tag:blogger.com,1999:blog-14605233643038004592023-03-17T03:58:13.427+01:00Natalino BusaNat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comBlogger78125tag:blogger.com,1999:blog-1460523364303800459.post-3133071344536409832013-01-11T15:03:00.000+01:002013-01-12T16:21:00.848+01:00Child's eyesWhat do you see?<br />Can you tell me?<br /><br />What's all around us?<br />Can you tell me?<br /><br />I know it must be great.<br /><br />Can you put your foot<br />behind your head?<br /><br />Let's jump and shout<br />around, then run <br />for an ice cream.<br /><br />Tell me son, <br />did you like it?<br /><br />You can't tell,<br />but I see your <br />wide eyes <br />glitter.<br /><br />Sure, it's awesome.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-77932229952439868592012-01-03T23:53:00.000+01:002013-01-12T22:28:51.264+01:00Euler product formula<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-bj7vvXTtUys/UOaeOuiN0KI/AAAAAAAAJbY/NK-LKxDZNCU/s1600/eqn1609.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-bj7vvXTtUys/UOaeOuiN0KI/AAAAAAAAJbY/NK-LKxDZNCU/s1600/eqn1609.png" width="320" /></a></div> The Euler product formula can be used to calculate the asymptotic probability that s randomly selected integers are set-wise coprime. Intuitively, the probability that any single number is divisible by a prime (or any integer), p is 1/p.<br /><br />Hence the probability that s numbers are all divisible by this prime is 1/p^s, and the probability that at least one of them is not is 1 − 1/p^s. Now, for distinct primes, these divisibility events are mutually independent because the candidate divisors are coprime (a number is divisible by coprime divisors n and m if and only if it is divisible by nm, an event which occurs with probability 1/(nm).)<br /><br />Thus the asymptotic probability that s numbers are coprime is given by a product over all primes,Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-66961206685354653422012-01-03T23:19:00.000+01:002013-01-12T22:29:46.290+01:00Gamma, the Euler–Mascheroni constant.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://3.bp.blogspot.com/-gunlVc6vXS8/UOafTzdIuxI/AAAAAAAAJbo/B8-vdiq1yUw/s1600/eqn3150.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://3.bp.blogspot.com/-gunlVc6vXS8/UOafTzdIuxI/AAAAAAAAJbo/B8-vdiq1yUw/s1600/eqn3150.png" height="400" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Gamma, the Euler–Mascheroni constant. </td></tr></tbody></table> <br />The number γ has not been proved algebraic or transcendental. In fact, it is not even known whether γ is irrational. Continued fraction analysis reveals that if γ is rational, its denominator must be greater than 10242080. The ubiquity of γ revealed by the large number of equations makes the irrationality of γ a major open question in mathematics.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-28316997587207880652012-01-02T23:31:00.000+01:002013-01-04T21:22:16.022+01:00Experience and consciousness are largely unrelatedWe owe a lot to the rationalists of the eighteen century. In particular to Descartes and his "cogito ergo sum". Still I would like to set asides catchy phrases and concentrate a bit more on the notion of experience. Experience could be defined as simply as preserving for a given period of time the effect of an factor. Preserving somehow the producing event, in any form, can be regarded as experience. Western civilization poses a great deal on the individual and the centrality of the man as the subject and the actor of the experience. But if experience is just sharing on something we have felt and kept inside, i like to think that seashells have quietly experienced the miracle of the sea, and they are happy to tell us this story every time we put them next to our hears.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-7852785969582726892012-01-02T16:14:00.000+01:002013-01-03T18:58:59.472+01:00Something differentWindy swirl, dew&ink,<br/>steady, caring,<br/>chips of chirps.<br/><br/>Mother and child, <br/>tenderness.<br/><br/>Sweet, forgetful, thump,<br/>and bumping heart.<br/><br/>The carillon,<br/>the flesh of my flesh.<br/><br/>day, freedom,<br/>routine, and vacations.<br/><br/>Billboard, cassandra,<br/>coffee and tea.<br/><br/>together, ohohoh.<br/>and more, yes, more.<br/><br/>The hand in my hand.<br/>Together ohohoh.