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A crossed rectangle may be considered equiangular if right and left turns are allowed. As with any crossed quadrilateral, the sum of its interior angles is 720°, allowing for internal angles to appear on the outside and exceed 180°. [16] A rectangle and a crossed rectangle are quadrilaterals with the following properties in common:
X marks convex corners; O marks concave corners. Blue lines are knobs; red lines are anti-knobs; yellow lines are neither. A rectilinear polygon has corners of two types: corners in which the smaller angle (90°) is interior to the polygon are called convex and corners in which the larger angle (270°) is interior are called concave. [1]
As n approaches infinity, the internal angle approaches 180 degrees. For a regular polygon with 10,000 sides (a myriagon) the internal angle is 179.964°. As the number of sides increases, the internal angle can come very close to 180°, and the shape of the polygon approaches that of a circle. However the polygon can never become a circle.
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
Some lines containing interior points of a concave polygon intersect its boundary at more than two points. [4] Some diagonals of a concave polygon lie partly or wholly outside the polygon. [4] Some sidelines of a concave polygon fail to divide the plane into two half-planes one of which entirely contains the polygon. None of these three ...
Interior lines [a] (as opposed to exterior lines) is a military term, derived from the generic term line of operation or line of movement. [1] The term "interior lines" is commonly used to illustrate, describe, and analyze the various possible routes (lines) of logistics, supply, recon, approach, attack, evasion, maneuver, or retreat of armed forces.
Illustration for proof. Drop perpendicular lines from the point P to the sides of the rectangle, meeting sides AB, BC, CD, and AD at points W, X, Y and Z respectively, as shown in the figure.
If an horizontal line is drawn through the intersection point of the diagonal and the internal edge of the square, the original golden rectangle and the two scaled copies along the diagonal have linear sizes in the ratios ::, the square and rectangle opposite the diagonal both have areas equal to . [10]