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1. math/0010302 Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings
- arxiv.org
- From: Catherine Yan view email Date (v1): Mon, 30 Oct 2000 17:25:58 GMT (27kb) Date (revised v2): Wed, 24 Jan 2001 20:40:16 GMT (28kb) Date (revised v3): Wed, 16 Jun 2004 16:32:52 GMT (106kb) Date (revised v4): Thu, 15 Jul 2004 16:10:05 GMT (107kb) Date (revised v5): Fri, 11 Mar 2005 17:34:27 GMT (107kb) Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings.
- The second in a series on Apollonian circle packings beginning with math. ... More revision in July, 2004: interchange sections 7 and 8, revised sections 1 and 2 to match, and added matrix formulations for super-Apollonian group and its Lorentz version. Slight revision in March 10, 2005 Subj-class: Metric Geometry; Group Theory; Number Theory Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. ... It observed there exist infinitely many types of integral Apollonian packings in which all circles had integer curvatures, with the integral structure being related to the integral nature of the Apollonian group. Here we consider the action of a larger discrete group, the super-Apollonian group, also having an integral structure, whose orbits describe the Descartes quadruples of a geometric object we call a super-packing. ... Certain Apollonian packings and super-packings are strongly integral in the sense that the curvatures of all circles are integral and the curvature$\times$centers of all circles are integral. We show that (up to scale) there are exactly 8 different (geometric) strongly integral super-packings, and that each contains a copy of every integral Apollonian circle packing (also up to scale). We show that the super-Apollonian group has finite volume in the group of all automorphisms of the parameter space of Descartes configurations, which is isomorphic to the Lorentz group $O(3, 1)$. ...
2. Archetypal Guitar Lessons
- guitarhistory.us
- Apollonian Guitar Lessons .
- Apollonian Guide.
- What is an Apollonian?.
- Apollonian creativity, form, and lyricism can be found in the music of Bach, Haydn, Mozart, and Hindemith. ... Edgar Myers, Bryan Johanson, John Williams (the composer), and Pat Metheny have Apollonian characteristics, apparent in their appreciation of form and structure, though each of them displays many Dionysian characteristics as well. ...
- Pat Metheny is probably the best example of an Apollonian out of the list, yet least obviously so because he is by reputation an improviser, a characteristic that, while generally Dionysian, is not contrary to Apollonian ideals. ... Metheny is a perfect example of what every Apollonian musician should strive for; to be without classification while remaining stable and consistent. Apollonian culture loves this kind of duality, which is why Pat Metheny is an Apollonian rather than a Dionysian. ...
- Any tool is good enough for an Apollonian if it gets the job done. ...
- The Apollonian musician is focused on developing skill and cunning, and also eventually being a pillar of society or knowledge. Vision and creativity are very important to both Dionysian and Apollonian, but the way they go about developing and expressing their creativity are philosophically different. ... The distinction here is that Apollonian music is purposeful and expressive, where as Dionysian music is thick with mood and expression. A powerful Dionysian might tackle an obstacle by directly and aggressively because of an urge but a skilled Apollonian will achieve his goal quickly, almost indifferently, with precision and meticulous intention.
3. Apollonian Yeasayers
- www.syc427.org
- Apollonian Yeasayers .
- Apollonian Yeasayers (along with Team Endeavor) is proud to be involved in our annual Food Drive to benefit local families. ...
- Apollonian Yeasayers and Endeavor will highlight the core value of respect during the month of September. ...
4. Apollonian Vs Dionysian (WebSeitz/wikilog)
- webseitz.fluxent.com
- Apollonian Vs Dionysian .
- Kara Long and Thomas Valeo gloss the Apollonian and Dionysian drives: The Apollonian drive, according to Nietzche, strives to find order in a confused, chaotic, and cruel world. ...
5. Garden Of Shadows lyrics - Garden Of Shadows Apollonian Realm lyrics
- www.musicsonglyrics.com
- Garden Of Shadows Apollonian Realm lyrics.
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6. Fibonacci-Like Sequences of Apollonian Circle Packings
- www.nmt.edu
- 3501 Clean Clean MicrosoftInternetExplorer4 Fibonacci-Like Sequences of Apollonian Circle Packings.
- We consider an Apollonian Circle packing of the unit circle and illustrate a novel way to number the circles in the packing. ...
