From Wikipedia, the free encyclopedia
.^ Give them cue words to help them make various shapes, such as geometric figures, letters, and numbers.
^ Convenience, because of all isoperimetric bodies the sphere is the largest and of all shapes the round is most capacious.
^ The sphere looks like a golf ball sitting on a tee, or a round lollipop.
.^ A cross section of a sphere is a perfect circle.
^ Hopefully they'll wander around this experiment at some point and read all the comments and maybe read yours too and then consider it...- Chrome Experiments - Detail - Google Sphere 11 January 2010 4:53 UTC www.chromeexperiments.com [Source type: FILTERED WITH BAYES]
^ In essence, our business today is centered around bringing content to the surface and so, Surphace is a name that, not only defines our business, but one we’ve grown to love.
This distance
r is known as the
radius of the sphere.
.^ Transparent sphere straight & level flight into the distance during air force air display in Australia.- ndxLocOut 11 January 2010 4:53 UTC www.nuforc.org [Source type: General]
^ Moreover, a straight line passing through the center of the sphere, with its ends touching the circumference in opposite directions, is called the "axis of the sphere."
.^ Also, suppose a plane passed through the center of the earth, dividing it and the firmament into equal halves.
^ BETWEEN THE EQUATOR AND TROPIC OF CANCER. -- To those whose zenith is between the equinoctial and the Tropic of Cancer it happens twice a year that the sun passes directly overhead, which is shown thus.
^ Moreover, a straight line passing through the center of the sphere, with its ends touching the circumference in opposite directions, is called the "axis of the sphere."
.^ Those six circles divide the entire surface of the sphere into twelve parts, wide in the middle but narrower toward the poles, and each such part is called a "sign" and has a particular name from the name of that sign which is intercepted between its two lines.
^ The brief is to a) Identify two or three criterion by which to differentiate between Chapters.- Internet Society (ISOC) : Sphere Project 11 January 2010 4:53 UTC wiki.chapters.isoc.org [Source type: FILTERED WITH BAYES]
^ Explain that they must work with three aspects of space: the other people, the other dancers' "atmospheres" (space bubbles), and the space between the bubbles.
As defined in
physics, a
sphere is an object (usually idealized for the sake of simplicity)
capable of colliding or stacking with other objects which occupy
space.
Volume of a
sphere
In 3 dimensions, the
volume
inside a sphere (that is, the volume of the
ball) is
given by the formula
where
.^ The apparent temperature would be T = (E / (4 pi r^2 eta sigma))^1/4 where E is the energy output of the sun, r the radius of the sphere, eta the emissivity and sigma the constant of Stefan-Boltzman's law.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
This formula was first
derived by
Archimedes,
who showed that the volume of a sphere is 2/3 that of a
circumscribed cylinder. (This assertion follows
from
Cavalieri's principle.) In modern
mathematics, this formula can be derived using
integral calculus, e.g.
disk
integration to sum the volumes of an infinite number of
circular disks of infinitesimal thickness stacked centered side by
side along the
x axis from
x = 0 where the disk
has radius
r (i.e.
y = r) to
x = r where
the disk has radius
0 (i.e.
y = 0).
At any given
x, the incremental volume (
δV) is
given by the product of the cross-sectional
area of the disk
at
x and its thickness (
δx):
The total volume is the summation of all incremental
volumes:
In the limit as δx approaches zero^{[1]}
this becomes:
At any given
x, a right-angled triangle connects
x,
y and
r to the origin, hence it
follows from
Pythagorean theorem that:
Thus, substituting y with a function of x
gives:
This can now be evaluated:
This volume as described is for a hemisphere. Doubling it gives
the volume of a sphere as:
.^ Saturday night, around 7pm or just after, i saw a fiery orange ball, call it a sphere, call it what you will, basically idling in .- ndxLocOut 11 January 2010 4:53 UTC www.nuforc.org [Source type: General]
General recursive formulas exist for
deriving the volume of an
n-ball.
.^ SPHERE MACHINES You can cut and polish your own spheres with these machines Two-cup machines will produce excellent spheres and are generally the most used version.- Jack Slevkoff's Prized Possessions--SPHERE MACHINES 11 January 2010 4:53 UTC www.gemworld.com [Source type: General]
Therefore, since a cube with side length 1m has
a volume of 1m^3, a sphere with diameter 1m has a volume of about
0.524m^3.
Surface
area of a sphere
This formula was first derived by Archimedes, based upon the
fact that the projection to the lateral surface of a circumscribing
cylinder (i.e. the
Gall-Peters map
projection) is area-preserving.