<br/><br/>Kisses<br/>NanniNat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-84724825008651863212011-11-27T17:08:00.000+01:002013-01-03T18:58:59.476+01:00Love and deathThe question is,<br/>have I learned anything about life?<br/><br/>Only that human beings<br/>are divided into mind and body.<br/><br/>The mind embraces all the nobler<br/>aspirations, like poetry and philosophy,<br/>but the body has all the fun.<br/><br/>The important thing, I think,<br/>is not to be bitter.<br/><br/>You know, if it turns out that there<br/>is a God, I don't think that he's evil.<br/>I think the worst you can say about him<br/>is that basically he's an underachiever.<br/><br/>After all, you know,<br/>there are worse things in life than death.<br/><br/>If you've ever spent an evening<br/>with an insurance salesman,<br/>you know exactly what I mean.<br/><br/>The key here, I think,<br/>is to not think of death as an end,<br/>but think of it more as a very effective<br/>way of cutting down on your expenses.<br/><br/>Regarding love...<br/>You know, what can you say?<br/><br/>It's not the quantity<br/>of your sexual relations that count.<br/><br/>It's the quality.<br/><br/>On the other hand, if the quantity<br/>drops below once every eight months,<br/>I would definitely look into it.<br/><br/>Well, that's about it for me, folks.<br/>Goodbye.<br/><br/>Thanks to Woody Allen to put it into words,<br/>thanks to the rest of the new yorkers for the field<br/>experimentation and to provide evidence for the theory.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-81820860801229544912011-11-24T23:26:00.000+01:002013-01-04T21:22:16.052+01:00Can estetics be the foundation of analytical sciencesDirac used to say that formulas must be beautiful and elegant. He was convinced that beautiful formula's have a better chance in providing an analytical frame for physical phenomena. I have to say that Dirac's equation is indeed very beautiful. As a side effect, it was the first equation to provide a theoretical framework for antimatter and it the first equation to join quantum mechanics, special relativity, and classic electromagnetism. Not bad for a beautiful equation.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-56170988227913560362011-11-24T23:16:00.000+01:002013-01-04T21:22:16.039+01:00We are the tools of our toolsA tool exists for the sole purpose of being used. Hence the existence of the tool implies an entity who uses the tool to perform a task. We, humans, are great inventors of tools but also great users of tools. In a way we depend on our tools. So our existence depends on those tools as much as the existence of those tools depend from us. So at the end, who and what is the tool?Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-70273246701579418552011-10-31T16:06:00.000+01:002013-01-03T18:58:59.460+01:00The funny thing about the future<blockquote>Here is the thing about the future. <br/>Every time you look at, it changes.<br/>it changes, because you looked at it, <br/>and that changes everything else.<br/><br/>quoted from "Next", last scene.<br/></blockquote><br/><br/>We can travel through time,<br/>because time is what we were and what we will be.<br/><br/>We can visit, live and interpret<br/>the past, the future and the present<br/>a million time ... <br/><br/>The past is mutable, because we change, <br/>the future is mutable, because we dream.<br/><br/>Time is the drawing, not the canvas.<br/>and all the drawings are on the same canvas.<br/><br/>Pick yours. And pick it as many times as you want.<br/>You are all the stories, not just the story being told.<br/><br/>Nothing special happened today.<br/>That's enough for me to celebrate.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-67758329214741985332011-09-23T17:36:00.000+02:002013-01-03T18:58:59.455+01:00Human butterflyI fear death,<br/>cause I can't comprehend life.<br/><br/>My logic fogs my<br/>capacity to feel<br/><br/>and as I get older,<br/>my thoughts are more<br/>a burden than a gain.<br/><br/>My feelings <br/>have always been<br/>my best wealth.<br/><br/>A glimpse of love and pain.<br/>And I am so grateful for it.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-23753026237593311632011-06-28T15:54:00.000+02:002013-01-04T21:22:16.020+01:00Love costs all we are and will beIn the flush of love's light<br/>we dare be brave<br/>And suddenly we see<br/>that love costs all we are<br/>and will ever be.<br/>Yet it is only love<br/>which sets us free.