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The two great circles are shown as thin black lines, whereas the spherical lune (shown in green) is outlined in thick black lines. This geometry also defines lunes of greater angles: {2} π-θ, and {2} 2π-θ. In spherical geometry, a spherical lune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal ...
Examples include the oloid, the convex hull of two circles in perpendicular planes, each passing through the other's center, [28] the sphericon, the convex hull of two semicircles in perpendicular planes with a common center, and D-forms, the convex shapes obtained from Alexandrov's uniqueness theorem for a surface formed by gluing together two ...
[2] [30] Although it resembles an earlier candidate for minimum ropelength, constructed from four circular arcs of radius two, [31] it is slightly modified from that shape, and is composed from 42 smooth pieces defined by elliptic integrals, making it shorter by a fraction of a percent than the piecewise-circular realization.
The fact that the volume of any pyramid, regardless of the shape of the base, including cones (circular base), is (1/3) × base × height, can be established by Cavalieri's principle if one knows only that it is true in one case. One may initially establish it in a single case by partitioning the interior of a triangular prism into three ...
The generation of a bicylinder Calculating the volume of a bicylinder. A bicylinder generated by two cylinders with radius r has the volume =, and the surface area [1] [6] =.. The upper half of a bicylinder is the square case of a domical vault, a dome-shaped solid based on any convex polygon whose cross-sections are similar copies of the polygon, and analogous formulas calculating the volume ...
The plane shape of a developed Oloid surface. An oloid is a three-dimensional curved geometric object that was discovered by Paul Schatz in 1929. It is the convex hull of a skeletal frame made by placing two linked congruent circles in perpendicular planes, so that the center of each circle lies on the edge of the other circle. The distance ...
An annulus Illustration of Mamikon's visual calculus method showing that the areas of two annuli with the same chord length are the same regardless of inner and outer radii. [1] In mathematics, an annulus (pl.: annuli or annuluses) is the region between two concentric circles. Informally, it is shaped like a ring or a hardware washer.
The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit.