Heine–Cantor theorem: Difference between revisions

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[[Image:Degree diagram.svg|thumb|One degree (shown in red) and<br />eighty nine (shown in blue)]]
A right analysis promptly can avoid other problems. Article Source: Alex works for vitiligotreatmentoil. Appearance of color changes inside mouth, nose, genital and rectal areas. Others believe it is due to some inherited conditions leading to melanocytes injury. Would he have felt loved and supported unconditionally and not just as an outgrowth of his staggering talent. <br><br>In this connection, we will only discuss about the skin disorder when the immune system becomes dysfunctional. As this disease happens to be complicated, its treatment has to be applicable to every single patient affected by this disease. By fighting the free radicals that damage and age your skin and the rest of your body, it helps your skin remain healthy and radiant, while also working to fight off infections. Novel patches also come into view over time and can be generalized over large portion of the body or localized to a meticulous part. Several herbal remedies employ various herbal components which contain psoralens, a group of naturally occurring substances. <br><br>The medical coding career is indispensable to the health care industry. Here is what you should know about using these aspects to deal with vitiligo:. The immunofluorescense assay is done to detect antibodies to a specific virus. The clay should be mixed in ginger juice in a ratio of 1:1, and applied over the white spots once a day. Eventually, vitiligo occurs after trauma and sunburn. <br><br>But for nearly everyone people who have Vitiligo, depigmentation happens on different organs of the body (generalized pattern). Psoralea corylifolia (Babchi) is the main ingredient in the pigmento. Yellow spots, liver spots; urticaria worse from warmth of bed. Kapalbhati Pranayama is a miraculous yoga breathing exercise, invented by Indian yogis thousands years ego, for complete body fitness. Depigmentation is a concept of loss of pigment cells in skin. <br><br>People with dark skin experience more prominent patches. Boil the concoction until only a liter of it is left. When you then combine these foods with garlic and a few berries you may have a incredibly powerful Vitiligo diet regime that can provide you with relief by enhancing your immune method, lessen free radicals and boost melanin production in your skin. 'Amla' juice with honey is helpful for the treatment of leucoderma. Autoimmunity is the to the point reason for vitiligo. <br><br>So it is easy enough now, to see how to treat the cause. Apply this paste on the affected area and wash off when dry. Most people have some moles but the scientists do not know why they develop nor for what purpose. Although it is commonly known as Vitiligo causing white patches on the skin is a skin disorder disease with a different name as Anti vitiligo oil can be affected to any race, both sexes, any age whether they are old or young. It was a treatment for a skin condition called vitiligo, which causes patches of depigmented skin all over the body.<br><br>If you loved this article and you simply would like to obtain more info pertaining to vitiligo treatments ([http://discover-prague.info/sitemap/ discover-prague.info]) nicely visit the web site.
A '''degree''' (in full, a '''degree of arc''', '''arc degree''', or '''arcdegree'''), usually denoted by '''°''' (the [[degree symbol]]), is a measurement of [[plane (mathematics)|plane]] [[angle]], representing <sup>1</sup>⁄<sub>360</sub> of a [[Turn (geometry)|full rotation]]. It is not an [[SI unit]], as the SI unit for angles is [[radian]], but it is mentioned in the SI brochure as an [[Non-SI units mentioned in the SI|accepted unit]].<ref>http://www.bipm.org/en/si/si_brochure/chapter4/table6.html</ref> Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians.
 
==History==
[[Image:Equilateral chord.svg|thumb||right|A circle with an equilateral [[Chord (geometry)|chord]] (red). One sixtieth of this arc is a degree. Six such chords complete the circle.]]
The original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year.<ref>[http://mathworld.wolfram.com/Degree.html Degree], MathWorld</ref> Ancient [[astronomers]] noticed that the sun, which follows through the [[ecliptic]] path over the course of the year, seems to advance in its path by approximately one degree each day. Some ancient [[calendar]]s, such as the [[Iranian calendar|Persian calendar]], used 360 days for a year. The use of a calendar with 360 days may be related to the use of [[sexagesimal]] numbers. One of the earliest recorded use of 360 as the total days in a year is found in the Hebrew Bible, Genesis 8-9 as it describes the duration of the Great Flood over 12 months of 30 days each.
 
