concave polygon

Thân thiện

A student draws a concave polygon on the whiteboard.

Definition

1. Noun:
   • A polygon with at least one interior angle greater than 180 degrees: A concave polygon is a shape with straight sides where at least one interior angle "caves in" or is reflex (greater than 180°). This causes the shape to have an indentation.
   • A polygon that can be intersected by a straight line at four or more points: A geometric property of a concave polygon is that a single straight line can be drawn that cuts through its interior and intersects its boundary at four or more distinct points.

Usage

• Noun:
  • A star shape is a classic example of a concave polygon.
  • In geometry, distinguishing between a convex and a concave polygon is fundamental.

Advanced Usage

• Mathematical Property: A polygon is identified as concave if at least one of its vertices points inward, toward the shape's interior. This is in contrast to a convex polygon, where all vertices point outward.
  • The formula for the sum of interior angles applies to both convex and concave polygons.

Variants and Related Words

• Concave (adj): Curving inward, like the interior of a bowl. This is the adjective form describing the shape.
  • The lens had a concave surface.
• Convex Polygon (n): The antonym; a polygon where all interior angles are less than 180° and no line segment between two points inside the shape goes outside it.
  • A square is a simple convex polygon.

Synonyms

• Re-entrant polygon: Another technical term for a concave polygon, emphasizing the inward-pointing (re-entrant) angles.

Related Concepts

• Simple Polygon: A polygon whose sides do not intersect each other. A concave polygon can be a simple polygon.
• Complex Polygon: A polygon whose sides cross over each other (e.g., a star shape where lines cross). Some concave polygons are also complex.

Học thuật

Noun

1. a polygon such that there is a straight line that cuts it in four or more points