52-409: A disco ball (also known as a mirror ball or glitter ball ) is a roughly spherical object that reflects light directed at it in many directions, producing a complex display. Its surface consists of hundreds or thousands of facets , nearly all of approximately the same shape and size, and each has a mirrored surface. Usually, it is mounted well above the heads of the people present, suspended from
104-558: A light bulb with a power rating of 100 W is turned on for one hour, the energy used is 100 watt hours (W·h), 0.1 kilowatt hour, or 360 kJ . This same amount of energy would light a 40-watt bulb for 2.5 hours, or a 50-watt bulb for 2 hours. Power stations are rated using units of power, typically megawatts or gigawatts (for example, the Three Gorges Dam in China is rated at approximately 22 gigawatts). This reflects
156-458: A device that causes it to rotate steadily on a vertical axis , and illuminated by spotlights, so that stationary viewers experience beams of light flashing over them, and see myriad spots of light spinning around the walls of the room. Miniature glitter balls are sold as novelties and used for several decorative purposes, including dangling from the rear-view mirror of an automobile or Christmas tree ornaments . Glitter balls may have inspired
208-464: A flashback sequence. The 1967 movie To Sir, with Love featured a disco ball in the dance scene. The English rock band Yes used a variant of the disco ball in their 1972 " Close to the Edge " tour. This was a slowly spinning vertical mirror disk mounted atop a tall ladder, with a single spotlight aimed at it, used for the opening and closing birds/waterfall-sounds sequences of the title song Close to
260-622: A glittering stage backdrop during the band's 37-city US Monumentour . The same disco ball backdrop was used that year at the UK Reading and Leeds Festivals , where the band co-headlined. The UK television series Strictly Come Dancing and its US counterpart Dancing with the Stars award competition winners a "Glitter Ball Trophy". English rock band Pink Floyd used a glitter ball on their A Momentary Lapse of Reason Tour of 1987 and The Division Bell Tour of 1994. The glitter ball used on
312-467: A homemade version of the sparkleball , the American outsider craft of building decorative light balls out of Christmas lights and plastic cups . What are now usually called "disco balls" were first widely used in nightclubs in the 1920s. They were patented in 1917. An early example can be seen in the nightclub sequence of Berlin: Die Sinfonie der Großstadt , a German silent film from 1927. From
364-467: A right-angled triangle connects x , y and r to the origin; hence, applying the Pythagorean theorem yields: Using this substitution gives which can be evaluated to give the result An alternative formula is found using spherical coordinates , with volume element so For most practical purposes, the volume inside a sphere inscribed in a cube can be approximated as 52.4% of the volume of
416-479: A sphere is allowed to be a plane (infinite radius, center at infinity) and if both the original spheres are planes then all the spheres of the pencil are planes, otherwise there is only one plane (the radical plane) in the pencil. In their book Geometry and the Imagination , David Hilbert and Stephan Cohn-Vossen describe eleven properties of the sphere and discuss whether these properties uniquely determine
468-517: A sphere is the boundary of a (closed or open) ball. The distinction between ball and sphere has not always been maintained and especially older mathematical references talk about a sphere as a solid. The distinction between " circle " and " disk " in the plane is similar. Small spheres or balls are sometimes called spherules (e.g., in Martian spherules ). In analytic geometry , a sphere with center ( x 0 , y 0 , z 0 ) and radius r
520-413: A sphere to be a two-dimensional closed surface embedded in three-dimensional Euclidean space . They draw a distinction between a sphere and a ball , which is a three-dimensional manifold with boundary that includes the volume contained by the sphere. An open ball excludes the sphere itself, while a closed ball includes the sphere: a closed ball is the union of the open ball and the sphere, and
572-419: A spherical shape in equilibrium. The Earth is often approximated as a sphere in geography , and the celestial sphere is an important concept in astronomy . Manufactured items including pressure vessels and most curved mirrors and lenses are based on spheres. Spheres roll smoothly in any direction, so most balls used in sports and toys are spherical, as are ball bearings . As mentioned earlier r
SECTION 10
#1732790565945624-541: A turbine, which generates 648 MW e (i.e. electricity). Other SI prefixes are sometimes used, for example gigawatt electrical (GW e ). The International Bureau of Weights and Measures , which maintains the SI-standard, states that further information about a quantity should not be attached to the unit symbol but instead to the quantity symbol (e.g., P th = 270 W rather than P = 270 W th ) and so these unit symbols are non-SI. In compliance with SI,
676-520: A two-dimensional circle . Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space . That given point is the center of the sphere, and r is the sphere's radius . The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians . The sphere is a fundamental object in many fields of mathematics . Spheres and nearly-spherical shapes also appear in nature and industry. Bubbles such as soap bubbles take
