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| {{For|trough-shaped reflector|Parabolic trough}}
| | Raspberry Ketone is a health supplement. It originates from those delicious raspberries you may discover inside the grocery aisle. Yet, we can't get enough of these small berries to receive the full impact of them. Researchers say that it would take 90 pounds of these raspberries to receive the full benefit that comes in their pill shape.<br><br>Apples are the perfect pre-dinner snack. Soluble fiber inside apples, called pectin, reduces the amount of glucose plus calories that's absorbed into the bloodstream after a meal. That's good news for people who wish To avoid sort 2 diabetes, however it furthermore makes apples one of the right snacks for dieters. Apple pectin prevents spikes inside blood glucose which lead to improved fat storage. It can assist you avoid the blood glucose "crash" which leaves we craving more food and will keep you satiated for as much as 2 hours.<br><br>Hi-Health.com, that advertises toward the end of the Dr. Oz Show each day, appears to jump on the wise practitioners recommendations plus qualities them found on the front page of its webpage. The site features 2 goods which contain it. Best deal: Ultra Plan raspberry ketone Plus Rhodiola, for $24.99. Rhodiola is a flowering plant that is mentioned to boost mood and energy.<br><br>Because odds are you aren't starving, diabetes is the likely culprit. In diabetes, the body is unable to use glucose, the usable shape of carbohydrates, plus therefore should rely on your body fat for stamina. Though this will appear like a positive method to lose weight, ketones equally build up inside your blood stream. Whenever too several ketones are present inside the blood, a condition known as acidosis occurs. Acidosis is when the bloods acidic level is too high. Prolonged acidosis usually cause death. Other possible however lees probably causes of ketonuria are liver disease or too several excellent fat, low carbohydrate food. In fact, whenever the Atkins Diet was prevalent, various instances of ketonuria were watched by doctors.<br><br>Dr. Oz views [http://safedietplansforwomen.com/raspberry-ketones raspberry ketones] as his "number one weight loss miracle in a bottle," he declared on his show recently. This compound, which is made from red raspberries, helps to control adiponectin, which is a hormone that stimulates your body to boost your metabolism. Some say it also suppresses their appetite. The result: your body burns fat more effectively and faster. Think you can just substitute red raspberries?<br><br>So, the product functions effectively inside a program and aids raspberry ketone diet the functions of weight loss. Clinically proven it aims at slimming down a body in a natural technique.<br><br>If you achieve rapid fat loss without exercise and without fat reduction, that's not the sort of fat loss we desire. This type of weight reduction causes you to still have excellent body fat and lost muscle. You usually regain the weight whenever we begin to eat frequently again.<br><br>When taking the supplements, it is significant to follow the instructions. This signifies taking the recommended dosage that is between 100 to 200 mg a day. Losing weight is not something that ought to be done overnight. Safe weight reduction should be gradual with the perfect rate being regarding 4 or 5 lbs every week. It is important to remember which for permanent results, exercise and eating a healthy diet is imperative. Anyone with an existing condition could speak to the doctor before taking any supplements. |
| [[Image:Paraboloid of Revolution.svg|thumb|right|150px|Circular paraboloid]]
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| A '''parabolic''' (or '''paraboloid''' or '''paraboloidal''') '''reflector''' (or '''dish''' or '''mirror''') is a [[Mirror|reflective]] surface used to collect or project [[energy]] such as [[light]], [[sound]], or [[radio wave]]s. Its shape is part of a [[circular paraboloid]], that is, the surface generated by a [[parabola]] revolving around its axis. The parabolic reflector transforms an incoming [[plane wave]] traveling along the axis into a [[spherical wave]] converging toward the focus. Conversely, a spherical wave generated by a [[point source]] placed in the focus is reflected into a plane wave propagating as a collimated beam along the axis.
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| Parabolic reflectors are used to collect energy from a distant source (for example sound waves or incoming [[star]] light) and bring it to a common [[Focus (optics)|focal point]], thus correcting [[spherical aberration]] found in simpler [[spherical reflector]]s. Since the principles of [[Specular reflection|reflection]] are reversible, parabolic reflectors can also be used to project energy of a source at its focus outward in a parallel beam,<ref name="AutoVC-2"/> used in devices such as [[Stage lighting instrument#Spotlights|spotlights]] and [[headlight|car headlights]].
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| [[File:Solar dish at Ben-Gurion National Solar Energy Center in Israel.jpg|thumb|200px|One of the world's largest solar parabolic dishes at the [[Ben-Gurion National Solar Energy Center]] in [[Israel]]]]
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| == Theory ==
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| {{unreferenced section|date=November 2012}}
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| Strictly, the three-dimensional shape of the reflector is called a ''[[paraboloid]]''. A parabola is the two-dimensional figure. (The distinction is like that between a sphere and a circle.) However, in informal language, the word ''parabola'' and its associated adjective ''parabolic'' are often used in place of ''paraboloid'' and ''paraboloidal''.
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| The dimensions of a symmetrical paraboloidal dish are related by the equation: <math> \scriptstyle 4FD = R^2,</math> where <math> \scriptstyle F</math> is the focal length, <math> \scriptstyle D</math> is the depth of the dish (measured along the axis of symmetry from the vertex to the plane of the rim), and <math> \scriptstyle R</math> is the radius of the rim. All units must be the same. If two of these three quantities are known, this equation can be used to calculate the third.
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| A more complex calculation is needed to find the diameter of the dish ''measured along its surface''. This is sometimes called the "linear diameter", and equals the diameter of a flat, circular sheet of material, usually metal, which is the right size to be cut and bent to make the dish. Two intermediate results are useful in the calculation: <math>\scriptstyle P=2F</math> (or the equivalent: <math>\scriptstyle P=\frac{R^2}{2D})</math> and <math>\scriptstyle Q=\sqrt {P^2+R^2},</math> where <math> \scriptstyle F,</math> <math> \scriptstyle D,</math> and <math> \scriptstyle R</math> are defined as above. The diameter of the dish, measured along the surface, is then given by: <math>\scriptstyle \frac {RQ} {P} + P \ln \left ( \frac {R+Q} {P} \right ),</math> where <math>\scriptstyle \ln(x)</math> means the [[natural logarithm]] of <math> \scriptstyle x </math>, i.e. its logarithm to base "[[e (mathematical constant)|e]]".
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| The volume of the dish, the amount of liquid it could hold if the rim were horizontal and the vertex at the bottom (e.g. the capacity of a paraboloidal [[wok]]), is given by <math>\scriptstyle \frac {1} {2} \pi R^2 D ,</math> where the symbols are defined as above. This can be compared with the formulae for the volumes of a [[Cylinder (geometry)|cylinder]] <math>\scriptstyle (\pi R^2 D),</math> a [[sphere|hemisphere]] <math>\scriptstyle (\frac {2}{3} \pi R^2 D,</math> where <math>\scriptstyle D=R),</math> and a [[Cone (geometry)|cone]] <math>\scriptstyle ( \frac {1} {3} \pi R^2 D ).</math> <math>\scriptstyle \pi R^2 </math> is the aperture area of the dish, the area enclosed by the rim, which is proportional to the amount of sunlight the reflector dish can intercept.
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| [[File:Parabola with focus and arbitrary line.svg|thumb|200px|Parallel rays coming in to a parabolic mirror are focused at a point F. The vertex is V, and the axis of symmetry passes through V and F.]]
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| The parabolic reflector functions due to the geometric properties of the paraboloidal shape: any incoming [[ray (optics)|ray]] that is parallel to the axis of the dish will be reflected to a central point, or "[[Focus (optics)|focus]]". (For a geometrical proof, click [[Parabola#Proof of the reflective property|here]].) Because many types of energy can be reflected in this way, parabolic reflectors can be used to collect and concentrate energy entering the reflector at a particular angle. Similarly, energy radiating from the focus to the dish can be transmitted outward in a beam that is parallel to the axis of the dish.
