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Topic: Three Spheres II

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	Three Spheres II
		Escher was particularly intrigued by reflections and by the concept of a sphere acting as a mirror.
		All three spheres are reflected in the polished surface on which they rest.
		The spheres at right and left are reflected in the center sphere.
	www.nga.gov /collection/gallery/ggescher/ggescher-53944.0.html (133 words)

	Preparation of vinyl ester resin polymer spheres - Patent 4348309
		Spheres were prepared from a recipe consisting of 15 pounds (6.8 kilograms) water, 85.1 grams of a 20 percent aqueous solution of Vinol 523, polyvinyl alcohol, 15 pounds (6.8 kilograms) of Derakane.RTM.
		Spheres were produced having diameters in the range of 0.5 to 22 microns with an average of 2 microns.
		Spheres were obtained with diameters in the range of 0.5 to 10 microns with an average of 2 microns.
	www.freepatentsonline.com /4348309.html (2180 words)

	The Identity of Indiscernibles (Stanford Encyclopedia of Philosophy)
		In that case the Principle is consistent with a universe in which there are three qualitatively identical spheres A, B, and C where B and C are 3 units apart, C and A are 4 units apart and A and B are 5 units apart.
		Consider, for instance, a perfectly symmetrical universe consisting solely of three qualitatively identical spheres, A, B and C, each of which is the same distance, 2 units, away from the others.
		The upshot is that it is not merely the two spheres we took to be indistinguishable that are said to be identical but all three, including the middle one which seemed clearly distinguished from the other two by means of a pure relational property.
	plato.stanford.edu /entries/identity-indiscernible (2750 words)

	NASA - Exploration Systems - Synchronized Position Hold, Engage, Reorient, Experimental Satellites (SPHERES)
		SPHERES consists of three self-contained satellites, which are 18 sided polyhedrons that are 0.2 meter in diameter and weigh 3.5 kilograms.
		SPHERES test sessions begun during Expedition 13, demonstrated maneuvers that would lead to the docking of a satellite to a beacon, tested algorithms which automatically determine the mass properties of the satellites and performed initial two sphere satellite tests.
		Other SPHERES test sessions performed during Expedition 13 demonstrated the functionality of the Global Metrology System (during all previous sessions the satellites calculated their position with respect to a single beacon or with respect to other satellites, but not with respect to the U.S. Laboratory frame).
	exploration.nasa.gov /programs/station/SPHERES.html (1587 words)

	Three Spheres II - Definition, explanation
		Three Spheres II is a lithograph print by the Dutch artist M.
		The sphere on the left is transparent with a photorealistic depiction of the refracted light cast through it onto the flat surface.
		In the reflection you can clearly see the image of the three spheres on the paper Escher is drawing on and in the center sphere of that image one can vaguely make out the reflection of Escher’s studio.
	www.calsky.com /lexikon/en/txt/t/th/three_spheres_ii.php (163 words)

	World of Escher Gallery - Three Spheres II, 1946 (Site not responding. Last check: 2007-09-04)
		Three spheres, of equal size but different in aspect, are placed next to each other on a shiny table.
		The attributes of the middle one are the same as those described in connection with (Hand With Reflecting Sphere); the whole of the surrounding area is reflected in it.
		Furthermore it achieves, in two different ways, a triple unity, for not only does it reflect its companions to the left and right, but all three of them are shown in the drawing on which the artist is working.
	www.worldofescher.com /gallery/A58.html?learn (175 words)

	Art:21 . Louise Bourgeois' "Cell (Glass Spheres and Hands)" \| PBS
		With hands clasped in a gesture of prayer, the isolated arms appear to be soft and vulnerable in spite of their rock-hard substance.
		Encircling the table are five glass spheres of different sizes, each resting on its own worn chair.
		The chairs and spheres face the table in a united front, cornering and further isolating the hands.
	www.pbs.org /art21/artists/bourgeois/card1.html (406 words)

	Three circles and common tangents
		Now consider their common tangent planes: these intersect in three lines A', B' and C' corresponding to the three points A, B and C in the theorem.
		Name the three circles a, b, and c, so that the common tangents of a and b meet at C, those of a and c at B, and those of b and c at A. We assign each circle a mass
		Of the three circles, either all have the same orientation or the orientation of one differs from that of the other two.
	www.cut-the-knot.org /proofs/threecircles.shtml (969 words)

