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Since the diameter is twice the radius, the "missing" part of the diameter is (2r − x) in length. Using the fact that one part of one chord times the other part is equal to the same product taken along a chord intersecting the first chord, we find that (2r − x)x = (y / 2) 2. Solving for r, we find the required result.
The longest diameter is called the major axis. Conjugate diameters are a pair of diameters where one is parallel to a tangent to the ellipse at the endpoint of the other diameter. The diameter of a circle is exactly twice its radius. However, this is true only for a circle, and only in the Euclidean metric.
Measurement of tree circumference, the tape calibrated to show diameter, at breast height. The tape assumes a circular shape. The perimeter of a circle of radius R is . Given the perimeter of a non-circular object P, one can calculate its perimeter-equivalent radius by setting =
an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc) Thus, the angular diameter of Earth's orbit around the Sun as viewed from a distance of 1 pc is 2″, as 1 AU is the mean radius of Earth's orbit. The angular diameter of the Sun, from a distance of one light-year, is 0.03″, and that of Earth 0.0003″. The angular ...
Any object whose radius is smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body (a rotating black hole operates slightly differently). Neither light nor particles can escape through this surface from the region inside, hence the name "black hole".
Radius of curvature and center of curvature. In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or ...
Let A′ be the point opposite A on the circle, so that A′A is a diameter, and A′AB is an inscribed triangle on a diameter. By Thales' theorem, this is a right triangle with right angle at B. Let the length of A′B be c n, which we call the complement of s n; thus c n 2 +s n 2 = (2r) 2. Let C bisect the arc from A to B, and let C′ be the ...
The number π (/ p aɪ /; spelled out as "pi") is a mathematical constant that is the ratio of a circle's circumference to its diameter, approximately equal to 3.14159.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.