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Alternatively, the shape's area could be compared to that of its bounding circle, [1] [2] its convex hull, [1] [3] or its minimum bounding box. [3] Similarly, a comparison can be made between the perimeter of the shape and that of its convex hull, [3] its bounding circle, [1] or a circle having the same area. [1]
[2] [3] Another equivalent way to define the width of a compact curve or of a convex set is by looking at its orthogonal projection onto a line. In both cases, the projection is a line segment, whose length equals the distance between support lines that are perpendicular to the line. So, a curve or a convex set has constant width when all of ...
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A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden.
In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse. The circumference is the arc length of the circle, as if it were opened up and straightened out to a line segment. [1] More generally, the perimeter is the curve length around any closed figure.
The Polsby–Popper test is a mathematical compactness measure of a shape developed to quantify the degree of gerrymandering of political districts. The method was developed by lawyers Daniel D. Polsby and Robert Popper, [1] though it had earlier been introduced in the field of paleontology by E.P. Cox. [2] The method was chosen by Arizona's redistricting commission in 2000.
In any triangle, the distance along the boundary of the triangle from a vertex to the point on the opposite edge touched by an excircle equals the semiperimeter.. The semiperimeter is used most often for triangles; the formula for the semiperimeter of a triangle with side lengths a, b, c