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| In contrast with [[spherical reflector]]s, which suffer from a [[spherical aberration]] that becomes stronger as the ratio of the beam diameter to the focal distance becomes larger, parabolic reflectors can be made to accommodate beams of any width. However, if the incoming beam makes a non-zero angle with the axis (or if the emitting point source is not placed in the focus), parabolic reflectors suffer from an [[Aberration in optical systems|aberration]] called [[Coma (optics)|coma]]. This is primarily of interest in telescopes because most other applications do not require sharp resolution off the axis of the parabola. | |
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| The precision to which a parabolic dish must be made in order to focus energy well depends on the wavelength of the energy. If the dish is wrong by a quarter of a wavelength, then the reflected energy will be wrong by a half wavelength, which means that it will interfere destructively with energy that has been reflected properly from another part of the dish. To prevent this, the dish must be made correctly to within about {{frac|20}} of a wavelength. The wavelength range of visible light is between about 400 and 700 nanometres (nm), so in order to focus all visible light well, a reflector must be correct to within about 20 nm. For comparison, the diameter of a human hair is usually about 50,000 nm, so the required accuracy for a reflector to focus visible light is about 2500 times less than the diameter of a hair.
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| Microwaves, such as are used for satellite-TV signals, have wavelengths of the order of ten millimetres, so dishes to focus these waves can be wrong by half a millimetre or so and still perform well.
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| ==Focus-balanced reflector==
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| It is sometimes useful if the [[centre of mass]] of a reflector dish coincides with its [[Focus (geometry)|focus]]. This allows it to be easily turned so it can be aimed at a moving source of light, such as the Sun in the sky, while its focus, where the target is located, is stationary. The dish is rotated around [[wikt:axis|axes]] that pass through the focus and around which it is balanced. If the dish is [[symmetrical]] and made of uniform material of constant thickness, and if ''F'' represents the focal length of the paraboloid, this "focus-balanced" condition occurs if the depth of the dish, measured along the axis of the paraboloid from the vertex to the plane of the [[wikt:rim|rim]] of the dish, is 1.8478 times ''F''. The radius of the rim is 2.7187 ''F''.{{efn|The closeness of this number to the value of "e", the base of natural logarithms, is just an accidental coincidence, but it does make a useful mnemonic.}} The angular radius of the rim as seen from the focal point is 72.68 degrees.<ref>http://solarcooking.wikia.com/wiki/Focus-Balanced_Paraboloidal_Reflector#Calculating_the_Dimensions_of_the_Paraboloid</ref>
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| ==Scheffler reflector==
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| The focus-balanced configuration (see above) requires the depth of the reflector dish to be greater than its focal length, so the focus is within the dish. This can lead to the focus being difficult to access. An alternative approach is exemplified by the '''Scheffler Reflector''', named after its inventor, [[Wolfgang Scheffler (inventor)|Wolfgang Scheffler]]. This is a paraboloidal mirror which is rotated about axes that pass through its centre of mass, but this does not coincide with the focus, which is outside the dish. If the reflector were a rigid paraboloid, the focus would move as the dish turns. To avoid this, the reflector is flexible, and is bent as it rotates so as to keep the focus stationary. Ideally, the reflector would be exactly paraboloidal at all times. In practice, this cannot be achieved exactly, so the Scheffler reflector is not suitable for purposes that require high accuracy. It is used in applications such as [[Solar cooker#Paraboloidal reflectors|solar cooking]], where sunlight has to be focused well enough to strike a cooking pot, but not to an exact point.<ref>http://www.solare-bruecke.org/index.php?option=com_content&view=article&id=2&Itemid=2&lang=en</ref>
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| ==Off-axis reflectors==
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| [[File:ASTRA2Connect Dish.jpg|thumb|200px|right|Off-axis satellite dish. The vertex of the paraboloid is below the bottom edge of the dish. The curvature of the dish is greatest near the vertex. The axis, which is aimed at the satellite, passes through the vertex and the receiver module, which is at the focus.]]
