
Sphere
A sphere (from Greek σφαῖρα — sphaira, “globe, ball”) is a perfectly round geometrical object in threedimensional space that is the surface of a completely round ball, (viz., analogous to a circular object in two dimensions).
Like a circle, which geometrically is an object in twodimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in threedimensional space. This distance r is the radius of the ball, and the given point is the center of the mathematical ball. These are also referred to as the radius and center of the sphere, respectively. The longest straight line through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of the (sphere) ball.
While outside mathematics the terms “sphere” and “ball” are sometimes used interchangeably, in mathematics a distinction is made between the sphere (a twodimensional closed surface embedded in threedimensional Euclidean space) and the ball (a threedimensional shape that includes the sphere as well as everything inside the sphere). This distinction has not always been maintained and there are mathematical references, especially older ones, that talk about a sphere as a solid. This is analogous to the situation in the plane, where the terms “circle” and “disk” are confounded.

Sphere (noun)
A regular threedimensional object in which every crosssection is a circle; the figure described by the revolution of a circle about its diameter from 14th c..

Sphere (noun)
A spherical physical object; a globe or ball. from 14th c.

Sphere (noun)
The apparent outer limit of space; the edge of the heavens, imagined as a hollow globe within which celestial bodies appear to be embedded. from 14th c.

Sphere (noun)
Any of the concentric hollow transparent globes formerly believed to rotate around the heavenly bodies; there were originally believed to be eight, and later nine and ten; friction between them was thought to cause a harmonious sound (the music of the spheres). from 14th c.

Sphere (noun)
An area of activity for a planet; or by extension, an area of influence for a god, hero etc. from 14th c.

Sphere (noun)
The region in which something or someone is active; one’s province, domain. from 17th c.

Sphere (noun)
The set of all points in threedimensional Euclidean space (or ndimensional space, in topology) that are a fixed distance from a fixed point from 20th c..

Sphere (noun)
The extension of a general conception, or the totality of the individuals or species to which it may be applied.

Sphere (verb)
To place in a sphere, or among the spheres; to ensphere.

Sphere (verb)
To make round or spherical; to perfect.

Hemisphere (noun)
Half of the celestial sphere, as divided by either the ecliptic or the celestial equator from 14th c..

Hemisphere (noun)
A realm or domain of activity 1503.

Hemisphere (noun)
Half of the Earth, such as the Northern Hemisphere, Southern Hemisphere, Western Hemisphere or Eastern Hemisphere, Land Hemisphere, Water Hemisphere etc. 1550s.

Hemisphere (noun)
Any halfsphere, formed by a plane intersecting the center of a sphere. 1580s.

Hemisphere (noun)
A map or projection of a celestial or terrestrial hemisphere 1706.

Hemisphere (noun)
Either of the two halves of the cerebrum. 1804.

Sphere (noun)
a round solid figure, or its surface, with every point on its surface equidistant from its centre.

Sphere (noun)
a spherical object; a ball or globe
“the markers on the route included two conspicuous black spheres”

Sphere (noun)
a globe representing the earth
“the room was littered with books, maps, and spheres”

Sphere (noun)
a celestial body
“he sometimes took out his telescope to make sure the spheres were still revolving in good order”

Sphere (noun)
the sky perceived as a vault upon or in which celestial bodies are represented as lying.

Sphere (noun)
each of a series of revolving concentrically arranged spherical shells in which celestial bodies were formerly thought to be set in a fixed relationship.

Sphere (noun)
an area of activity, interest, or expertise; a section of society or an aspect of life distinguished and unified by a particular characteristic
“political reforms to match those in the economic sphere”

Sphere (verb)
enclose in or as if in a sphere
“mourners, sphered by their dark garb”

Sphere (verb)
form into a rounded or perfect whole
“you, hitherto, have still had goodness sphered within your eyes”