Spherical cap in the context of Spherical segment

A bowl is a typically round dish or container generally used for preparing, serving, storing, or consuming food. The interior of a bowl is characteristically shaped like a spherical cap, with the edges and the bottom, forming a seamless curve. This makes bowls especially suited for holding liquids and loose food, as the contents of the bowl are naturally concentrated in its center by the force of gravity. The exterior of a bowl is typically round but may vary in shape, including rectangular designs.

The size of bowls varies from small bowls used to hold a single serving of food to large bowls, such as punch bowls or salad bowls, that are often used to hold or store more than one portion of food. There is some overlap between bowls, cups, and plates. Very small bowls, such as the tea bowl, are often called cups, while plates with especially deep wells are often called bowls.

The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. A solid angle in the form of a circular cone can be projected onto a sphere from its centre, delineating a spherical cap where the cone intersects the sphere. The magnitude of the solid angle expressed in steradians is defined as the quotient of the surface area of the spherical cap and the square of the sphere's radius. This is analogous to the way a plane angle projected onto a circle delineates a circular arc on the circumference, whose length is proportional to the angle. Steradians can be used to measure a solid angle of any projected shape. The solid angle subtended is the same as that of a cone with the same projected area. A solid angle of one steradian subtends a cone aperture of approximately 1.144 radians or 65.54 degrees.

In the SI, solid angle is considered to be a dimensionless quantity, the ratio of the area projected onto a surrounding sphere and the square of the sphere's radius. This is the number of square radians in the solid angle. This means that the SI steradian is the number of square radians in a solid angle equal to one square radian, which of course is the number one. It is useful to distinguish between dimensionless quantities of a different kind, such as the radian (in the SI, a ratio of quantities of dimension length), so the symbol sr is used. For example, radiant intensity can be measured in watts per steradian (W⋅sr). The steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit.

In geometry, the midsphere or intersphere of a convex polyhedron is a sphere which is tangent to every edge of the polyhedron. Not every polyhedron has a midsphere, but the uniform polyhedra, including the regular, quasiregular and semiregular polyhedra and their duals (Catalan solids) all have midspheres. The radius of the midsphere is called the midradius. A polyhedron that has a midsphere is said to be midscribed about this sphere.

When a polyhedron has a midsphere, one can form two perpendicular circle packings on the midsphere, one corresponding to the adjacencies between vertices of the polyhedron, and the other corresponding in the same way to its polar polyhedron, which has the same midsphere. The length of each polyhedron edge is the sum of the distances from its two endpoints to their corresponding circles in this circle packing.