	TextureLecture/018 - cs348b-06 (Site not responding. Last check: 2007-09-04)
		The image of 3 sphere balls above is called "Three Spheres II".
		Left to right, the spheres are made of: 1) Glass, filled with water (which is why it is transparent and also reflects light) 2) Mirror coating 3) A diffuse / matt material.
		Notice that the middle sphere reflects both of the spheres to its sides.
	graphics.stanford.edu /cs348b-06/TextureLecture/018 (85 words)

	Three Spheres II - Wikipedia, the free encyclopedia
		Three Spheres II is a lithograph print by the Dutch artist M.
		The sphere on the left is transparent with a photorealistic depiction of the refracted light cast through it onto the flat surface.
		In the reflection you can clearly see the image of the three spheres on the paper Escher is drawing on and in the center sphere of that image one can vaguely make out the reflection of Escher’s studio.
	en.wikipedia.org /wiki/Three_Spheres_II (194 words)

	Prophecy Being Fulfilled? The World Divides Into Three Spheres > The Good News : March/April 2003 (Site not responding. Last check: 2007-09-04)
		Of the three, this force is the youngest.
		But the lines of delineation between the three competing spheres are there nonetheless, becoming clearer as the three systems confront each other over Iraq.
		Before World War II the British Empire was the dominant force in the world and had been for two centuries.
	www.gnmagazine.org /issues/gn45/prophecy.htm (2541 words)

	Escher Posters Page 4 (Site not responding. Last check: 2007-09-04)
		"Hand with Reflecting Sphere" shows a self portrait of Escher in a mirrored sphere which he is holding.
		"Balcony" shows a coastal scene in which the middle appears to bulge out, as if a sphere were bein pushed into a sheet of rubber.
		"Three Spheres II" depicts three spheres - one made of glass and half full of water, one mirrored, and one solid and unreflective.
	www.mathartfun.com /shopsite_sc/store/html/EscherPosters4.html (257 words)

	Guide for the Perplexed
		But this is not the case: for the science of astronomy does not aim at demonstrating them, although it includes subjects that can be proved; e.g., it has been proved that the path of the sun is inclined against the equator; this cannot be doubted.
		He will, besides, endeavour to find such an hypothesis which would require the least complicated motion and the least number of spheres; he will therefore prefer an hypothesis which would explain all the phenomena of the stars by means of three spheres to an hypothesis which would require four spheres.
		Nevertheless the species of the stars can be numbered, and therefore we would still be justified in counting the spheres of the fixed stars collectively as one, just as the five spheres of the planets, together with the numerous spheres they contain, are regarded by us as one.
	www.ccel.org /ccel/maimonides/guide.vi.xii.html?bcb=0 (875 words)

	The Music of the Spheres
		Three experiments were performed by packing marbles of different sizes.
		In the pictures below, marbles of three different sizes (Note that marbles of the same color are the same size) were packed together.
		Model II describes the situation where the outer spheres are suspended off the surface but attached to the central sphere.
	invsee.asu.edu /nmodules/Spheresmod/marbles.html (242 words)

	HALLEX II-4-1-1
		We then explain that this means that a child's impairment(s) must substantially reduce or, in the case of infants from birth to the attainment of age 1, be expected to substantially reduce his or her ability to grow, develop, or mature in an age-appropriate manner.
		Similarly, step three [the "meets/equals" step of the adult sequence] streamlines the decision process by identifying those claimants whose medical impairments are so severe that it is likely they would be found disabled regardless of their vocational background.
		In paragraph (b), "Age categories," we define the three age categories we use as guidance for assessing age-appropriate activities: newborn and young infants (birth to attainment of age 1), older infants and toddlers (age 1 to attainment of age 3), and children (age 3 to attainment of age 18).
	www.ssa.gov /OP_Home/hallex/II-04/II-4-1-1.html (14379 words)

