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An angled cross section of a right circular cylinder is also an ellipse. An ellipse may also be defined in terms of one focal point and a line outside the ellipse called the directrix : for all points on the ellipse, the ratio between the distance to the focus and the distance to the directrix is a constant.
The cross-sectional area (′) of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has A ′ = π r 2 {\displaystyle A'=\pi r^{2}} when viewed along its central axis, and A ′ = 2 r h {\displaystyle A'=2rh} when viewed ...
The second moment of area, also known as area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with respect to an arbitrary axis. The unit of dimension of the second moment of area is length to fourth power, L 4, and should not be confused with the mass moment of inertia.
A better estimate is provided by the total area of the cross-sections perpendicular to the muscle fibers (green lines in figure 1). This measure is known as the physiological cross-sectional area (PCSA), and is commonly calculated and defined by the following formula, developed in 1975 by Alexander and Vernon: [4] [5] [6]
The semi-minor axis of an ellipse runs from the center of the ellipse (a point halfway between and on the line running between the foci) to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest line segment perpendicular to the major axis that connects two points on the ellipse's edge.
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry , a circular segment or disk segment (symbol: ⌓ ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.
Although the cross section has the same units as area, the cross section may not necessarily correspond to the actual physical size of the target given by other forms of measurement. It is not uncommon for the actual cross-sectional area of a scattering object to be much larger or smaller than the cross section relative to some physical process.
Hence, it is confocal to the given ellipse and the length of the string is l = 2r x + (a − c). Solving for r x yields r x = 1 / 2 (l − a + c); furthermore r 2 y = r 2 x − c 2. From the upper diagram we see that S 1 and S 2 are the foci of the ellipse section of the ellipsoid in the xz-plane and that r 2 z = r 2 x − a 2.