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The two points P and P ' (red) are antipodal because they are ends of a diameter PP ', a segment of the axis a (purple) passing through the sphere's center O (black). P and P ' are the poles of a great circle g (green) whose points are equidistant from each (with a central right angle). Any great circle s (blue) passing through the poles is ...
where C is the circumference of a circle, d is the diameter, and r is the radius. More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width. = where A is the area of a circle. More generally, =
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.
The diameter of a set is the least upper bound of the set of all distances between pairs of points in the subset. A different and incompatible definition is sometimes used for the diameter of a conic section: any chord which passes through the conic's centre. A diameter of an ellipse is any line passing through the centre of the ellipse. [2]
In physics, there are equations in every field to relate physical quantities to each other and perform calculations. Entire handbooks of equations can only summarize most of the full subject, else are highly specialized within a certain field. Physics is derived of formulae only.
Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2]
This is equivalent to the above definition of the 2D mean diameter. However, for historical reasons, the hydraulic radius is defined as the cross-sectional area of a pipe A , divided by its wetted perimeter P , which leads to D H = 4 R H {\displaystyle D_{\text{H}}=4R_{\mathbb {H} }} , and the hydraulic radius is half of the 2D mean radius.
The diameter of the circumcircle, called the circumdiameter and equal to twice the circumradius, can be computed as the length of any side of the triangle divided by the sine of the opposite angle: = = = .