Another theory is that the Babylonians  subdivided the circle using the angle of an equilateral triangle as the basic unit and further subdivided the latter into 60 parts following their [[sexagesimal]] numeric system.<ref>[[J.H. Jeans]] (1947), ''The Growth of Physical Science'', [http://books.google.co.uk/books?hl=en&lr=&id=JX49AAAAIAAJ&oi=fnd&pg=PA7 p.7]; [[Francis Dominic Murnaghan (mathematician)|Francis Dominic Murnaghan]] (1946), ''Analytic Geometry'', p.2</ref> The [[history of trigonometry|earliest trigonometry]], used by the [[Babylonian astronomy|Babylonian astronomers]] and their [[Greek astronomy|Greek]] successors, was based on [[chord (geometry)|chords]] of a circle. A chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard [[sexagesimal]] divisions, was a degree.
 
[[Aristarchus of Samos]] and [[Hipparchus|Hipparchos]] seem to have been among the first [[Greek astronomy|Greek scientists]] to exploit Babylonian astronomical knowledge and techniques systematically.<ref>For more information see [http://www.dioi.org/cot.htm#dqsr D.Rawlins] on Aristarchus; and [[G. J. Toomer]], "Hipparchus and Babylonian astronomy."</ref> [[Timocharis]], Aristarchus, [[Aristillus]], [[Archimedes]], and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 [[arc minute]]s ([http://www.dioi.org/vols/we0.pdf DIO 14] ‡2 p.&nbsp;19 n.24). [[Eratosthenes]] used a simpler [[sexagesimal]] system dividing a circle into 60 parts.
 
The division of the circle into 360 parts also occurred in ancient [[India]], as evidenced in the [[Rigveda]]:<ref>[[Dirghatamas]], Rigveda 1.164.48</ref>
 
{{quotation
|Twelve spokes, one wheel, navels three.<br />
Who can comprehend this? <br />
On it are placed together <br />
three hundred and sixty like pegs. <br />
They shake not in the least.
|[[Dirghatamas]]
|Rigveda 1.164.48}}
 
Another motivation for choosing the number 360 may have been that it is [[highly composite number|readily divisible]]: 360 has 24 [[divisor]]s,<ref>The divisors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.</ref> making it one of only 7 numbers such that no number less than twice as much has more divisors {{OEIS|id=A072938}}.<ref>[http://translate.google.com/translate?sl=auto&tl=en&js=n&prev=_t&hl=en&ie=UTF-8&layout=2&eotf=1&u=http%3A%2F%2Fwww.brefeld.homepage.t-online.de%2Fteilbarkeit.html&act=url Divisibility highly composite numbers], Werner Brefeld</ref> Furthermore, it is divisible by every number from 1 to 10 except 7.<ref>Contrast this with the relatively unwieldy 2520, which is the [[least common multiple]] for every number from 1 to 10.</ref> This property has many useful applications, such as dividing the world into 24 [[time zone]]s, each of which is nominally 15° of [[longitude]], to correlate with the established [[hour|24-hour]] [[day]] convention.
 
Finally, it may be the case that more than one of these factors has come into play.  According to that theory, the number is approximately 365 because of the apparent movement of the sun against the celestial sphere and that it was rounded to 360 for some of the mathematical reasons cited above.
 
==Subdivisions==
For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in [[astronomy]] or for [[latitude]]s and [[longitude]]s on the Earth, degree measurements may be written with [[decimal]] places: for example, 40.1875°, with the degree symbol behind the decimals.
 
Alternatively, the traditional [[sexagesimal]] [[Units of measurement|unit]] subdivisions can be used. One degree is divided into 60 ''minutes (of arc)'', and one minute into 60 ''seconds (of arc)''. These units, also called the ''[[arcminute]]'' and ''[[arcsecond]]'', are respectively represented as a single and double [[prime (symbol)|prime]]: for example, 40.1875° = 40°&nbsp;11′&nbsp;15″ . Sometimes  single and double quotation marks are used instead:  40°&nbsp;11'&nbsp;15" .
 
