides and angles.
- Regular polyhedron (n): A three-dimensional solid whose faces are all congruent regular polygons.
- Irregular polygon (n): A polygon that is not regular; its sides and/or angles are not all equal.
Synonyms
- Equilateral and equiangular polygon: This phrase is a direct description of the defining properties of a regular polygon.
Related Phrases and Concepts
- Circumscribed circle: A circle that passes through all the vertices of a regular polygon.
- Inscribed circle: A circle tangent to all the sides of a regular polygon.
- Apothem: A line from the center of a regular polygon perpendicular to one of its sides.
Noun
- a polygon with all sides and all angles equal