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PDF Editor FAQ

What is the significance of number 999?

It is 1 number from 1000999/3=333So 999 is in the 111 times table111222333444555666777888999111012111332If 999/1000 people like a product 99.9% of people like it.It is in the 37 times table also3774111148185222259296333370407444481518555592629666703740777814851888925962999 ta da

What are some mind-blowing facts about mathematics?

Let me discuss about “James Bond & Golden ratio or the number PHI”Now you are pretty interested in reading this answer right????I will come back to the “James Bond” thing later. At first let me tell you about “PHI”. Mind you “PHI” isn’t “PI”!PI is a very important number I agree but PHI well its is called the “GOLDEN RATIO”. I came across the term “Golden ratio” in the book “Da Vinci’s Code” by Dan Brown I developed a keen interest in this particular number.PHI is 1.6.80339887…..Now you might be wondering about what is golden ratio and why PHI is called a golden ratio?We find the golden ratio when we divide a line into two parts so that:the whole length divided by the long part is also equal to the long part divided by the short part.i.e(a+b)/a should be equal to a/b. (considering a is the longer part and b the shorter part)PHI is an irrational number just like PI but PHI has got a lot of mathematical properties.There is a close relationship between FIBONACCI series and GOLDEN RATIO.when we take any two successive Fibonacci Numbers,their ratio is very close to the Golden Ratio.Example: 1,2,3,5,8,13,…..,144,237,377….then3/2=1.5 ;8/5=1.6 ;13/8=1.6;237/144=1.618055556...377/237=1.618025751...Now coming back to “James Bond”.Our favorite spy 007 drove an Aston Martin DB5 in the movies GoldFinger and GoldenEye, and it is said that Golden ratio was at the heart of the designing of the automobiles!Da Vinci and The Golden RatioDa Vinci used the Golden ratio to define all of the proportions in his Last Supper, including the dimensions of the table and the proportions of the walls and backgrounds. The Golden ratio also appears in da Vinci's Vitruvian Man and the Mona Lisa. Other artists who employed the Golden ratio include Michelangelo, Raphael, Rembrandt, Seurat, and Salvador Dali.PyramindsHistorically, the number can be seen in the architecture of many ancient creations, like the Great Pyramids and the Parthenon. In the Great Pyramid of Giza, the length of each side of the base is 756 feet with a height of 481 feet. The ratio of the base to the height is roughly 1.5717, which is close to the Golden ratio.PentagramNo I am not going to ramble about witchcraft or voodo! It has got Golden Ratio in it.a/b=1.618…; c/c=1.618…; c/d=1.618Phi and logosPHI has been used to design various logos . You get to see one of the miracle of PHI designing everyday and that is the logo of GOOGLE.Many structure and patterns in this universe involves the number PHI. For example :Shells: Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral.Spiral Galaxies. Tree Branches, Flower Petals etc.Even our own body !!The ratio of the forearm to hand is PhiEven your feet show phiThe middle of the arch of the footThe widest part of the footThe base of the toe line and big toeThe top of the toe line and base of the “index” toeHuman faces are abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself (which follows along a spiral).No doubt PHI / Golden ratio is considered to be “Design’s Biggest Myth”P.S: There are a lot of facts related to PHI. I tried to cover the major points. You can google it an find out more about PHI!

What role does sleep play in the functioning of the human immune system?

Immune response promotes sleep (especially NREM sleep) and vice versa. The role of interleukin-1, interleukin-6, and tumor necrosis factor α, in the regulation of NREM sleep is well-established and the list of proinflammatory cytokines and immune factors with sleep-promoting properties continue to grow [1-3]. Sleep is involved in the acute phase response to infections [4]. NREM sleep acts in concert with the circadian system to generate a pro-inflammatory hormonal milieu with enhanced growth hormone and prolactin and reduced cortisol release [5]. There is significant overlap between neurohormonal factors and cytokines in regard to their effects on sleep-wake regulation [6].Sleep deprivation can negatively affect inflammatory, immune, and host defense functions, but the effects will vary depending on the threat or injury [7, 8]. The effects of sleep deprivation on wound healing remains controversial. At least one study found no effect of total sleep deprivation [9] and another study found no effect of REM sleep deprivation [10] on wound healing rates. However, one study found that sleep deprivation can disrupt skin barrier function [11]. Chronic sleep deprivation disrupts neurogenesis in adult rodents [12] but short-term sleep deprivation was found to stimulate neurogenesis following global cerebral ischemia [13].References:[1] Majde JA, Krueger JM. Links between the innate immune system and sleep. J Allergy Clin Immunol. 2005 Dec;116(6):1188-1198.[2] Gamaldo CE, Shaikh AK, McArthur JC. The sleep-immunity relationship. Neurol Clin. 2012 Nov;30(4):1313-1343.[3] Besedovsky L, Lange T, Born J. Sleep and immune function. Pflugers Archiv. 2012;463(1):121-137.[4] Trammell R, Jhaveri K, Toth LA. Inflammation and sleep. In: Pandi-Perumal SR, Chrousos G, Cardinali DP (Editors). Neuroimmunology of Sleep. New York: Springer Press; 2007. pp. 233-256.[5] Kelley KW, Weigent DA, Kooijman R. Protein hormones and immunity. Brain Behav Immun. 2007 May; 21(4):384-392.[6] Kapsimalis F, Richardson G, Opp MR, Kryger M. Cytokines and normal sleep. Curr Opin Pulm Med. 2005 Nov;11(6):481-484.[7] Mullington JM, Simpson NS, Meier-Ewert HK, Haack M. Sleep loss and inflammation. Best Practice & Research. Clinical Endocrinology & Metabolism. 2010;24(5):775-784.[8] Benca RM, Quintas J. Sleep and host defenses: a review. Sleep. 1997 Nov;20(11):1027-1037.[9] Landis CA, Whitney JD. Effects of 72 hours sleep deprivation on wound healing in the rat. Res Nurs Health. 1997 Jun;20(3):259-267.[10] Mostaghimi L, Obermeyer WH, Ballamudi B, Martinez-Gonzalez D, Benca RM. Effects of sleep deprivation on wound healing. J Sleep Res. 2005 Sep;14(3):213-219.[11] Altemus, M., Rao, B., Dhabhar, F. S., Ding, W. and Granstein, R. D. Stress-induced changes in skin barrier function in healthy women. J. Invest. Dermatol., 2001, 117: 309–317.[12] Fernandes C, Rocha NBF, Rocha S, et al. Detrimental role of prolonged sleep deprivation on adult neurogenesis. Frontiers in Cellular Neuroscience. 2015; 9:140.[13] Cheng O, Li R, Zhao L, et al. Short-term sleep deprivation stimulates hippocampal neurogenesis in rats following global cerebral ischemia/reperfusion. Zhang Q, ed. PLoS ONE. 2015;10(6): e0125877.

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