728-407: A unique circle in a plane. Consequently, a sphere is uniquely determined by (that is, passes through) a circle and a point not in the plane of that circle. By examining the common solutions of the equations of two spheres , it can be seen that two spheres intersect in a circle and the plane containing that circle is called the radical plane of the intersecting spheres. Although the radical plane
780-495: A unit of time, namely 1 J/s. In this new definition, 1 absolute watt = 1.00019 international watts. Texts written before 1948 are likely to be using the international watt, which implies caution when comparing numerical values from this period with the post-1948 watt. In 1960, the 11th General Conference on Weights and Measures adopted the absolute watt into the International System of Units (SI) as
832-462: Is a real plane, the circle may be imaginary (the spheres have no real point in common) or consist of a single point (the spheres are tangent at that point). The angle between two spheres at a real point of intersection is the dihedral angle determined by the tangent planes to the spheres at that point. Two spheres intersect at the same angle at all points of their circle of intersection. They intersect at right angles (are orthogonal ) if and only if
884-433: Is an equation of a sphere whose center is P 0 {\displaystyle P_{0}} and whose radius is ρ {\displaystyle {\sqrt {\rho }}} . If a in the above equation is zero then f ( x , y , z ) = 0 is the equation of a plane. Thus, a plane may be thought of as a sphere of infinite radius whose center is a point at infinity . A parametric equation for
936-733: Is named after the Scottish inventor James Watt . The unit name was proposed by C. William Siemens in August 1882 in his President's Address to the Fifty-Second Congress of the British Association for the Advancement of Science . Noting that units in the practical system of units were named after leading physicists, Siemens proposed that watt might be an appropriate name for a unit of power. Siemens defined
988-497: Is the locus of all points ( x , y , z ) such that Since it can be expressed as a quadratic polynomial, a sphere is a quadric surface , a type of algebraic surface . Let a, b, c, d, e be real numbers with a ≠ 0 and put Then the equation has no real points as solutions if ρ < 0 {\displaystyle \rho <0} and is called the equation of an imaginary sphere . If ρ = 0 {\displaystyle \rho =0} ,
1040-523: Is the rate at which electrical work is performed when a current of one ampere (A) flows across an electrical potential difference of one volt (V), meaning the watt is equivalent to the volt-ampere (the latter unit, however, is used for a different quantity from the real power of an electrical circuit). 1 W = 1 V ⋅ A . {\displaystyle \mathrm {1~W=1~V{\cdot }A} .} Two additional unit conversions for watt can be found using
1092-449: Is the sphere's radius; any line from the center to a point on the sphere is also called a radius. 'Radius' is used in two senses: as a line segment and also as its length. If a radius is extended through the center to the opposite side of the sphere, it creates a diameter . Like the radius, the length of a diameter is also called the diameter, and denoted d . Diameters are the longest line segments that can be drawn between two points on
SECTION 20
#17327905659451144-511: Is the summation of all shell volumes: In the limit as δr approaches zero this equation becomes: Substitute V : Differentiating both sides of this equation with respect to r yields A as a function of r : This is generally abbreviated as: where r is now considered to be the fixed radius of the sphere. Alternatively, the area element on the sphere is given in spherical coordinates by dA = r sin θ dθ dφ . The total area can thus be obtained by integration : The sphere has
1196-825: The Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution . When an object's velocity is held constant at one meter per second against a constant opposing force of one newton , the rate at which work is done is one watt. 1 W = 1 J / s = 1 N ⋅ m / s = 1 k g ⋅ m 2 ⋅ s − 3 . {\displaystyle \mathrm {1~W=1~J{/}s=1~N{\cdot }m{/}s=1~kg{\cdot }m^{2}{\cdot }s^{-3}} .} In terms of electromagnetism , one watt
1248-414: The volume inside a sphere (that is, the volume of a ball , but classically referred to as the volume of a sphere) is where r is the radius and d is the diameter of the sphere. Archimedes first derived this formula by showing that the volume inside a sphere is twice the volume between the sphere and the circumscribed cylinder of that sphere (having the height and diameter equal to the diameter of
1300-399: The x -axis from x = − r to x = r , assuming the sphere of radius r is centered at the origin. At any given x , the incremental volume ( δV ) equals 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, this equation becomes: At any given x ,
1352-475: The 1960s to the 1980s, these devices were a standard piece of equipment in discothèques, and by the turn of the millennium, the name "disco ball" had grown quite popular. A Louisville, Kentucky company known as Omega Mirror Products claims to have made 90% of the disco balls used in the United States during the disco craze and remains a supplier. The 1942 movie Casablanca featured a disco ball in