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7. The BIrth of Tragedy
- stjohns-chs.org
- We shall do a great deal for the science of aesthetics, once we perceive not merely by logical inference, but with the immediate certainty of intuition, that the continuous development of art is bound up with the Apollonian and Dionysian duality: just as procreation depends on the duality of the sexes, involving perpetual strife with only periodically intervening reconciliations. The terms Dionysian and Apollonian we borrow from the Greeks, who disclose to the discerning mind the profound mysteries of their view of art, not, to be sure, in concepts, but in the impressively clear figures of their gods. Through Apollo and Dionysus, the two art-deities of the Greeks, we come to recognize that in the Greek world there existed a sharp opposition, in origin and aims, between the Apollonian art of sculpture, and the non-plastic, Dionysian, art of music. These two distinct tendencies run parallel to each other, for the most part openly at variance; and they continually incite each other to new and more powerful births, which perpetuate an antagonism, only superficially reconciled by the common term "Art"; till at last, by a metaphysical miracle of the Hellenic will, they appear coupled with each other, and through this coupling eventually generate the art-product, equally Dionysian and Apollonian, of Attic tragedy.
- These physiological phenomena present a contrast analogous to that existing between the Apollonian and the Dionysian. ...
- Thus far we have considered the Apollonian and its antithesis, the Dionysian, as artistic energies which burst forth from nature herself, without the mediation of the human artist; energies in which nature's art impulses are satisfied in the most immediate and direct way: first, on the one hand, in the pictorial world of dreams, whose completeness is not dependent upon the intellectual attitude or the artistic culture of any single being; and, on the other hand, as drunken reality, which likewise does not heed the single unit, but even seeks to destroy the individual and redeem him by a mystic feeling of Oneness. With reference to these immediate art-states of nature, every artist is an "imitator," that is to say, either an Apollonian artist in dreams, or a Dionysian artist in ecstasies, or finally--as for example in Greek tragedy--at once artist in both dreams and ecstasies: so we may perhaps picture him sinking down in his Dionysian drunkenness and mystical self-abnegation, alone, and apart from the singing revelers, and we may imagine how now, through Apollonian dream-inspiration, his own state, i. ...
- Perhaps we may picture the process to ourselves somewhat as follows: out of the original Titan thearchy of terror the Olympian thearchy of joy gradually evolved through the Apollonian impulse towards beauty, just as roses bud from thorny bushes. ... At the Apollonian stage of development, the "will" longs so vehemently for this existence, the Homeric man feels himself so completely at one with it, that lamentation itself becomes a song of praise.
- Wherever we meet with the "naive" in art, we recognize the highest effect of the Apollonian culture, which in the first place has always to overthrow some Titanic empire and slay monsters, and which, through its potent dazzling representations and its pleasurable illusions, must have triumphed over a terrible depth of world-contemplation and a most keen sensitivity to suffering. But how seldom do we attain to the naive--that complete absorption in the beauty of appearance ! And hence how inexpressibly sublime is Homer, who, as individual being, bears the same relation to this Apollonian folk-culture as the individual dream-artist does to the dream faculty of the people and of nature in general. The Homeric "naivety" can be understood only as the complete victory of the Apollonian illusion: an illusion similar to those which Nature so frequently employs to achieve her own ends. ...
8. Nancy A. Taylor, Apollonian vs. Dionysian Lecture
- www.csun.edu
- "Apollonian Vs. ...
- By analyzing Dionysian & Apollonian aspects, we gain insight into who we are and how we behave in this world:.
- We forge into the discovery of ourselves, by better understanding ourselves with the help of the Apollonian and Dionysian chapter.
- German philosopher who defined the terms Apollonian and Dionysian: .
- APOLLONIAN.
9. The Similarties Between Nietzsche and Freud on Personality :: Essay Sample. Free term papers for college students
- www.essaysample.com
- This battle involves the two most basic parts of society, the artistic Dionysian and the intelligent Apollonian. ... Thus it is the object of this paper to prove that the Freudian theory about the unconscious id, and ego are analogous to the idea on the Apollonian and Dionysian duality's presented by Nietzsche. ...
- In this book he introduced his famous distinction between the Apollonian, or rational, element in human nature and the Dionysian, or passionate, element, as exemplified in the Greek gods Apollo and Dionysus. ...
- "Much will have been gained for esthetics once we have succeeded in apprehending directly-rather than merely ascertaining- that art owes its continuous evolution to the Apollonian-Dionysiac duality," proposes Nietzsche, "even as the propagation of the species depends on the duality of the sexes, their constant conflicts and periodic acts of reconciliation," (AD in Jacobus, 550). It is by these two, "art-sponsoring deities," (AD, in Jacobus, 550), Apollo and his brethren Dionysos, the we come to grasp the idea of that splinter between the, "plastic Apollonian arts and the non-visual art of music inspired by Dionysos," (AD, in Jacobus, 550). ...
- The experience of the Dionysiac is compartiavly different from that of the Apollonian. ... By creating the art-loving Dionysian, he Nietzsche has also created the equal but opposite Apollonian. ...