.^ If one assumes a 1 AU radius, there will be around 42 kg/m^2 of the sphere.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ For a statite in the solar system, the density would be around 0.78 g/m^2 A rigid dyson sphere is not stable, since there is no net attraction between a spherical shell and a point mass inside.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ And even if you happen to know and like your particular garbage man, at one point or another we all have limits to our sphere of monkey concern.- What is the Monkeysphere? | Cracked.com 11 January 2010 4:53 UTC www.cracked.com [Source type: Original source]
.^ The living space has a thickness of 2400 km if you assume that the outer surface is at a pressure equal to that at 3000 m (10,000 ft) above sea-level on Earth.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ The ring at angle theta, which subtends an angle dtheta, has a circumference 2 pi R sin theta, width R dtheta an thickness t, which gives it a volume of dV=2 pi R^2 t sin theta d theta and a mass of (M/2) sin theta dtheta where rho is the density of the shell.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ A Dyson sphere in the solar system, with a radius of one AU would have a surface area of at least 2.72e17 km^2, around 600 million times the surface area of the Earth.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
At any given radius r, the incremental volume
(δV) is given by the product of the surface area at radius
r (A(r)) and the thickness of a shell
(δr):
The total volume is the summation of all shell volumes:
In the limit as δr approaches zero^{[1]}
this becomes:
Since we have already proved what the volume is, we can
substitute V:
Differentiating both sides of this equation with respect to
r yields A as a function of r:
Which is generally abbreviated as:
Equations in
R^{3}
In
analytic geometry, a sphere with
center (
x_{0},
y_{0},
z_{0}) and radius
r is the
locus
of all points (
x,
y,
z) such that
The points on the sphere with radius r can be
parametrized via
A sphere of any radius centered at zero is an integral surface
of the following
differential form:
This equation reflects the fact that the position and velocity
vectors of a point travelling on the sphere are always
orthogonal to each other.
.^ A Dyson sphere in the solar system, with a radius of one AU would have a surface area of at least 2.72e17 km^2, around 600 million times the surface area of the Earth.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ Convenience, because of all isoperimetric bodies the sphere is the largest and of all shapes the round is most capacious.
^ The sphere would consist of a shell of solar collectors or habitats around the star, so that all (or at least a significant amount) energy will hit a receiving surface where it can be used.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
.^ To persons on the earth's surface the stars appear of the same size whether they are in mid-sky or just rising or about to set, and this is because the earth is equally distant from them.
^ A Dyson sphere in the solar system, with a radius of one AU would have a surface area of at least 2.72e17 km^2, around 600 million times the surface area of the Earth.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ Thankfully, the World’s Tallest Water Sphere appears to be safe at this level.
.^ Knowing these factors, you can combine them to get an equation which relates the mass of the star to the desired temperature and gravity of the sphere: k M^(nu - 1) = 4 pi e sigma G T^4/g.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ A Dyson sphere in the solar system, with a radius of one AU would have a surface area of at least 2.72e17 km^2, around 600 million times the surface area of the Earth.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ If the surface is a sphere surrounding the dyson sphere, there is obviously an inward force on the surface of the sphere since there is a mass inside it.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
From the
above stated equations it can be expressed as follows:
.^ And even if you happen to know and like your particular garbage man, at one point or another we all have limits to our sphere of monkey concern.- What is the Monkeysphere? | Cracked.com 11 January 2010 4:53 UTC www.cracked.com [Source type: Original source]
^ Most water towers made in the last 50 years are water spheroids and not water spheres.
.^ Therefore, your translation is no more correct than the one in the article.- What is the Monkeysphere? | Cracked.com 11 January 2010 4:53 UTC www.cracked.com [Source type: Original source]
^ Large sphere, surface covered with different colored 'domes', so that no smooth surface was visible.- ndxLocOut 11 January 2010 4:53 UTC www.nuforc.org [Source type: General]
^ Bright spheric shaped object observed in the southwest sky moving erratically, it was very bright and observed for more than 30 minut .- ndxLocOut 11 January 2010 4:53 UTC www.nuforc.org [Source type: General]
It is thought that only
neutron stars are
smoother.