	Packinon - pg_geo.py - makes geodesic spheres
		In Class I and II patterns the frequency value refers to the number of divisions of an edge, by balls or struts.
		The Class II pattern is equivalent to 1,1 with frequency value corresponding to half the divisions along an edge.
		For Class I and II patterns freq (default 2) is the number of divisions along an edge, for Class III patterns (and those specified by two numbers) freq is the number of times the pattern is repeated along an edge.
	packinon.sourceforge.net /py_progs/pg_geo.html (732 words)

	Buy.com - Three Spheres II by M.C. Maurits Cornelius Escher 22.25x30.25
		Buy.com - Three Spheres II by M.C. Maurits Cornelius Escher 22.25x30.25
		Three Spheres II by M.C. Maurits Cornelius Escher 22.25x30.25
		Spheres reflect one another the artist the room in which he works and the paper upon which they rest, Lithograph on natural fiber, Matte fl frame, Wipe clean with a dry cloth
	www.buy.com /prod/three-spheres-ii-by-m-c-maurits-cornelius-escher-22-25x30-25/q/loc/101/203225534.html (154 words)

	14 Spheres
		The set of points in space whose distance to a fixed point (the center) is a fixed positive number (the radius) is a sphere.
		The area of a sphere of radius r is 4
		The area of a spherical polygon (that is, of a polygon on the sphere whose sides are arcs of great circles) is
	www.geom.uiuc.edu /docs/reference/CRC-formulas/node59.html (212 words)

	Radical Theory The Four Spheres
		You can’t say a sphere of social life is determined by a basic function that has to be socially fulfilled in all societies, and then call something a sphere of social life which does not exist due to their having to be some social function.
		The reason this is true for three of the schools of thought, I think, is because feminism, anarchism, and nationalism represent an effort to understand and conceptualize the particular sphere they focus on from the perspective of the most oppressed group.
		If the kind of change in the one sphere is such that the others can accommodate to it without disrupting themselves entirely, then you can have a revolution in the first sphere and changes in the other ones and come into a stable accord with it.
	www.zmag.org /ParEcon/radth6.htm (7728 words)

	Chemical Bonding Concept/Skills Development
		In this investigation, plastic spheres are used to study the regular geometric shapes of metal and ionic crystals.
		Three types of packing in crystals will be investigated-hexagonal close packing, face-centered close packing, and body-centered packing-using equivalent spheres.
		Count the number of spheres closest the central sphere in the structure.
	www.okstate.edu /jgelder/bondpage14.html (362 words)

	Current projects by ceramic sculptor Daniel Oberti
		In 1998, I was invited to speak at the University of Arizona Astronomy Department with a focus on Art and Astronomy.
		I was invited to present my works at INSAP II, The Inspiration of Astronomical Phenomena Conference, held in Malta in January of 1999.
		In September of 1999, I was invited by her to make a presentation of my works and lecture with the “Spheres of Influence” slide show at the Onsala Space Observatory in Sweden.
	www.danieloberti.com /current_ic.html (568 words)

	Optical Illusions Etc: free, scary, word & picture optical illusions
		Escher, however, who had been very fond of and inspired by the landscape in Italy, was decidedly unhappy in Switzerland, so two years later, in 1937, the family moved again, this time to Ukkel, a small town near Brussels, Belgium.
		World War II forced them to move for the last time in January 1941, this time to Baarn, the Netherlands, where Escher lived until 1970.
		Most of Escher's better-known pictures date from this period; the (sometimes) cloudy, cold, wet weather of the Netherlands allowed him to focus entirely on his works, and only in 1962, when he had to undergo surgery, was there a time when no new images were created.
	illusionsetc.blogspot.com /2004_05_01_illusionsetc_archive.html (1711 words)

	Ximaxian Levels (and stuff on the Spheres too)
		I see all Ximaxian magic as being a variation of one of three techniques of manipulating car'all, which are known as the three Spheres.
		Sphere 1 causes the element's properties to become more strongly/weakly expressed, by directly strengthening or weakening the xeua links connected to ounia of that element.
		This is by far the most powerful sphere, since it can be used to cast what are essentially augmented forms of Sphere 1 and 2 spells as well.
	www.santharia.com /dev/index.php?topic=10705.0 (3184 words)

