Tests of special relativity: Difference between revisions

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| number =  5040
| divisor = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 28,  30, 35, 36, 40, 42, 45, 48, 56,  60, 63, 70, 72, 80, 84, 90, 105,  112, 120, 126, 140, 144, 168,  180, 210, 240, 252, 280, 315,  336, 360, 420, 504, 560, 630,  720, 840, 1008, 1260, 1680,  2520, 5040
}}
'''5040''' is a [[factorial]] (7!), a [[highly composite number]], a [[superior highly composite number]], a [[colossally abundant number]], and the [[number]] of [[permutation]]s of 4 items out of 10 choices (10 × 9 × 8 × 7 = 5040).
 
==Philosophy==
[[Plato]] mentions in his [[Laws (dialogue)|Laws]] that 5040 is a convenient number to use for [[division (mathematics)|dividing]] many things (including both the citizens and the land of a state) into lesser parts. He remarks that this number can be divided by all the [[natural numbers|(natural) numbers]] from [[1 (number)|1]] to [[12 (number)|12]] with the single exception of [[11 (number)|11]].  He rectifies this "defect" by suggesting that two families could be subtracted from the citizen body to produce the number 5038, which is [[divisible]] by 11.  Plato also took notice of the fact that 5040 can be divided by 12 twice over.  Indeed, Plato's repeated insistence on the use of 5040 for various state purposes is so evident that it is written, "Plato, writing under [[Pythagoreanism|Pythagorean]] influences, seems really to have supposed that the well-being of the city depended almost as much on the number 5040 as on [[justice]] and [[moderation]]."<ref>[http://www.gutenberg.org/files/1750/1750-h/1750-h.htm Laws], by Plato at Project Gutenberg; retrieved 7 July 2009</ref>
 
==Number Theory==
If <math>\sigma(n)</math> is the [[divisor function]] and <math>\gamma</math> is the [[Euler-Mascheroni constant]], then 5040 is the largest known number for which this [[Inequality (mathematics)|inequality]] holds:
:<math>\sigma(n) \geq e^\gamma n\log \log n </math>.
This is somewhat unusual, since in the [[limit (mathematics)|limit]] we have:
:<math>\limsup_{n\rightarrow\infty}\frac{\sigma(n)}{n\ \log \log n}=e^\gamma.</math>
Guy Robin showed in 1984 that the inequality fails for all larger numbers [[if and only if]] the [[Riemann hypothesis]] is true.
 
==Other==
▪ 5040 is considered an important number in some systems of [[numerology]], not only because of the Plato connection, but because using round figures, the sum of the [[radius|radii]] of both the [[Earth]] and [[Moon]] (in miles) is 3960 + 1080 = 5040.<ref>''City of Revelation: On the Proportions and Symbolic Numbers of the Cosmic Temple'', by [[John Michell (writer)|John Michell]] (ISBN 0-345-23607-6), p. 61.</ref> Incidentally, the sum of their [[diameter]]s is also the number of minutes in a week (7 days × 24 hours × 60 minutes = 10,080).
 
▪ The [[ratio]] of the [[radius]] of the moon and the radius of the earth is 1080/3960, which simplifies to 3/11. This ratio can also be expressed as (4 - [[π]])/π, when using 22/7 as the value of π. This means that the sizes of the earth and the moon are related by a simple function of π.
 
▪ Given that the radius of the moon is 3/11 that of the earth, the sum of their radii can be broken into 3/14 (for the radius of the moon) and 11/14 (for the radius of the earth). Further, the sum of their radii in miles is 5040, which when divided by 14 is 360 (the number of degrees in a circle). This would not happen for another pair of objects with radii in the same ratio - it only happens when the sum of their radii is 5040.
 
▪ 5040 has exactly 60 divisors, counting itself and 1.
 
▪ In a [[vigesimal]] system, 5040 is represented as 12 groups of 20 and 12 groups of 20-squared (12 • 20 = 240, 12 • 20<sup>2</sup> = 4800, and 240 + 4800 = 5040).
 
▪ 5040 is the sum of 42 consecutive primes (23 + 29 + 31 + 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67 + 71 + 73 + 79 + 83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 + 151 + 157 +163 + 167 + 173 + 179 + 181 + 191 + 193 + 197 + 199 + 211 + 223 + 227 + 229).
 
==Notes==
<references/>
 
==External links==
* [[Mathworld]] [http://mathworld.wolfram.com/PlatosNumbers.html article on Plato's numbers]
 
[[Category:Integers|59e03 5040]]
[[Category:Plato]]

Latest revision as of 11:26, 30 December 2014

Japanese researchers have successfully grown hair on hairless mice by implanting follicles created from stem tissue, they announced Wednesday, sparking new hopes of a cure for baldness. If you are not eating a well-balanced diet, you may well be anemic or have a necessary protein deficiency, both of which can lead to hair loss. Have a multivitamin containing vitamins A, B (including B12, B6 and biotin), D and E, zinc and iron to decrease the opportunity of continued hair loss. After about 12 weeks, users should see outcomes, which can range from a slower rate of hair loss to the growth of new hair. Often, however, hair that develops with minoxidil is shorter and thinner than earlier hair, and if use is discontinued new hair will cease to grow. It may take around 12 weeks for the development of new hair to be seen.

Some medical conditions can ultimately lead to significant hair damage - anorexia, lupus and diabetes will be disorders or diseases that may have this effect. This product allows doctors to examine and measure the hair down to the microscopic level, making it possible to accurately identify shrinking and degeneration of the hair follicles. Chronic telogen effluvium is a hair loss problem that manifests in women between your ages of 30 and 60, and it can be missed if steps are not taken to seek out it specifically. Some of the diseases that may cause hair damage are detectable through screening, incorporating lupus, anemia, thyroid sickness and nutritional deficiencies.

Sea veggies or weeds are rich in minerals, vitamins and proteins and have exceptional curative powers. Seaweeds such as for example Himanthalia Elongata and Atlantic Kelp may be used to stop hair loss and foster hair growth. It is one of many ingredients found in many hair loss treatments and can be obtained in both capsule and tea contact form. This herb not only encourages the progress of terminal hair but additionally acts as a hair restorative in accordance with a study published by American Botanical Council. This herb has been used being an ingredient in many hair care products such as hair restorative shampoos and oils.

Minerals such as for example calcium, iron, copper, chromium, iodine, zinc, and magnesium are essential to keep up healthy hair growth. Oxygen deficiency in your bloodstream weakens the hair follicles, resulting in dryness of the scalp and hair loss. It happens to be far better on the crown, where most women experience reduction, than on the sides.

Unfortunately not all of these are safe, and they can cause more serious medical conditions than hair loss. If your son or daughter is loosing hair you should not take it lightly as there are many reasons for the occurrence of hair loss consistently. Either it is the case of children hair loss or it is related to men hair loss both should be taken care of immediately.

If you are you looking for more information about hair loss cure 2013 take a look at our own web site.

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