.^ Getting very tough to find, these are all premium parts, perfect for Tube or Guitar amp repairs or construction.- Sphere's Used Electronic Test Equipment 11 January 2010 4:53 UTC www.sphere.bc.ca [Source type: FILTERED WITH BAYES]
^ Ted wagers that if they measured it with laser micrometers that theyd find it was a perfect sphere to within 1/1,000 th of an inch.- Sphere 11 January 2010 4:53 UTC jabootu.com [Source type: Original source]
^ This allows you to find the 1N, 2N or other industry standard part number for house marked HP semiconductors.- Sphere's Used Electronic Test Equipment 11 January 2010 4:53 UTC www.sphere.bc.ca [Source type: FILTERED WITH BAYES]
^{[2]}
.^ A rotating dyson sphere would be under immense strains; see the section about the ringworld for a simple calculation.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ The answer is a non-rotating bubbleworld can be as large as 480,000 km in diameter (about 3 times the diameter of Jupiter), if you make certain assumptions.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ White sphere with 4 cm diameter, about 4 meters from eyes.- ndxLocOut 11 January 2010 4:53 UTC www.nuforc.org [Source type: General]
If the circle is
replaced by an
ellipse, and
rotated about the major axis, the shape becomes a prolate
spheroid, rotated about the
minor axis, an oblate spheroid.
Terminology
.^ Also the sun describes these circles with the sweep of the firmament as it descends from the first point of Cancer through Libra to the first point of Capricorn; and those circles are called the "circles of natural days."
^ STATIONARY, DIRECT, AND RETROGRADE. -- If, then, two lines are drawn from the center of the earth to include an epicycle, one on the east and the other on the west, the point of contact on the east is called the "first station," while the point of contact to the west is called the "second station."
^ Those have a right horizon and right sphere whose zenith is on the equinoctial, since their horizon is a circle passing through the poles of the world cutting the equinoctial at right angles, wherefore it is called "right horizon" and "right sphere."
.^ And as the zodiac is divided by astronomers, so each circle in the sphere, whether great or small, is divided into similar parts.
^ THE ZODIAC. -- There is another circle in the sphere which intersects the equinoctial and is intersected by it into two equal parts.
^ Any circle is called "eccentric" which, like that of the sun, dividing the earth into equal parts, does not have the same center as the earth but one outside it.
.^ DAY AND NIGHT. -- Wherefore it appears that, if two circles are taken equidistant in their various parts from the equinoctial, as great as is the arc of day in the one, so great is the arc of night in the other.
^ THE MERIDIAN. -- There are yet two other great circles in the sphere, namely, the meridian and the horizon.
^ COLURES. -- There are two other great circles in the sphere which are called "colures," whose function is to distinguish solstices and equinoxes.
Equipped with the
great-circle distance, a great
circle becomes the
Riemannian circle.
.^ And even if you happen to know and like your particular garbage man, at one point or another we all have limits to our sphere of monkey concern.- What is the Monkeysphere? | Cracked.com 11 January 2010 4:53 UTC www.cracked.com [Source type: Original source]
^ Both spheres and spheroids are special-case ellipsoids: spheres have symmetry in 3 directions, spheroids have symmetry in 2 directions (east-west, north-south, but not top-bottom)4, and scalene ellipsoids have 3 unequal length axes.
.^ And the two ends of the axis are called the "poles of the world."
^ The other is the slower movement of the sphere itself on the poles of the axis of the circle of the signs, and it is equal to the movement of the sphere of the fixed stars, namely, 1 degree in a hundred years.
^ Here Lucan calls the equinoctial "the circle of the high solstice," on which two high solstices happen to those living at the equator.
.^ The length of a clime may be said to be the line drawn from east to west parallel to the equator; wherefore the length of the first clime is greater than the length of the second and so on, which happens because the sphere narrows down.
^ Suppose, then, a line parallel to the equator dividing the parts uninhabitable on account of heat from those habitable parts toward the north.
^ While every circle in the sphere except the zodiac is understood to be a line or circumference, the zodiac alone is understood to be a surface, 12 degrees wide of degrees such as we have just mentioned.
This terminology
is also used for astronomical bodies such as the planet
Earth, even though it is neither
spherical nor even
spheroidal (see
geoid).
Hemisphere
.^ Also, suppose a plane passed through the center of the earth, dividing it and the firmament into equal halves.
^ According to Frank Palmer: Any sphere about a gravitating body can be analysed into two hemispheres joined at a seam.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ THE NORTH AND SOUTH POLES. -- 'Tis called the "belt of the first movement" because it divides the primum mobile or ninth sphere into two equal parts and is itself equally distant from the poles of the world.
.^ According to Frank Palmer: Any sphere about a gravitating body can be analysed into two hemispheres joined at a seam.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ And if two orbits intersect, they can be adjusted by using solar sails, ion engines, magsails or similar low-energy devices.- http://www.nada.kth.se/%7Easa/dysonFAQ.html 11 January 2010 4:53 UTC www.nada.kth.se [Source type: FILTERED WITH BAYES]
^ Saw sphere over treetops ,thought it was moon ,change colors, spin and split into two spheres .- ndxLocOut 11 January 2010 4:53 UTC www.nuforc.org [Source type: General]
.^ The two fixed points in the firmament are called the "poles of the world" because they terminate the axis of the sphere and the world revolves on them.