	The Medici. Piero di Cosimo de' Medici and St. Peter Martyr. The Medici and Renaissance art.
		Pope Pius II himself had been a follower of the anti-pope elected by the Council of Basel and was brought back into the orthodox Catholic fold only in 1445.
		Heresy was still seen to be a problem by Antoninus, archbishop of Florence, who prosecuted one Giovanni del Cane of Montecatini in 1450 for the crime and passed him to the secular authorities for burning.
		The Medici had little or no involvement in the Santa Maria Novella quarter; its churches were dominated by old patrician families, many of whom, such as the Strozzi and Rucellai were hostile to or suspicious of the new regime.
	www.threemonkeysonline.com /article3.php?id=326 (3954 words)

	Three Spheres Subsector F (Site not responding. Last check: 2007-09-04)
		Due to the confluence of the Solomani Confederation, the Hive Federation and the Independent systems, this subsector bears the name Three Spheres.
		These special administrative centers, the other two in the sector are Pihras (2621) and Damol II (1831), are indicated by the "Fd" designations in the notes of their data entries.
		The Three Spheres Subsector contains 26 systems with a known population of 21.626 billion sapients.
	home.earthlink.net /~ngc5139/FDA/Spica-ssF.html (550 words)

	Minimal containing sphere for a set of spheres? - GameDev.Net Discussion Forums
		Basically, given a set of spheres defined by their centers and radii, determine the center and radius of the minimal volume sphere that completely contains all of these spheres.
		I was originally doing this because I wanted to figure out the bounding sphere for a model, given the bounding spheres of all its submeshes.
		Posted - 10/19/2006 6:20:18 AM One solution might be to find the enclosing sphere for all midpoints of the spheres (by finding the longest distance between to sphere midpoints) and then intersect all the spheres with the enclosing sphere.
	www.gamedev.net /community/forums/topic.asp?topic_id=420056 (502 words)

	Science Fiction Cool Stuff
		Three million years from now, the last man left alive and his holographic friend laugh it up across the galaxy
		Three million years later, Lister is released from stasis to find he's absolutely alone.
		The Starbug is made from three spheres and, as its name implies, resembles a fat, round bug.
	www.scifi.com /sfw/issue420/cool.html (807 words)

	Ed Driscoll.com: Reagan, Solzhenitsyn and John Paul II
		With Reagan and Solzhenitsyn, John Paul II represents the three forces of opposition to communism that shattered the evil empire, the Soviet Union --the American-led West, the Eastern European resistance, and the Russian dissident movement.
		John Paul II has loved God, but he has also loved human beings and regarded each human being as sacred and imbued with innate dignity, and above all deserving of freedom.
		It was John Paul II's instinctive and sustained support for the Polish trade union movement, Solidarity, and its exuberant and brave leader, Lech Walesa, that was critical in leading to the downfall of communism in Poland.
	eddriscoll.com /archives/006922.php (698 words)

	Ibn 'Arabi and the Mystical Journey
		James Morris notes that Ibn ‘Arabi prefers the term "night journey" (isra) to that of "ascension" (mi'raj) for three reasons: (a) The phrase "night journey or voyage" is not limited to ascent alone but includes equally ascent (from creation to God) and return (from God to creation).
		The first three levels (mineral, vegetal, and animal) are reminiscent of a poem of Rumi where he speaks of the mineral dying and coming to live as a plant, the plant dying and coming to live as an animal, the animal dying and coming to live as a human.
		The first three spheres are, in my view, first sketches of faith, hope and love.
	www.unc.edu /depts/sufilit/AL-ARABI.htm (7146 words)

	Thursday
		Notice that the source of light for the composition may be guessed, for the bright window above and to the left of the viewer is reflected in the sphere.
		His woodcut Three Intersecting Planes is a good place to begin a review of these works, for it exemplifies the artist's concern with the dimensionality of space, and with the mind's ability to discern three-dimensionality in a two-dimensional representation.
		The spheres relfect one another, the artist, the room in which he works, and the paper upon which he draws the spheres.
	www.ihm-ky.org /ArtsWeek/Thursday2006.htm (5747 words)

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