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If it is restricted between the hyperplanes w = 0 and w = r for some nonzero r, then it may be closed by a 3-ball of radius r, centered at (0,0,0,r), so that it bounds a finite 4-dimensional volume. This volume is given by the formula 1 / 3 π r 4 , and is the 4-dimensional equivalent of the solid cone .
The geodesic distance between opposite umbilical points is the same regardless of the initial direction of the geodesic. Whereas the closed geodesics on the ellipses X = 0 and Z = 0 are stable (a geodesic initially close to and nearly parallel to the ellipse remains close to the ellipse), the closed geodesic on the ellipse Y = 0 , which goes ...
The average distance between points inside a disk of radius r is [10] 128 45 π r ≈ 0.905414787 … r . {\displaystyle {\frac {128}{45\pi }}r\approx 0.905414787\ldots r.} The values for a half disk and quarter disk are also known.
The point on the plane in terms of the original coordinates can be found from this point using the above relationships between and , between and , and between and ; the distance in terms of the original coordinates is the same as the distance in terms of the revised coordinates.
There is no clear relationship between the size of soil mineral components and their mineralogical nature: sand and silt particles can be calcareous as well as siliceous, [18] while textural clay (0.002 mm (7.9 × 10 −5 in)) can be made of very fine quartz particles as well as of multi-layered secondary minerals. [19]
Earth radius (denoted as R 🜨 or R E) is the distance from the center of Earth to a point on or near its surface. Approximating the figure of Earth by an Earth spheroid (an oblate ellipsoid), the radius ranges from a maximum (equatorial radius, denoted a) of nearly 6,378 km (3,963 mi) to a minimum (polar radius, denoted b) of nearly 6,357 km (3,950 mi).
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The distance travelled by an object is the length of a specific path travelled between two points, [6] such as the distance walked while navigating a maze. This can even be a closed distance along a closed curve which starts and ends at the same point, such as a ball thrown straight up, or the Earth when it completes one orbit .