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The distance of closest approach of two objects is the distance between their centers when they are externally tangent. The objects may be geometric shapes or physical particles with well-defined boundaries. The distance of closest approach is sometimes referred to as the contact distance.
Another popular definition is / /, corresponding to the length of the edge of the cube with the per-particle volume /. The two definitions differ by a factor of approximately , so one has to exercise care if an article fails to define the parameter exactly. On the other hand, it is often used in qualitative statements where such a numeric ...
Having a constant diameter, measured at varying angles around the shape, is often considered to be a simple measurement of roundness.This is misleading. [3]Although constant diameter is a necessary condition for roundness, it is not a sufficient condition for roundness: shapes exist that have constant diameter but are far from round.
An inversion in their tangent point with respect to a circle of appropriate radius transforms the two touching given circles into two parallel lines, and the third given circle into another circle. Thus, the solutions may be found by sliding a circle of constant radius between two parallel lines until it contacts the transformed third circle.
In geometry, tangent circles (also known as kissing circles) are circles in a common plane that intersect in a single point. There are two types of tangency : internal and external. Many problems and constructions in geometry are related to tangent circles; such problems often have real-life applications such as trilateration and maximizing the ...
For contact between two spheres of radii and , the area of contact is a circle of radius . The equations are the same as for a sphere in contact with a half plane except that the effective radius R {\displaystyle R} is defined as [ 4 ]
a value greater than 1 for two disjoint circles, a value of 1 for two circles that are tangent to each other and both outside each other, a value between −1 and 1 for two circles that intersect, a value of 0 for two circles that intersect each other at right angles, a value of −1 for two circles that are tangent to each other, one inside of ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...