If still more accuracy is required, current practice is to use decimal divisions of the second: for example, 40°&nbsp;11′&nbsp;15.4″ . The older system of thirds, fourths, etc., which continues the sexagesimal unit subdivision, was used by [[al-Kashi]] and other ancient astronomers, but is rarely used today. These subdivisions were denoted{{Citation needed|date=January 2008}} by writing the [[Roman numeral]] for the number of sixtieths in superscript: 1<sup>I</sup> for a "prime" (minute of arc), 1<sup>II</sup> for a second, 1<sup>III</sup> for a third, 1<sup>IV</sup> for a fourth, etc. Hence the modern symbols for the minute and second of arc, and the word "second" also refer to this system. {{Citation needed|date=April 2009}}
 
==Alternative units==
{{See also|Angle#Measuring angles|l1=Measuring angles}}
 
[[File:Degree-Radian Conversion.svg|thumb|300px|A chart to convert between degrees and radians]]
In most [[mathematics|mathematical]] work beyond practical geometry, angles are typically measured in [[radian]]s rather than degrees. This is for a variety of reasons; for example, the [[trigonometric function]]s have simpler and more "natural" properties when their arguments are expressed in radians. These considerations outweigh the convenient divisibility of the number 360. One complete [[Turn (geometry)|turn]] (360°) is equal to 2''[[Pi|π]]'' radians, so 180° is equal to π radians, or equivalently, the degree is a [[mathematical constant]]: 1° = <sup>''π''</sup>⁄<sub>180</sub>.
 
The [[Turn (geometry)|turn]] (or revolution, full circle, full rotation, cycle) is used in technology and science. 1 turn = 360°.
 
With the invention of the [[metric system]], based on powers of ten, there was an attempt to define a "decimal degree" ('''[[grad (angle)|grad]]''' or '''gon'''), so that the number of decimal degrees in a right angle would be 100&nbsp;''gon'', and there would be 400&nbsp;''gon'' in a circle. Although this idea was abandoned already by Napoleon, some groups have continued to use it and many scientific [[calculator]]s still support it.  Decigrades {{frac|4000}} were used with French artillery sights in World War I.
 
An [[angular mil]], which is most used in military applications, has at least three specific variants, ranging from {{frac|6400}} to {{frac|6000}}, each approximately equal to one milliradian. However, {{frac|6000}} used by the Russian Army originated in Imperial Russia, where an equilateral chord was divided into tenths to give a circle of 600 units (this may be seen on a dial sight, a device for accurate aiming of artillery, also known as an aiming circle, dating from about 1900, in the St Petersberg Museum of Artillery).
 
===Conversion of some common angles===
{|class = wikitable style="text-align:center;"
! Units !! colspan=13 | Values
|-
|style = "background:#f2f2f2; text-align:left;" | '''[[Turn (geometry)|Turns]]'''&nbsp;&nbsp;
|style = "width:3em;" | 0
|style = "width:3em;" | 1/24
|style = "width:3em;" | 1/12
|style = "width:3em;" | 1/10
|style = "width:3em;" | 1/8
|style = "width:3em;" | 1/6
|style = "width:3em;" | 1/5
|style = "width:3em;" | 1/4
|style = "width:3em;" | 1/3
|style = "width:3em;" | 2/5
|style = "width:3em;" | 1/2
|style = "width:3em;" | 3/4
|style = "width:3em;" | 1
|-
|style = "background:#f2f2f2; text-align:left;" | '''[[Radian]]s'''
| 0
| <math>\tfrac{\pi}{12}</math>
| <math>\tfrac{\pi}{6}</math>
| <math>\tfrac{\pi}{5}</math>
| <math>\tfrac{\pi}{4}</math>
| <math>\tfrac{\pi}{3}</math>
| <math>\tfrac{2\pi}{5}</math>
| <math>\tfrac{\pi}{2}</math>
| <math>\tfrac{2\pi}{3}</math>
| <math>\tfrac{4\pi}{5}</math>
| <math>\pi\,</math>
| <math>\tfrac{3\pi}{2}</math>
| <math>2\pi\,</math>
|-
|style = "background:#f2f2f2; text-align:left;" | '''Degrees'''&nbsp;&nbsp;
|style = "width:3em;" | 0°
|style = "width:3em;" | 15°
|style = "width:3em;" | 30°
|style = "width:3em;" | 36°
|style = "width:3em;" | 45°
|style = "width:3em;" | 60°
|style = "width:3em;" | 72°
|style = "width:3em;" | 90°
|style = "width:3em;" | 120°
|style = "width:3em;" | 144°
|style = "width:3em;" | 180°
|style = "width:3em;" | 270°
|style = "width:3em;" | 360°
|-
|style = "background:#f2f2f2; text-align:left;" | '''[[Grad (angle)|Grads]]'''
| 0<sup>g</sup>
| <math>16{2\over 3}^g</math>
| <math>33{1\over 3}^g</math>
| 40<sup>g</sup>
| 50<sup>g</sup>
| <math>66{2\over 3}^g</math>
| 80<sup>g</sup>
| 100<sup>g</sup>
| <math>133{1\over 3}^g</math>
| 160<sup>g</sup>
| 200<sup>g</sup>
| 300<sup>g</sup>
| 400<sup>g</sup>
|}
 