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| A circular paraboloid is theoretically unlimited in size. Any practical reflector uses just a small segment of it. Often, the segment includes the [[Vertex (curve)|vertex]] of the paraboloid, where its [[curvature]] is greatest, and where the [[axis of symmetry]] intersects the paraboloid. However, if the reflector is used to focus incoming energy onto a receiver, the shadow of the receiver falls onto the vertex of the paraboloid, which is part of the reflector, so part of the reflector is wasted. This can be avoided by making the reflector from a segment of the paraboloid which is offset from the vertex and the axis of symmetry. For example, in the above diagram the reflector could be just the part of the paraboloid between the points P<sub>1</sub> and P<sub>3</sub>. The receiver is still placed at the focus of the paraboloid, but it does not cast a shadow onto the reflector. The whole reflector receives energy, which is then focused onto the receiver. This is frequently done, for example, in satellite-TV receiving dishes, and also in some types of astronomical telescope.
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| Accurate off-axis reflectors, for use in telescopes, can be made quite simply by using a [[rotating furnace]], in which the container of molten glass is offset from the axis of rotation. To make less accurate ones, suitable as satellite dishes, the shape is designed by a computer, then multiple dishes are stamped out of sheet metal.
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| == History ==
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| The principle of parabolic reflectors has been known since [[classical antiquity]], when the mathematician [[Diocles (mathematician)|Diocles]] described them in his book ''On Burning Mirrors'' and proved that they focus a parallel beam to a point.<ref name="AutoVC-3"/> [[Archimedes]] in the third century BC studied paraboloids as part of his study of [[hydrostatic equilibrium]],<ref name="AutoVC-4"/> and it has been [[Archimedes#Discoveries and inventions|claimed]] that he used reflectors to set the Roman fleet alight during the [[Siege of Syracuse (212 BC)|Siege of Syracuse]].<ref name="AutoVC-5"/> This seems unlikely to be true, however, as the claim does not appear in sources before the 2nd century AD, and Diocles does not mention it in his book.<ref name="AutoVC-6"/> Parabolic mirrors were also studied by the [[physicist]] [[Ibn Sahl]] in the 10th century.<ref name="AutoVC-7"/> [[James Gregory (astronomer and mathematician)|James Gregory]], in his 1663 book ''Optica Promota'' (1663), pointed out that a [[reflecting telescope]] with a mirror that was parabolic would correct [[spherical aberration]] as well as the [[chromatic aberration]] seen in [[refracting telescope]]s. The design he came up with bears his name: the "[[Gregorian telescope]]"; but according to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one.<ref name="AutoVC-8"/> [[Isaac Newton]] knew about the properties of parabolic mirrors but chose a spherical shape for his [[Newtonian telescope]] mirror to simplify construction.<ref name="AutoVC-9"/> [[Lighthouse]]s also commonly used parabolic mirrors to collimate a point of light from a lantern into a beam, before being replaced by more efficient [[Fresnel lens]]es in the 19th century.
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| == Applications ==
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| [[File:Olympic Torch 2010.jpg|thumb|Lighting the Olympic Flame]]
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| The most common modern applications of the parabolic reflector are in [[satellite dish]]es, [[reflecting telescope]]s, [[radio telescope]]s, [[parabolic microphone]]s, [[solar cooker]]s, and many [[electric light|lighting]] devices such as [[Stage lighting instrument#Spotlights|spotlights]], [[headlight|car headlights]], [[Parabolic aluminized reflector light|PAR lamps]] and LED housings.<ref name="AutoVC-10"/>
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| The [[Olympic Flame]] is traditionally lit at [[Olympia, Greece]], using a parabolic reflector concentrating [[sunlight]], and is then transported to the venue of the Games. Parabolic mirrors are one of many shapes for a [[burning-glass]].
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| Parabolic reflectors are popular for use in creating [[optical illusion]]s. These consist of two opposing parabolic mirrors, with an opening in the center of the top mirror. When an object is placed on the bottom mirror, the mirrors create a [[real image]], which is a virtually identical copy of the original that appears in the opening. The quality of the image is dependent upon the precision of the optics. Some such illusions are manufactured to tolerances of millionths of an inch.