<br/><br/>Maya Angelou - Touched by An AngelNat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-64827937763458241242011-06-28T06:47:00.000+02:002013-01-03T18:58:59.452+01:00The definition and etymology of the sanskrit word "Maya"from Myths and Symbols of Indian Art and Civilization, by Heinrich Zimmer <br/>New York: Harper & Row, 1962, pp. 24-26.<br/><br/>The Hindu mind associates such ideas as "transitory, ever-changing, elusive, ever-returning," with "unreality," and conversely, imperishable, changeless, steadfast, and eternal," with "the real." As long as the experiences and sensations that stream through the consciousness of an individual remain untouched by any widening, devaluating vision, the perishable creatures that appear and vanish in the unending cycle of life (samsara, the round of rebirth) are regarded by him as utterly real. But the moment their fleeting character is discerned, they come to seem almost unreal – an illusion or mirage, a deception of the senses, the dubious figment of a too restricted, ego-centered consciousness. When understood and experienced in this manner, the world is Maya-maya, "of the stuff of Maya." Maya is "art": that by which an artifact, an appearance, is produced. Maya is precisely the maker’s power or art, "Magic" in Jacob Boehme’s sense: "It is a mother in all three worlds, and makes each thing after the model of that thing’s will. It is not the understanding, but it is a creatrix according to the understanding, and lends itself to good or to evil . . . from eternity a ground and support of all things ... In sum: Magic is the activity in the Will-spirit." (Sex Puncta Mystica, V. -- Ananda K. Coomaraswami)<br/><br/>The noun maya is related etymologically to "measure." It is from the root ma, which means "to measure or lay out instance, the ground plan of a building, or the outlines of a figure); to produce, shape, or create; to display." Maya is the measuring out, or creation, or display of forms; maya is any illusion, trick, artifice, deceit, jugglery, sorcery, or work of witchcraft; an illusory image or apparition, phantasm, deception, of the sight; maya is also any diplomatic trick or political artifice designed to deceive. The maya of the gods is their power to assume diverse shapes by displaying at will various aspects of their subtle essence. But the gods are themselves the productions of a greater maya: the spontaneous self-transformation of an originally undifferentiated, all-generating divine Substance. And this greater maya produces, not the gods alone, but the universe in which they operate. All the universes co-existing in space and succeeding each other in time, the planes of being and the creatures of those planes whether natural or supernatural, are manifestations from an inexhaustible, original and eternal well of being, and are made manifest by a play of maya. In the period of non-manifestation, the interlude of the cosmic night, maya ceases to operate and the display dissolves.<br/><br/>Maya is Existence: both the world of which we are aware, and ourselves who are contained in the growing and dissolving environment, growing and dissolving in our turn. At the same time, Maya is the supreme power that generates and animates the display: the dynamic aspect of the universal Substance. Thus it is at once, effect (the cosmic flux), and cause (the creative power). In the latter regard it is known as Shakti, "Cosmic Energy." The noun shakti is from the root shak, signifying "to be able, to be possible." Shakti is power, ability, capacity, faculty, strength, energy, prowess; regal power; the power of composition, poetic power, genius; the power or signification of a word or term; the power inherent in cause to produce its necessary effect; an iron spear, lance, pike, dart; a sword"; shakti is the female organ; shakti is the active power of a deity and is regarded, mythologically, as his goddess-consort and queen.<br/><br/>Maya-Shakti is personified as the world-protecting, feminine, maternal side of the Ultimate Being, and as such, stands for the spontaneous, loving acceptance of life’s tangible reality. Enduring the suffering, sacrifice, death and bereavements that attend all experience of the transitory, she affirms, she is, she represents and enjoys, the delirium of the manifested forms. She is the creative joy of life: herself the beauty, the marvel, the enticement and seduction of the living world. She instills into us - and she is, herself – surrender to the changing aspects of existence. . . .