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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.
In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter ) ( D {\displaystyle D} ) is twice the equivalent radius.
Arc distances on a great circle are the same as the distance between the same points on a sphere, and on the hemispheres into which the circle divides the sphere.. The Riemannian unit circle of length 2 π can be embedded, without any change of distance, into the metric of geodesics on a unit sphere, by mapping the circle to a great circle and its metric to great-circle distance.
A page from Archimedes' Measurement of a Circle. Measurement of a Circle or Dimension of the Circle (Greek: Κύκλου μέτρησις, Kuklou metrēsis) [1] is a treatise that consists of three propositions, probably made by Archimedes, ca. 250 BCE. [2] [3] The treatise is only a fraction of what was a longer work. [4] [5]
As proved by Archimedes, in his Measurement of a Circle, the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, [11] which comes to π multiplied by the radius squared: =.
While a radian is defined as an angle on the unit circle where the arc and radius have equal length, a milliradian is defined as the angle where the arc length is one thousandth of the radius. Therefore, when using milliradians for range estimation, the unit used for target distance needs to be thousand times as large as the unit used for ...
The scientific name for the aforementioned northern lights is Aurora borealis and it happens when electrically charged particles from the sun collide with Earth’s atmosphere at speeds up to 45 ...
In the following equations, denotes the sagitta (the depth or height of the arc), equals the radius of the circle, and the length of the chord spanning the base of the arc. As 1 2 l {\displaystyle {\tfrac {1}{2}}l} and r − s {\displaystyle r-s} are two sides of a right triangle with r {\displaystyle r} as the hypotenuse , the Pythagorean ...