==See also==
* [[Compass]]
* [[Geographic coordinate system]]
* [[Gradian]]
* [[Meridian arc]]
* [[Square degree]]
* [[Steradian]]
 
== Notes and references ==
{{Reflist|2}}
 
==External links==
{{Commons category|Degree (angle)}}
* [http://www.mathopenref.com/degrees.html Degrees as an angle measure], with interactive animation
* [http://mathworld.wolfram.com/Degree.html Degree] at [[MathWorld]]
* {{cite web|last=Gray|first=Meghan|title= ° Degree of Angle|url=http://www.sixtysymbols.com/videos/degree.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|coauthors=Merrifield, Michael; Moriarty, Philip|year=2009}}
 
{{SI units}}
 
{{DEFAULTSORT:Degree (Angle)}}
[[Category:Units of angle]]
[[Category:Imperial units]]
[[Category:Mathematical constants]]
[[Category:Customary units of measurement in the United States]]

Latest revision as of 14:13, 5 May 2014

A right analysis promptly can avoid other problems. Article Source: Alex works for vitiligotreatmentoil. Appearance of color changes inside mouth, nose, genital and rectal areas. Others believe it is due to some inherited conditions leading to melanocytes injury. Would he have felt loved and supported unconditionally and not just as an outgrowth of his staggering talent.

In this connection, we will only discuss about the skin disorder when the immune system becomes dysfunctional. As this disease happens to be complicated, its treatment has to be applicable to every single patient affected by this disease. By fighting the free radicals that damage and age your skin and the rest of your body, it helps your skin remain healthy and radiant, while also working to fight off infections. Novel patches also come into view over time and can be generalized over large portion of the body or localized to a meticulous part. Several herbal remedies employ various herbal components which contain psoralens, a group of naturally occurring substances.

The medical coding career is indispensable to the health care industry. Here is what you should know about using these aspects to deal with vitiligo:. The immunofluorescense assay is done to detect antibodies to a specific virus. The clay should be mixed in ginger juice in a ratio of 1:1, and applied over the white spots once a day. Eventually, vitiligo occurs after trauma and sunburn.

But for nearly everyone people who have Vitiligo, depigmentation happens on different organs of the body (generalized pattern). Psoralea corylifolia (Babchi) is the main ingredient in the pigmento. Yellow spots, liver spots; urticaria worse from warmth of bed. Kapalbhati Pranayama is a miraculous yoga breathing exercise, invented by Indian yogis thousands years ego, for complete body fitness. Depigmentation is a concept of loss of pigment cells in skin.

People with dark skin experience more prominent patches. Boil the concoction until only a liter of it is left. When you then combine these foods with garlic and a few berries you may have a incredibly powerful Vitiligo diet regime that can provide you with relief by enhancing your immune method, lessen free radicals and boost melanin production in your skin. 'Amla' juice with honey is helpful for the treatment of leucoderma. Autoimmunity is the to the point reason for vitiligo.

So it is easy enough now, to see how to treat the cause. Apply this paste on the affected area and wash off when dry. Most people have some moles but the scientists do not know why they develop nor for what purpose. Although it is commonly known as Vitiligo causing white patches on the skin is a skin disorder disease with a different name as Anti vitiligo oil can be affected to any race, both sexes, any age whether they are old or young. It was a treatment for a skin condition called vitiligo, which causes patches of depigmented skin all over the body.

If you loved this article and you simply would like to obtain more info pertaining to vitiligo treatments (discover-prague.info) nicely visit the web site.