<br/><br/>Now the character of Maya-Shakti-Devi (devi = "goddess") is multifariously ambiguous. Having mothered the universe and the individual (macro- and microcosm) as correlative manifestations of the divine, Maya then immediately muffles consciousness within the wrappings of her perishable production. The ego is entrapped in a web, a queer cocoon. "All this around me," and "my own existence" – experience without and experience within – are the warp and woof of the subtle fabric. Enthralled by ourselves and the effects of our environment, regarding the bafflements of Maya as utterly real, we endure an endless ordeal of blandishment, desire and death; whereas, from a standpoint just beyond our ken (that represented in the perennial esoteric tradition and known to the illimited, supra-individual consciousness of ascetic, yogic experience) Maya – the world, the life, the ego, to which we cling – is as fugitive and evanescent as cloud and mist.<br/><br/>The aim of Indian thought has always been to learn the secret of the entanglement, and, if possible, to cut through into a reality outside and beneath the emotional and intellectual convolutions that enwrap our conscious being.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-28109729335951217612011-05-17T15:34:00.000+02:002013-01-12T22:31:20.883+01:00Integral of rational function<div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-2tYKhHnSQLk/UOaj5Zcc1YI/AAAAAAAAJcM/kqg7F2zop8E/s1600/formula7.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-2tYKhHnSQLk/UOaj5Zcc1YI/AAAAAAAAJcM/kqg7F2zop8E/s1600/formula7.jpg" height="297" width="400" /></a></div><br /><div style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.200000762939453px; margin-bottom: 0.5em; margin-top: 0.4em;">From <a href="http://en.wikipedia.org/wiki/Catenary">http://en.wikipedia.org/wiki/Catenary</a>:</div><div style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.200000762939453px; margin-bottom: 0.5em; margin-top: 0.4em;">The word <i>catenary</i> is derived from the Latin word <i>catena,</i> which means "<a href="http://en.wikipedia.org/wiki/Chain" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: initial;" title="Chain">chain</a>". The English word <i>catenary</i> is usually attributed to <a href="http://en.wikipedia.org/wiki/Thomas_Jefferson" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: initial;" title="Thomas Jefferson">Thomas Jefferson</a>, who wrote in a letter to <a href="http://en.wikipedia.org/wiki/Thomas_Paine" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: initial;" title="Thomas Paine">Thomas Paine</a> on the construction of an arch for a bridge:</div><blockquote style="background-color: white; font-family: sans-serif; font-size: 13px; line-height: 19.200000762939453px;"><div style="line-height: 1.5em; margin-bottom: 0.5em; margin-top: 0.4em;">I have lately received from Italy a treatise on the <a href="http://en.wikipedia.org/wiki/Mechanical_equilibrium" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: initial;" title="Mechanical equilibrium">equilibrium</a> of arches, by the Abbé Mascheroni. It appears to be a very scientifical work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the catenary is in perfect equilibrium.<sup class="reference" id="cite_ref-5" style="line-height: 1em;"><a href="http://en.wikipedia.org/wiki/Catenary#cite_note-5" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: initial; white-space: nowrap;">[5]</a></sup></div></blockquote><div style="background-color: white; font-family: sans-serif; margin-bottom: 0.5em; margin-top: 0.4em;"><span style="font-size: 13px; line-height: 19.200000762939453px;">It is often said that <a href="http://en.wikipedia.org/wiki/Galileo_Galilei" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: initial;" title="Galileo Galilei">Galileo</a> thought the curve of a hanging chain was parabolic. In his <i><a href="http://en.wikipedia.org/wiki/Two_New_Sciences" style="background-image: none; background-position: initial initial; background-repeat: initial initial; color: #0b0080; text-decoration: initial;" title="Two New Sciences">Two New Sciences</a></i> (1638), Galileo says that a hanging cord is an approximate parabola, and he correctly observes that this approximation improves as the curvature gets smaller and is almost exact when the elevation is less than 45°.