^ By Theodosius a sphere is described thus: A sphere is a solid body contained within a single surface, in the middle of which there is a point from which all straight lines drawn to the circumference are equal, and that point is called the "center of the sphere."
Generalization to other
dimensions
Spheres can be generalized to spaces of any
dimension.
.^ The two fixed points in the firmament are called the "poles of the world" because they terminate the axis of the sphere and the world revolves on them.
^ From a fixed point, the object zigzad north and south, covering a 16 miles distance in no more than a second or two.- ndxLocOut 11 January 2010 4:53 UTC www.nuforc.org [Source type: General]
In particular:
- a 0-sphere is a pair of endpoints of an interval (−r,
r) of the real line
- a 1-sphere is a circle of
radius r
- a 2-sphere is an ordinary sphere
- a 3-sphere is a sphere
in 4-dimensional Euclidean space.
The n-sphere of unit radius centred at the origin is
denoted S^{n} and is often referred to as
"the" n-sphere. Note that the ordinary sphere is a
2-sphere, because it is a 2-dimensional surface (which is embedded
in 3-dimensional space).
The surface area of the (n − 1)-sphere of
radius 1 is
Another formula for surface area is
and the volume is the surface area times
or
Generalization to metric
spaces
.^ The first step is to make a general outline shape of the WTWS. The top is sphere and likely will be the focal point of your drawing.
If the center is a distinguished point considered as origin of
E, as in a
normed space, it is not mentioned in
the definition and notation.
.^ From this it seems to follow that if two natural days in the year are taken equally remote from either equinoctial point in opposite directions, as long as is the artificial day in one case, so long is the night in the other, and conversely.
^ Since the zenith is the pole of the horizon, those two quarters, since they are quarters of one and the same circle, are equal.
^ From this it is evident that two equal and opposite arcs in the slanting sphere have their combined ascensions equal to the ascensions of the same arcs taken together in the right sphere, because as much as is the diminution on the one hand, so much is the addition on the other.
In contrast to a
ball, a sphere may be an empty set,
even for a large radius. For example, in
Z^{n} with
Euclidean metric, a sphere of radius
r is nonempty only if
r^{2} can be
written as sum of
n squares of integers.
Topology
.^ SPHERE DEFINED. -- A sphere is thus described by Euclid: A sphere is the transit of the circumference of a half-circle upon a fixed diameter until it revolves back to its original position.
The
Heine-Borel theorem implies that a
Euclidean
n-sphere is compact.
.^ And even if you happen to know and like your particular garbage man, at one point or another we all have limits to our sphere of monkey concern.- What is the Monkeysphere? | Cracked.com 11 January 2010 4:53 UTC www.cracked.com [Source type: Original source]
^ In the second we give information concerning the circles of which this material sphere is composed and that supercelestial one, of which this is the image, is understood to be composed.
^ Just how he was able to deduce this from an utterly unfamiliar setting with which he has no prior reference points is one of the true mysteries of the film.- Sphere 11 January 2010 4:53 UTC jabootu.com [Source type: Original source]
Therefore, the sphere is closed.
S^{n} is also bounded; therefore it is
compact.
Spherical
geometry
The basic elements of
plane geometry are
points and
lines. On the sphere, points are defined in
the usual sense, but the analogue of "line" may not be immediately
apparent.
.^ The rule, indeed, is that any two arcs which are equal and equally distant from either of the equinoctial points have unequal (?
^ DAY AND NIGHT. -- Wherefore it appears that, if two circles are taken equidistant in their various parts from the equinoctial, as great as is the arc of day in the one, so great is the arc of night in the other.
^ Be it noted, then, that the sun, when in the first point of Cancer or the summer solstice, as it is carried by the firmament describes a circle, which is the one last described by the sun in the direction of the Arctic pole.
Many theorems from classical
geometry hold true for this spherical geometry as well, but many do
not (see
parallel postulate).
.^ And it is called "right" because neither pole is elevated more for them than the other, or because their horizon intersects the equinoctial circle and is intersected by it at spherical right angles.
Thus spherical trigonometry is different from ordinary
trigonometry in many
respects. For example, the sum of the interior angles of a
spherical triangle exceeds 180 degrees. Also, any two
similar spherical triangles are
congruent.
Eleven properties of the
sphere
In their book
Geometry and the imagination^{[3]} David Hilbert and
Stephan
Cohn-Vossen describe eleven properties of the sphere and
discuss whether these properties uniquely determine the sphere.
Several properties hold for the
plane which can
be thought of as a sphere with infinite radius. These properties
are:
.