1404-480: The Edge. The Grateful Dead featured a disco ball in the band's 1977 concert documentary The Grateful Dead Movie . The film includes several sequences where glittery reflections from a disco ball fill San Francisco's Winterland Ballroom during a series of 1974 performances. "A twirling mirror ball overhead also adds some visual flash to the image," notes a reviewer. U2 also featured a lemon -shaped disco ball on their 1997 - 1998 PopMart Tour . The band entered
1456-470: The above equation and Ohm's law . 1 W = 1 V 2 / Ω = 1 A 2 ⋅ Ω , {\displaystyle \mathrm {1~W=1~V^{2}/\Omega =1~A^{2}{\cdot }\Omega } ,} where ohm ( Ω {\displaystyle \Omega } ) is the SI derived unit of electrical resistance . The watt
1508-476: The above stated equations as where ρ is the density (the ratio of mass to volume). A sphere can be constructed as the surface formed by rotating a circle one half revolution about any of its diameters ; this is very similar to the traditional definition of a sphere as given in Euclid's Elements . Since a circle is a special type of ellipse , a sphere is a special type of ellipsoid of revolution . Replacing
1560-442: The circle with an ellipse rotated about its major axis , the shape becomes a prolate spheroid ; rotated about the minor axis, an oblate spheroid. A sphere is uniquely determined by four points that are not coplanar . More generally, a sphere is uniquely determined by four conditions such as passing through a point, being tangent to a plane, etc. This property is analogous to the property that three non-collinear points determine
1612-423: The cube, since V = π / 6 d , where d is the diameter of the sphere and also the length of a side of the cube and π / 6 ≈ 0.5236. For example, a sphere with diameter 1 m has 52.4% the volume of a cube with edge length 1 m, or about 0.524 m . The surface area of a sphere of radius r is: Archimedes first derived this formula from
Disco ball - Misplaced Pages Continue
1664-401: The discrepancy between the inner and outer surface area of any given shell is infinitesimal, and the elemental volume at radius r is simply the product of the surface area at radius r and the infinitesimal thickness. At any given radius r , the incremental volume ( δV ) equals the product of the surface area at radius r ( A ( r ) ) and the thickness of a shell ( δr ): The total volume
1716-515: The energy company Ørsted A/S uses the unit megawatt for produced electrical power and the equivalent unit megajoule per second for delivered heating power in a combined heat and power station such as Avedøre Power Station . When describing alternating current (AC) electricity, another distinction is made between the watt and the volt-ampere . While these units are equivalent for simple resistive circuits , they differ when loads exhibit electrical reactance . Radio stations usually report
1768-523: The fact that the projection to the lateral surface of a circumscribed cylinder is area-preserving. Another approach to obtaining the formula comes from the fact that it equals the derivative of the formula for the volume with respect to r because the total volume inside a sphere of radius r can be thought of as the summation of the surface area of an infinite number of spherical shells of infinitesimal thickness concentrically stacked inside one another from radius 0 to radius r . At infinitesimal thickness
1820-419: The former was somewhat larger than normal but nowhere near as large as the glitter ball used on the 1994 tour. This particular glitter ball is one of the largest in the world: 4.90 metres in diameter, it rises to a height of 213 metres before opening to a width of 7.3 metres, revealing a 12 kilowatt Phoebus HMI lamp. Both can be seen on the video of each tour, Delicate Sound of Thunder and Pulse , during
1872-475: The lemon disco ball at the end of the main set and emerged from the lemon disco ball at the start of their encore. The band also released promotional disco balls to promote the band's album Pop , the single " Discothèque ", and lead singer Bono also sported the alter-ego of "Mirror Ball Man" during their 1992 tour Zoo TV Tour . Introducing disco balls to a new concert demographic, the pop-punk band Paramore showcased dozens of spinning disco balls in 2014 as
1924-460: The maximum power output it can achieve at any point in time. A power station's annual energy output, however, would be recorded using units of energy (not power), typically gigawatt hours. Major energy production or consumption is often expressed as terawatt hours for a given period; often a calendar year or financial year. One terawatt hour of energy is equal to a sustained power delivery of one terawatt for one hour, or approximately 114 megawatts for
1976-550: The only solution of f ( x , y , z ) = 0 {\displaystyle f(x,y,z)=0} is the point P 0 = ( x 0 , y 0 , z 0 ) {\displaystyle P_{0}=(x_{0},y_{0},z_{0})} and the equation is said to be the equation of a point sphere . Finally, in the case ρ > 0 {\displaystyle \rho >0} , f ( x , y , z ) = 0 {\displaystyle f(x,y,z)=0}
2028-422: The poles is called the equator . Great circles through the poles are called lines of longitude or meridians . Small circles on the sphere that are parallel to the equator are circles of latitude (or parallels ). In geometry unrelated to astronomical bodies, geocentric terminology should be used only for illustration and noted as such, unless there is no chance of misunderstanding. Mathematicians consider