</span><span style="font-size: 11px; line-height: 10.833333015441895px;"> </span><span style="font-size: x-small;"><span style="line-height: 19.200000762939453px;">That the curve followed by a chain is not a parabola was proven by </span></span><a href="http://en.wikipedia.org/wiki/Joachim_Jungius" style="background-image: none; color: #0b0080; font-size: 13px; line-height: 19.200000762939453px; text-decoration: initial;" title="Joachim Jungius">Joachim Jungius</a><span style="font-size: x-small;"><span style="line-height: 19.200000762939453px;"> (1587–1657); this result was published posthumously in 1669.</span></span></div>Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-5212351265878024702011-05-17T15:14:00.000+02:002013-01-12T22:32:27.605+01:00de Moivre's formula<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-kipdOXvmk1Y/UOaoFpi3LdI/AAAAAAAAJc8/uQ4XsjK1JmM/s1600/formula6.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-kipdOXvmk1Y/UOaoFpi3LdI/AAAAAAAAJc8/uQ4XsjK1JmM/s1600/formula6.jpg" height="297" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">de Moivre's formula </td></tr></tbody></table> From http://en.wikipedia.org/wiki/De_Moivre's_formula:<br /><br />By expanding the left hand side and then comparing the real and imaginary parts under the assumption that x is real, it is possible to derive useful expressions for cos (nx) and sin (nx) in terms of cos x and sin x. Furthermore, one can use a generalization of this formula to find explicit expressions for the nth roots of unity, that is, complex numbers z such that zn = 1.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-21430503614867590942011-05-17T14:38:00.000+02:002013-01-12T22:33:05.332+01:00Legendre's differential equation<div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-zVEnaBqQBLQ/UOap1TFqp-I/AAAAAAAAJdo/GIi4GSeqhb8/s1600/formula5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-zVEnaBqQBLQ/UOap1TFqp-I/AAAAAAAAJdo/GIi4GSeqhb8/s1600/formula5.jpg" height="297" width="400" /></a></div><br />They are named after Adrien-Marie Legendre. This ordinary differential equation is frequently encountered in physics and other technical fields. In particular, it occurs when solving Laplace's equation (and related partial differential equations) in spherical coordinates.<br /><br />The Legendre differential equation may be solved using the standard power series method. The equation has regular singular points at x = ±1 so, in general, a series solution about the origin will only converge for |x| < 1. When n is an integer, the solution Pn(x) that is regular at x = 1 is also regular at x = −1, and the series for this solution terminates (i.e. is a polynomial).Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-80450483037034658002011-05-17T14:16:00.000+02:002013-01-12T22:33:45.034+01:00The Sophomore's dream<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-4962hs5IW2c/UOaqfrdpM7I/AAAAAAAAJd4/oWOPyZtvDo4/s1600/formula4.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-4962hs5IW2c/UOaqfrdpM7I/AAAAAAAAJd4/oWOPyZtvDo4/s1600/formula4.jpg" height="297" width="400" /></a></div><br /> In mathematics, sophomore's dream is a name occasionally used for the above given identity discovered in 1697 by Johann Bernoulli.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-47509272328881252882011-05-17T13:06:00.000+02:002013-01-12T22:34:24.520+01:00Golden ratio countinuos fraction expansion<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-ck9I1QvAYCs/UOapP-9GGQI/AAAAAAAAJdY/JYm6QP6AsUA/s1600/formula3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-ck9I1QvAYCs/UOapP-9GGQI/AAAAAAAAJdY/JYm6QP6AsUA/s1600/formula3.jpg" height="297" width="400" /></a></div><br /> From http://en.wikipedia.org:<br /><br />In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.6180339887.<br /><br />Jean-Baptiste Mondino (born Aubervilliers, France in 1949) is a French fashion photographer and music video director. He has directed music videos for Madonna, David Bowie, Sting, Björk, China Moses (Dee Dee Bridgewater's daughter) and Les Rita Mitsouko.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-68839260530261091382011-05-17T12:52:00.000+02:002013-01-12T22:35:02.501+01:00Dirac delta function<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-OOddR5tRVzw/UOb7xAsCBfI/AAAAAAAAJeU/3N1SXaPFMrU/s1600/formula-copy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-OOddR5tRVzw/UOb7xAsCBfI/AAAAAAAAJeU/3N1SXaPFMrU/s1600/formula-copy.jpg" height="297" width="400" /></a></div><br /> From a purely mathematical viewpoint, the Dirac delta is not strictly a function, because any real function that is equal to zero everywhere but a single point must have total integral zero.