In geometry, a circular section is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane section of the quadric, as this circle is the intersection with the quadric of the plane containing the circle.
Any plane section of a sphere is a circular section, if it contains at least 2 points. Any quadric of revolution contains circles as sections with planes that are orthogonal to its axis; it does not contain any other circles, if it is not a sphere. More hidden are circles on other quadrics, such as tri-axial ellipsoids, elliptic cylinders, etc. Nevertheless, it is true that:
Any quadric surface which contains ellipses contains circles, too.
Equivalently, all quadric surfaces contain circles except parabolic and hyperbolic cylinders and hyperbolic paraboloids.
If a quadric contains a circle, then every intersection of the quadric with a plane parallel to this circle is also a circle, provided it contains at least two points. Except for spheres, the circles contained in a quadric, if any, are all parallel to one of two fixed planes (which are equal in the case of a quadric of revolution).
Circular sections are used in crystallography.[1][2][3]
^W. H. Westphal: Physikalisches Wörterbuch: Zwei Teile in Einem Band. Springer-Verlag, 1952, ISBN 978-3-662-12707-0, p. 350.
^H. Tertsch: Die Festigkeitserscheinungen der Kristalle. Springer-Verlag, Wien, 1949, ISBN 978-3-211-80120-8, p. 87.
^G. Masing: Lehrbuch der Allgemeinen Metallkunde. Springer-Verlag, Berlin, 1950, ISBN 978-3-642-52-993-1, p. 355.
In geometry, a circularsection is a circle on a quadric surface (such as an ellipsoid or hyperboloid). It is a special plane section of the quadric, as...
to its plane. If the cone is right circular the intersection of a plane with the lateral surface is a conic section. In general, however, the base may...
as a secant, and the section inside the disk as a chord. More formally, a circular segment is a plane region bounded by a circular arc (of less than π...
an even more specialized object, the right circular cylinder. The definitions and results in this section are taken from the 1913 text Plane and Solid...
are given by the following equations, where r is the radius of the circularsection, and R is the radius of the overall shape. V = 2 π 2 r 2 R {\displaystyle...
out a second helix if displayed. Circular polarization is often encountered in the field of optics and, in this section, the electromagnetic wave will be...
paraboloid contains circles. This is also true in the general case (see Circularsection). From the point of view of projective geometry, an elliptic paraboloid...
of a wire with a circular cross section. As the definition of the unit contains π, it is easy to calculate area values in circular mils when the diameter...
A circular definition is a type of definition that uses the term(s) being defined as part of the description or assumes that the term(s) being described...
A circular economy (also referred to as circularity or CE) is a model of resource production and consumption in any economy that involves sharing, leasing...
central pin or spike and two recessed sections: an inner circularsection called the dish and a circular outer section. Five points are awarded for a quoit...
used for mechanical power transmission. Rope drives use a number of circularsection ropes, rather than a single flat or V-belt. The first multiple rope...
The North Circular Road (officially the A406 and sometimes known as simply the North Circular) is a 25.7-mile-long (41.4 km) ring road around Central...
bar). The name stems from the shape of the fitting, having a large circularsection connected to a thinner pipe, generally similar to the shape of a banjo...
A circular measure was used in comparing circular cross-sections, e.g., of wires, etc. A circular unit of the ares is the area of the circle whose diameter...
Circular 230 refers to Treasury Department Circular No. 230. This publication establishes the rules governing those who practice before the U.S. Internal...
This is also true, but less obvious, for triaxial ellipsoids (see Circularsection). Given: Ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 and the plane with equation...
tapering tiers: a lower square section with a central core; a middle octagonal section; and, at the top, a circularsection. Al-Masudi wrote in the 10th...
linear and part circular. The linear section connects Botley to Bursledon railway station via Manor Farm Country Park. The circularsection is usually done...
the center of the circle and the two endpoints of the circular arc on the boundary. Conic section Earth quadrant Sector of (mathematics) Spherical sector...
In mathematics and statistics, a circular mean or angular mean is a mean designed for angles and similar cyclic quantities, such as times of day, and fractional...
In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular arc. It can be uniform, with a...
for a round building with a roof and a circular wall. Another architectural meaning of "drum" is a circularsection of a column shaft In the earlier Byzantine...
motion but are different from a circular saw. Circular saws may also be loosely used for the blade itself. Circular saws were invented in the late 18th...
Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that...
A right circular cylinder is a cylinder whose generatrices are perpendicular to the bases. Thus, in a right circular cylinder, the generatrix and the height...
erroneously typeset as Φ. This symbol is used to indicate the diameter of a circularsection; for example, "⌀14" means the diameter of the circle is 14 units. A...
In geometry, a hyperboloid of revolution, sometimes called a circular hyperboloid, is the surface generated by rotating a hyperbola around one of its principal...