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| [[File:ALMA antennas on Chajnantor.jpg|thumb|left|Antennas of the [[Atacama Large Millimeter Array]] on the Chajnantor Plateau.<ref>{{cite news|title=ALMA Doubles its Power in New Phase of More Advanced Observations|url=http://www.eso.org/public/announcements/ann13002/|accessdate=11 January 2013|newspaper=ESO Announcement}}</ref> ]]
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| A parabolic reflector pointing upward can be formed by rotating a reflective liquid, like mercury, around a vertical axis. This makes the [[liquid mirror telescope]] possible. The same technique is used in [[rotating furnace]]s to make solid reflectors.
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| Parabolic reflectors are also a popular alternative for increasing wireless signal strength. Even with simple ones, users have reported 3 [[decibel|dB]] or more gains.<ref name="AutoVC-11"/><ref name="AutoVC-12"/>
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| {{clear}}
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| == Footnotes ==
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| {{notelist}}
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| == See also ==
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| * [[John D. Kraus]]
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| * [[Parabolic antenna]]
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| * [[Parabolic trough]]
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| * [[Solar furnace]]
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| * [[Toroidal reflector]]
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| == References ==
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| {{reflist|refs=
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| <ref name="AutoVC-2">{{cite web|first=Richard |last=Fitzpatrick |url=http://farside.ph.utexas.edu/teaching/316/lectures/node136.html |title=Spherical Mirrors |publisher=Farside.ph.utexas.edu |date=2007-07-14 |accessdate=2012-11-08}}</ref>
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| <ref name="AutoVC-3">pp. 162–164, ''Apollonius of Perga's Conica: text, context, subtext'', Michael N. Fried and Sabetai Unguru, Brill, 2001, ISBN 90-04-11977-9.</ref>
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| <ref name="AutoVC-4">pp. 73–74, ''The forgotten revolution: how science was born in 300 BC and why it had to be reborn'', Lucio Russo, Birkhäuser, 2004, ISBN 3-540-20068-1.</ref>
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| <ref name="AutoVC-5">{{cite news | title = Archimedes' Weapon| publisher = [[Time (magazine)|Time Magazine]]|date = November 26, 1973| url = http://www.time.com/time/magazine/article/0,9171,908175,00.html?promoid=googlep|accessdate=2007-08-12}}</ref>
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| <ref name="AutoVC-6">p. 72, The Geometry of Burning-Mirrors in Antiquity, [[Wilbur Knorr]], [[Isis (journal)|''Isis'']] '''74''' #1 (March 1983), pp. 53–73, {{doi|10.1086/353176}}.</ref>
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| <ref name="AutoVC-7">pp. 465, 468, 469, A Pioneer in Anaclastics: Ibn Sahl on Burning Mirrors and Lenses, Roshdi Rashed, ''Isis'', '''81''', #3 (September 1990), pp. 464–491, {{doi|10.1086/355456}}.</ref>
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| <ref name="AutoVC-8">{{cite book|url=http://books.google.com/books?id=9EYBAAAAQAAJ&pg=PA175-IA1&dq=parabolic+James+Gregory |title=A biographical dictionary of eminent Scotsmen |first=Robert |last=Chambers |publisher=Google Books |date= |accessdate=2012-11-08}}</ref>
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| <ref name="AutoVC-9">{{cite book|url=http://books.google.com/books?id=FGHhZf-k8SkC&pg=PA77&dq=Isaac+Newton+reflecting+telescope+spherical+mirror |title=Electronic Imaging in Astronomy: Detectors and Instrumentation | first = Ian S | last = McLean | publisher = Google Books |date=2008-07-29 |accessdate=2012-11-08}}</ref>
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| <ref name="AutoVC-10">{{cite web|url=http://farside.ph.utexas.edu/teaching/316/lectures/node136.html |title=Spherical Mirrors |first=Richard |last=Fitzpatrick |publisher=Farside.ph.utexas.edu |date=2007-07-14 |accessdate=2012-11-08}}</ref>
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| <ref name="AutoVC-11">{{cite web|url=http://www.binarywolf.com/249/diy-parabolic-reflector.htm |title=Parabolic Reflector Free WiFi Booster | work = Do-It-Yourself Wireless Antennas Update and Wi-Fi Resource Center | WiFi Wireless Q & A |publisher=Binarywolf.com |date=2009-08-26 |accessdate=2012-11-08}}</ref>
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| <ref name="AutoVC-12">{{cite web|url=http://www.wired.com/culture/lifestyle/multimedia/2004/08/64440?slide=2&slideView=2 |title=Slideshow: Wi-Fi Shootout in the Desert |publisher=Wired |date=2004-08-03 |accessdate=2012-11-08}}</ref>
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| }}
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| == External links ==
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| * [http://www.falstad.com/ripple/ex-parabola.html Java demonstration of a parabolic reflector]
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| * [http://vzone.virgin.net/ljmayes.mal/var/parabola.htm Algorithm and spreadsheet for making a simple paraboloid]: Design and make a paraboloid for use as a solar concentrator, sound mirror or microwave antenna.