<br /><br />While for many purposes the Dirac delta can be manipulated as a function, formally it can be defined as a distribution that is also a measure. In many applications, the Dirac delta is regarded as a kind of limit (a weak limit) of a sequence of functions having a tall spike at the origin.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-658709821174067982011-05-17T12:30:00.000+02:002013-01-12T22:35:52.458+01:00Arcsin integral<div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-m3qNW_4NLzw/UOb8PeVtc0I/AAAAAAAAJek/FRYL5Ni5gzE/s1600/formula2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-m3qNW_4NLzw/UOb8PeVtc0I/AAAAAAAAJek/FRYL5Ni5gzE/s1600/formula2.jpg" height="297" width="400" /></a></div><br />Bring back the good old high school memories, One of my favorite hyperbolic integrals.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-49285469021159372882011-05-17T11:50:00.000+02:002013-01-12T22:36:35.128+01:00Sine function Taylor serie expansion<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-8RuWyDR74CQ/UOb92v_TB2I/AAAAAAAAJe8/ddWQwG5Ztgg/s1600/formula1.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-8RuWyDR74CQ/UOb92v_TB2I/AAAAAAAAJe8/ddWQwG5Ztgg/s1600/formula1.jpg" height="297" width="400" /></a></div><br />Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-88719232133190505332011-05-17T10:15:00.000+02:002013-01-12T22:38:03.777+01:00Euler's identity (tau notation)<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-xpmWqcdDGbo/UOamMgrFV-I/AAAAAAAAJck/3sNDOWeC5Gk/s1600/formula.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-xpmWqcdDGbo/UOamMgrFV-I/AAAAAAAAJck/3sNDOWeC5Gk/s1600/formula.jpg" height="297" width="400" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">Euler formula in Tau notation</td></tr></tbody></table><br /> One of the most astounding formula ever discovered, setting the foundation of complex mathematical analysis, here presented in tau (turns) notation and displaying, in my opinion, the five most important numbers in the history of mathematics.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-33629485671404478662011-02-22T00:14:00.000+01:002013-01-04T21:22:16.025+01:00God is symmetryPerfect symmetries are uncommon in nature. Though, through repetition and the everaging process of our mind, we all develop an instinctive notion of what a perfect symmetry is. When this is embodied in a person, it is at the same time real and unnatural, appealing and revolting. <br/><br/>A truly disturbing and yet intriguing experience for the viewer. The veneration of beauty, long from being a primitive cult, is a wonderful path to get to the essence of things.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-63495739280345670742011-02-11T17:11:00.000+01:002013-01-04T21:22:16.042+01:00There is always room for improvementAiming for perfection in many cases means to invest increasingly more for steadily smaller returns. What usually distinguishes business men from mathematicians is that the first ones eventually stop and collect the rewards, sometimes regretting the limits of their solution, while the second ones obtain true perfection but usually in infinite time. Which approach would you follow?Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-55064085163840114082011-01-07T18:23:00.000+01:002013-01-04T21:22:16.038+01:00Are exponential schemes applicable in real world scenarios?Today, many of the models we are confronted with have an exponential growth nature. Starting from the explosion in communication, to the computing power of microchips, from power grids to ponzi schemes, the world seems to be driven by a constant acceleration. How far can we push the exponential paradigm in our lives and in actual real-world models (economy, transportation, communication, relations, information, production, etc) ?Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.comtag:blogger.com,1999:blog-1460523364303800459.post-32845469841945833452011-01-07T10:14:00.000+01:002013-01-03T18:58:59.435+01:00Best wishesBurning logs, bubbles wiggle up,<br/>The night is dark, our hearts shine.Nat Busahttp://www.blogger.com/profile/11325862903778963438noreply@blogger.com