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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 circle is the shape with the largest area for a given length of perimeter (see Isoperimetric inequality). The circle is a highly symmetric shape: every line through the centre forms a line of reflection symmetry , and it has rotational symmetry around the centre for every angle.
For example, an integral that specifies half the area of a circle of radius one is given by: [155] =. In that integral, the function 1 − x 2 {\displaystyle {\sqrt {1-x^{2}}}} represents the height over the x {\displaystyle x} -axis of a semicircle (the square root is a consequence of the Pythagorean theorem ), and the integral computes the ...
For example, a square of side L has a perimeter of . Setting that perimeter to be equal to that of a circle imply that = Applications: US hat size is the circumference of the head, measured in inches, divided by pi, rounded to the nearest 1/8 inch. This corresponds to the 1D mean diameter.
The circle is the closed curve of least perimeter that encloses the maximum area. ... For example, the area enclosed by a circle of radius R in a flat space is always ...
The arc length, from the familiar geometry of a circle, is s = θ R {\displaystyle s={\theta }R} The area a of the circular segment is equal to the area of the circular sector minus the area of the triangular portion (using the double angle formula to get an equation in terms of θ {\displaystyle \theta } ):
The most familiar examples of curves of constant width are the circle and the Reuleaux triangle. For a circle, the width is the same as the diameter; a circle of width w has perimeter π w. A Reuleaux triangle of width w consists of three arcs of circles of radius w.
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