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| * [http://paralela.org/freeware_projects/parabolic_microphone_calculator.html JavaScript calculator and algorithm for designing paraboloids]: Design and make a paraboloid approximated by flat surface segments.
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| * [http://www.antenna-theory.com/antennas/reflectors/dish.php Parabolic Reflector Antennas] www.antenna-theory.com
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| * [http://qed.wikina.org/parabola/ Animations demonstrating parabola mirror] by QED
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| [[Category:Mirrors]]
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| [[Category:Parabolas]]
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| [[fr:Miroir (optique)#Miroir parabolique]]
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Raspberry Ketone is a health supplement. It originates from those delicious raspberries you may discover inside the grocery aisle. Yet, we can't get enough of these small berries to receive the full impact of them. Researchers say that it would take 90 pounds of these raspberries to receive the full benefit that comes in their pill shape.
Apples are the perfect pre-dinner snack. Soluble fiber inside apples, called pectin, reduces the amount of glucose plus calories that's absorbed into the bloodstream after a meal. That's good news for people who wish To avoid sort 2 diabetes, however it furthermore makes apples one of the right snacks for dieters. Apple pectin prevents spikes inside blood glucose which lead to improved fat storage. It can assist you avoid the blood glucose "crash" which leaves we craving more food and will keep you satiated for as much as 2 hours.
Hi-Health.com, that advertises toward the end of the Dr. Oz Show each day, appears to jump on the wise practitioners recommendations plus qualities them found on the front page of its webpage. The site features 2 goods which contain it. Best deal: Ultra Plan raspberry ketone Plus Rhodiola, for $24.99. Rhodiola is a flowering plant that is mentioned to boost mood and energy.
Because odds are you aren't starving, diabetes is the likely culprit. In diabetes, the body is unable to use glucose, the usable shape of carbohydrates, plus therefore should rely on your body fat for stamina. Though this will appear like a positive method to lose weight, ketones equally build up inside your blood stream. Whenever too several ketones are present inside the blood, a condition known as acidosis occurs. Acidosis is when the bloods acidic level is too high. Prolonged acidosis usually cause death. Other possible however lees probably causes of ketonuria are liver disease or too several excellent fat, low carbohydrate food. In fact, whenever the Atkins Diet was prevalent, various instances of ketonuria were watched by doctors.
Dr. Oz views raspberry ketones as his "number one weight loss miracle in a bottle," he declared on his show recently. This compound, which is made from red raspberries, helps to control adiponectin, which is a hormone that stimulates your body to boost your metabolism. Some say it also suppresses their appetite. The result: your body burns fat more effectively and faster. Think you can just substitute red raspberries?
So, the product functions effectively inside a program and aids raspberry ketone diet the functions of weight loss. Clinically proven it aims at slimming down a body in a natural technique.
If you achieve rapid fat loss without exercise and without fat reduction, that's not the sort of fat loss we desire. This type of weight reduction causes you to still have excellent body fat and lost muscle. You usually regain the weight whenever we begin to eat frequently again.
When taking the supplements, it is significant to follow the instructions. This signifies taking the recommended dosage that is between 100 to 200 mg a day. Losing weight is not something that ought to be done overnight. Safe weight reduction should be gradual with the perfect rate being regarding 4 or 5 lbs every week. It is important to remember which for permanent results, exercise and eating a healthy diet is imperative. Anyone with an existing condition could speak to the doctor before taking any supplements.