2080-488: The power of their transmitters in units of watts, referring to the effective radiated power . This refers to the power that a half-wave dipole antenna would need to radiate to match the intensity of the transmitter's main lobe . The terms power and energy are closely related but distinct physical quantities. Power is the rate at which energy is generated or consumed and hence is measured in units (e.g. watts) that represent energy per unit time . For example, when
2132-440: The smallest surface area of all surfaces that enclose a given volume, and it encloses the largest volume among all closed surfaces with a given surface area. The sphere therefore appears in nature: for example, bubbles and small water drops are roughly spherical because the surface tension locally minimizes surface area. The surface area relative to the mass of a ball is called the specific surface area and can be expressed from
Disco ball - Misplaced Pages Continue
2184-475: The song " Comfortably Numb ". American singer-songwriter Madonna has used glitter balls in several of her tours. During The Girlie Show in 1993, she descended while sitting on one before performing " Express Yourself ", and later in 2006, she used a 2-ton glitter ball that was embellished by 2 million dollars worth of Swarovski crystals, which used a hydraulic system to open like flower petals for her entrance during her Confessions Tour . Despite claims that
2236-510: The sphere has the same center and radius as the sphere, and divides it into two equal hemispheres . Although the figure of Earth is not perfectly spherical, terms borrowed from geography are convenient to apply to the sphere. A particular line passing through its center defines an axis (as in Earth's axis of rotation ). The sphere-axis intersection defines two antipodal poles ( north pole and south pole ). The great circle equidistant to
2288-522: The sphere with radius r > 0 {\displaystyle r>0} and center ( x 0 , y 0 , z 0 ) {\displaystyle (x_{0},y_{0},z_{0})} can be parameterized using trigonometric functions . The symbols used here are the same as those used in spherical coordinates . r is constant, while θ varies from 0 to π and φ {\displaystyle \varphi } varies from 0 to 2 π . In three dimensions,
2340-522: The sphere). This may be proved by inscribing a cone upside down into semi-sphere, noting that the area of a cross section of the cone plus the area of a cross section of the sphere is the same as the area of the cross section of the circumscribing cylinder, and applying Cavalieri's principle . This formula can also be derived using integral calculus (i.e., disk integration ) to sum the volumes of an infinite number of circular disks of infinitesimally small thickness stacked side by side and centered along
2392-516: The sphere. Several properties hold for the plane , which can be thought of as a sphere with infinite radius. These properties are: Watt The watt (symbol: W ) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m ⋅s . It is used to quantify the rate of energy transfer . The watt is named in honor of James Watt (1736–1819), an 18th-century Scottish inventor , mechanical engineer , and chemist who improved
2444-426: The sphere: their length is twice the radius, d = 2 r . Two points on the sphere connected by a diameter are antipodal points of each other. A unit sphere is a sphere with unit radius ( r = 1 ). For convenience, spheres are often taken to have their center at the origin of the coordinate system , and spheres in this article have their center at the origin unless a center is mentioned. A great circle on
2496-432: The square of the distance between their centers is equal to the sum of the squares of their radii. If f ( x , y , z ) = 0 and g ( x , y , z ) = 0 are the equations of two distinct spheres then is also the equation of a sphere for arbitrary values of the parameters s and t . The set of all spheres satisfying this equation is called a pencil of spheres determined by the original two spheres. In this definition
2548-569: The unit of power. In the electric power industry , megawatt electrical ( MWe or MW e ) refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt (MWt, MW t , or MWth, MW th ) refers to thermal power produced by the plant. For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2,109 MW t (i.e. heat), which creates steam to drive
2600-570: The unit within the existing system of practical units as "the power conveyed by a current of an Ampère through the difference of potential of a Volt". In October 1908, at the International Conference on Electric Units and Standards in London, so-called international definitions were established for practical electrical units. Siemens' definition was adopted as the international watt. (Also used: 1 A × 1 Ω.) The watt
2652-587: The world's largest disco ball can be found on the promenade in Blackpool , United Kingdom , it is smaller than the Guinness World Record holder. The ball was made for the 2014 Bestival event in England and is 10.33 metres (33 ft 11 in) in diameter. Sphere A sphere (from Greek σφαῖρα , sphaîra ) is a geometrical object that is a three-dimensional analogue to
SECTION 50
#17327905659452704-420: Was defined as equal to 10 units of power in the practical system of units. The "international units" were dominant from 1909 until 1948. After the 9th General Conference on Weights and Measures in 1948, the international watt was redefined from practical units to absolute units (i.e., using only length, mass, and time). Concretely, this meant that 1 watt was defined as the quantity of energy transferred in
#944055