- The Dionysian, the opposite of the Apollonian would then be considered his twin brother, cut from the same womb, but yet different in personality and equally independent. ...
- The Apollonian, ". ... music had long been familiar to the Greeks as an Apollonian art , as a regular beat like that of waves lapping the shore, a plastic rhythm expressly developed for the portrayal of Apollonian conditions," (AD, in Jacobus, 556). That "plastic rhythm" described by Nietzsche is the cardinal groundwork for the theory of the Apollonian. Apollonian people are those who are totally based in the scientific world. ... Most great scientists for instance are both Apollonian and Dionysian. They are mainly Apollinistic, due to the fact that they are clearly intelligent, which according to Nietzsche is the foundation for Apollonian thought, but they are also Dionysian. ... He is probably one of the most intelligent (and thus Apollonian) thinkers .
10. Arrogance and Ignorance
- www.vanguardnewsnetwork.com
- Every time I read something written by Apollonian I don't know whether to laugh or to cry. ...
- And I quote from Apollonian's latest drivel:.
- Does Apollonian understand that via the economic barter system and the printing of the Reichsmark that the National Socialists under Hitler had dealt the International Jewish Bankers a crushing defeat? The Jews lost their stranglehold of financial power over the Germans who had, as Dr. ...
- What Apollonian means is the same thing as preached by those Jews advocating World Kikedom, or the New World Order if you prefer. ... When in "reality," a word that Apollonian uses but doesn't appear to understand, the people who were played by the Jews were Britain and the U. ... There is so much evidence of this that it needs no faith or belief system as Apollonian must concoct. The lies that Jewish agents of the NWO promote are being adopted by Apollonian and he claims that Herr Linder and I are the ones being fooled. ...
- Another quote from Apollonian: .
- If Apollonian really believes that if a local government, say the City of Los Angeles, went WFP and started kicking out Jews, Blacks, Spics, Queers, Communists, et al, that ZOG would leave that city alone, then he's living in a cardboard box under a bridge. ... Apollonian, with his anti-Fed stance is a threat to no one, but simply causes confusion among some WNs. ...
- Has Apollonian ever gotten out of his house? Has he been part of any political activities or demonstrations? I doubt it. ...
- Sorry to inform you Apollonian, but America's Founding Fathers were more inspired by Plato, Adam Smith, and John Locke than by Jesus. ...
- Apollonian thinks only he has the keys, and that Herr Linder, myself and countless others, are being mislead or falling for something which is Jewish, but in reality, he is the one that falls for Jewish propaganda. ...
11. Review: Egypt
- gate.cia.edu
- Egypt can be understood as a culture which achieved a remarkable synthesis of the chthonian and Apollonian qualities, giving it a balance (MAAT) of unusual stability and enabling the culture to endure longer than any other so far (for 3,000 years or so!).
- That is, even Death forms a cycle which includes Life, the Apollonian aboveworld. Again, Ra, the sun God (who might be assumed to be entirely light- filled and Apollonian in nature) passes through the underworld each night himself (a chthonian motif), on his way to rebirth each morning. And one of the favorite Egyptian Gods is the scarab beetle (Figure 10), a creature who forms dung into little balls and rolls them in and out of holes in the ground (all earthy chthonian motifs!) But as a God he represents instead that crucial rebirth of the sun as he pushes its disk/ball out of the underworld each morning (that is, Apollonian ascent to the sky). ...
- But however chthonian these concepts may seem, they are often rendered in Egyptian art with a precision and crispness which is positively Apollonian in feeling. ... ) One of the greatnesses of Egyptian art is in its flat surfaces (pylon walls, tomb walls) in architecture covered with sharp, clear, linear bas-reliefs, another is in long (linear) narrative scrolls unwinding in exquisite line drawings (all Apollonian qualities) the progress of the soul after Death (chthonian theme!). ... (All of these qualities are Apollonian. ...
- Even here a subtle mix of chthonian and Apollonian qualities can be detected: each part of the body is seen from its own best or clearest (Apollonian) angle (head profile, eyes frontal, chest frontal, arms profile, etc. ...
12. Psychology History Timeline
- psych.athabascau.ca
- Apollonian aspect of human nature.
- Friedrich Nietzsche (1844-1900) believed there are two sides to human nature: the Apollonian (rational) aspect, characterized by tranquility, orderliness, and predictability; and Dionysian (irrational) aspect, characterized by creative chaos, passion, and change. ... For example, he referred to the animalistic urges of the Dionysian aspect as the id; the Apollonian aspect was said to sublimate those urges into works of art; and when the urges became too strong, the Apollonian aspect repressed them.
- Dionysian and Apollonian On-line Available: http://www. ...
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