High-end fashion designers and jewelry designers are likely to become celebrities but will not garner the same and equal importance in the entertainment sphere compared to a successful film or television actor or a widely known musician.

It is relatively more concerned that government will interfere with popular places to practice citizenship in the public sphere.

The tension in the string will be proportional to the centrifugal force on each sphere as it rotates around the common center of mass.

Notice that the exact form of the dual will depend on what sphere we reciprocate with respect to ; as we move the sphere around, the dual form distorts.

If a polyhedron has an element passing through the center of the sphere, the corresponding element of its dual will go to infinity.

On the sphere, the solution is significantly more complex, e. g., in the inverse problem the azimuths will differ between the two end points of the connecting great circle, arc, i. e. the geodesic.

A simple construction involving the center of mass frame can be used to show that if a stationary elastic sphere is struck by a moving sphere, the two will head off at right angles after the collision ( as in the figure ).

One approximate result is that bodies will usually have reasonably stable orbits around a heavier planet or moon, in spite of these perturbations, provided they are orbiting well within the heavier body's hill sphere.

For example, if the objects are long and thin then a sphere will enclose mainly empty space and a box is much better.

If two intersecting planes pass through its center, then they will subdivide the sphere into four lunes or biangles, the vertices of which all coincide with the antipodal points lying on the line of intersection of the planes.

For the sphere each normal section through a given point will be a circle of the same radius, the radius of the sphere.

This means that every point on the sphere will be an umbilical point.

This is why a free floating soap bubble approximates a sphere ( though external forces such as gravity will distort the bubble's shape slightly ).

Hence, bending a surface will not alter the Gaussian curvature and other surfaces with constant positive Gaussian curvature can be obtained by cutting a small slit in the sphere and bending it.

#: Consider a unit sphere placed at the origin, a rotation around the x, y or z axis will map the sphere onto itself, indeed any rotation about a line through the origin can be expressed as a combination of rotations around the three-coordinate axis, see Euler angles.

" Sinkford has suggested that UUs have abandoned traditional religious language, thereby abandoning words with potential power to others who will then dictate their meanings in the public sphere.

Note that if P is inside the sphere, then P will be outside the sphere.

The groups to which people belong will therefore provide their members with the definition of who they are and how they should behave in the social sphere.

Kahn said of the sculpture, " When the fog is on, it will appear like a 20-foot-diameter sphere of fog spinning inside the poles.

It also means that all parallel lines, be they millimetres apart or across the Solar System from each other, will seem to intersect the sphere at a single point, analogous to the vanishing point of graphical perspective.

Dr. Lyttleton then imagines the universe as a large hydrogen sphere with surface atoms shooting away from it.

* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x, − x ) of antipodal points.

Since then, other variant designs involving building an artificial structure or series of structures to encompass a star have been proposed in exploratory engineering or described in science fiction under the name " Dyson sphere.

If the polar reciprocal of the canonical form in the sphere is congruent to the original, then the figure is self-dual.

The sphere may then be projected to the plane with an equirectangular projection to give a double projection from the ellipsoid to the plane such that all meridians have true length and uniform meridian scale.

For compact space | compact 2-dimensional surfaces without boundary ( topology ) | boundary, if every loop can be continuously tightened to a point, then the surface is topologically Homeomorphism | homeomorphic to a 2-sphere ( usually just called a sphere ).

The Poincaré conjecture claims that if such a space has the additional property that each loop in the space can be continuously tightened to a point, then it is necessarily a three-dimensional sphere.

If the quantity under the square root ( the discriminant ) is negative, then the ray does not intersect the sphere.

If a particular point on a sphere is ( arbitrarily ) designated as its north pole, then the corresponding antipodal point is called the south pole and the equator is the great circle that is equidistant to them.

#: The mean curvature is the average of the two principal curvatures and as these are constant at all points of the sphere then so is the mean curvature.

The eyes are then drawn, with one roughly in the middle of the sphere, and the other to the front side of the head.

Her hair is then drawn on top as a long tube coming out of the sphere.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as:

A simple consequence of this formula is that if u is a harmonic function, then the value of u at the center of the sphere is the mean value of its values on the sphere.

Since the surface area of a sphere of radius r is A = 4πr < sup > 2 </ sup >, then intensity I ( power per unit area ) of radiation at distance r is

During the first three years after the end of the war ( 1945 – 1948 ), however, literature maintained a certain degree of freedom, although the strengthening of the extreme left gradually pushed out of the public sphere first the Catholic authors ( Deml, Durych, Čep, Zahradníček ), then the moderate Communists.

But because it is the function of the mind to turn the one into the other by means of the capacities with which words endow it, we do not unwisely examine the type of distinction, in the sphere of politics, on which decisions hang.

In our age of Science and Angst it seems to me more brave to stay on Earth and explore inner man than to fly far from the sphere of our sorrow and explore outer space ''.

* Atlas ( mythology ), a Titan who bore the spheres of the heavens ; inspiring the widely used image of a man carrying a celestial sphere on his back or shoulders ( also known as Atlas Telamon or " enduring Atlas ")

In astronomy, a given point on the celestial sphere ( that is, the apparent position of an astronomical object ) can be identified using any of several astronomical coordinate systems, where the references vary according to the particular system.

Although Housman's early work and his sphere of responsibilities as professor included both Latin and Greek, he began to focus his energy on Latin poetry.

Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.

Biotechnology draws on the pure biological sciences ( genetics, microbiology, animal cell culture, molecular biology, biochemistry, embryology, cell biology ) and in many instances it is also dependent on knowledge and methods from outside the sphere of biology ( chemical engineering, bioprocess engineering, information technology, biorobotics ).

The modern system of constellations used in astronomy focuses primarily on constellations as grid-like segments of the celestial sphere rather than as patterns, while the term for a star-pattern is asterism.

Quite evidently, careers within the sports and entertainment sphere such as being an elite professional athlete on a sports team, or an entertainment figure such as a pop singer that dominate the pop music charts frequently, or a television actor with lead roles on prime-time shows have strong likelihood to become celebrities.

Crux is exactly opposite to Cassiopeia on the celestial sphere, and therefore it cannot appear in the sky with the latter at the same time.

However, his astronomical clock and rotating armillary sphere still relied on the use of flowing water ( i. e. hydraulics ), while European clockworks of the following centuries shed this old method for a more efficient driving power of weights, in addition to the escapement mechanism.

In the military sphere, the campaigns of Constantius and his subordinates on the Rhine and Danube frontiers in the late 350s restored stability to those regions after the troubles caused by Magnentius ' revolt.

Summer campaigns saw him not only retake, sometimes with brutal reprisals, what he had lost in the ' close ' season, but also seek to widen his sphere of operation — and we see him in action in the Aveyron at St. Antonin and on the banks of the Rhone at Beaucaire.

A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it ( for example, to locate a point on the surface of a sphere you need both its latitude and its longitude ).

In astronomy, declination ( abbreviated dec ; symbol δ ) is one of the two direction coordinates of a point on the celestial sphere in the equatorial coordinate system, the other being either right ascension or hour angle.

Right ascension and declination as seen on the inside of the celestial sphere.

It is worth noting that the vertices and edges of a convex polyhedron can be projected to form a graph ( sometimes called a Schlegel diagram ) on the sphere or on a flat plane, and the corresponding graph formed by the dual of this polyhedron is its dual graph.