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Topic: Apollonian gasket


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In the News (Thu 23 May 19)

  
  Apollonian gasket - Wikipedia, the free encyclopedia
In mathematics, an Apollonian gasket or Apollonian net is a fractal generated from three circles, any two of which are tangent to one another.
An Apollonian gasket can also be constructed by replacing one of the generating circles by a straight line, which can be regarded as a circle passing through the point at infinity.
The Apollonian gasket is the limit set of a group of Möbius transformations known as a Kleinian group.
en.wikipedia.org /wiki/Apollonian_gasket   (650 words)

  
 Gasket - Wikipedia, the free encyclopedia
A gasket is a mechanical seal that serves to fill the space between two objects, generally to prevent leakage between the two objects while under compression.
Gaskets are commonly produced by cutting from sheet materials, such as gasket paper, rubber, silicone, metal, felt, fiberglass, or a plastic polymer.
One of the more desirable properties of an effective gasket in industrial applications for compressed fiber gasket material is the ability to withstand high compressive loads.
en.wikipedia.org /wiki/Gasket   (291 words)

  
 Apollonian Gasket
By analogy, it is called the Apollonian gasket, due to the obvious association with Apollonius' circles.
The Apollonian gasket is an example (the Mandelbrot set is another one) of a fractal that is not self-similar.
It is impossible therefore in its case to substitute the similarity dimension for the fractal dimension.
www.cut-the-knot.org /Curriculum/Geometry/ApollonianGasket.shtml   (220 words)

  
 Gasket - Biocrawler   (Site not responding. Last check: 2007-10-14)
For fractals, see Apollonian gasket and Sierpinski gasket.
Most industrial gasket applications involve bolts exerting compression well into the 2,000 psi range or higher.
You can find it there under the keyword Gasket (http://en.wikipedia.org/wiki/Gasket)The list of previous authors is available here: version history (http://en.wikipedia.org/w/index.php?title=Gasketandaction=history).
www.biocrawler.com /encyclopedia/Gasket   (334 words)

  
 Gasket Encyclopedia   (Site not responding. Last check: 2007-10-14)
In sailing, gaskets are lengths of rope or fabric used to hold a stowed sail in place.
Gaskets should never be left dangling, however, so when the sail is set they are brought around underneath the yard and up the back of it and then tied to the jackstay (metal rod) where they originated.
Gaskets should be tied with a slippery hitch to enable them to be let off quickly, though if the yard is large there may only be enough rope to form a clove hitch when the gasket is brought round it.
united.states.football.league.en.ogarnij.info /en/gasket   (10802 words)

  
 Apollonian gasket: Encyclopedia topic   (Site not responding. Last check: 2007-10-14)
It is named after Greek (Greek: A native or inhabitant of Greece) mathematician (mathematician: A person skilled in mathematics) Apollonius of Perga (Apollonius of Perga: apollonius of perga or perge (c....
In a sense, there is therefore only one Apollonian gasket, which can be thought of a tessellation (tessellation: The act of adorning with mosaic) of the hyperbolic plane by circles and hyperbolic triangles.
The Apollonian gasket is the limit set of a group of Möbius transformations known as a Kleinian group (Kleinian group: in mathematics, a kleinian group is a finitely generated discrete group γ of...
www.absoluteastronomy.com /reference/apollonian_gasket   (711 words)

  
 iqexpand.com   (Site not responding. Last check: 2007-10-14)
It is usually desirable that the gasket be made from a compressible or slightly compressible material such that it tightly fills the space it is designed for.
One of the more tried and tested is: "The more compressive load exerted on the gasket, the longer it will last." There are several ways to measure a gasket materials ability to withstand compressive loading.
Elastic Gasket is one of the most clever hacks IÂ’ve see in a long, long time.
gasket.iqexpand.com /index.php?title=Categories&article=Gasket   (441 words)

  
 The Geomblog: On Apollonian supergaskets, or how I always wanted to use 'syzygy' in a sentence.   (Site not responding. Last check: 2007-10-14)
One operation we have already seen: if we consider the two solutions to the 3-circle Apollonian problem, they invert to each other with respect to a fixed circle.
The mod 2 bend groups are symmetric with different axes of symmetry, and all outer circles having the same bends form symmetric patterns in the supergasket.
Apollonian circle problems were discussed in Sangaku (Japanese Temple Geometry) that I had talked about earlier.
geomblog.blogspot.com /2004/06/on-apollonian-supergaskets-or-how-i.html   (595 words)

  
 gasket   (Site not responding. Last check: 2007-10-14)
AutoblogGM to handle widespread intake manifold gasket problem on case-by...Autoblog, CA - 7 hours agoThe issue is the intake manifold gasket in some GM vehicles.
Intake gasket leak on GM engine a serious matterToronto Star, Canada - 23 hours agoAt the last service in October 2005, my GM dealership said the intake gasket was leaking coolant.
France pop a gasket in Pau as Tursunov takes Russia into semi...Guardian Unlimited, UK - Apr 9, 2006Dmitry Tursunov beat the teenager Richard Gasquet 6-1, 3-6, 6-7, 6-3, 7-5 in Pau yesterday to earn Russia a place in the Davis Cup semi-finals.
www.33beat.com /gasket.html   (341 words)

  
 Apollony fractal
The Apollonian gasket is usually the name given to the form that results from the same process described above but with an outer Soddy circle around the three circles above.
The following is the gasket above with the circles drawn as spheres and the outer sphere and three initial spheres removed.
Note the spheres are shaded with a red to blue colour ramp depending on their radius except for the 4 tetrahedral spheres that are grey.
astronomy.swin.edu.au /~pbourke/fractals/apollony   (496 words)

  
 Pressure Cooker Gasket -- Recommendations and Resources   (Site not responding. Last check: 2007-10-14)
Pressure Cooker mixes ska, rocksteady, and reggae with elements of jazz, calypso, and latin music creating a unique sound while still maintaining the traditional jamaican styles.
5 # Latte, Dr. Jorge and Rossi, Claudio: ''High Temperature Behavior of Compressed Fiber Gasket Materials, and an Alternative Approach to the Prediction of Gasket Life'', FSA presented Paper, 1995, pg.
Apollonius discovered that there are two other circles, ''C''4 and ''C''5, which have the property that they are tangent to all three of the original circles - these are called ''Apollonian circles'' (see Descartes' theorem).
www.becomingapediatrician.com /health/120/pressure-cooker-gasket.html   (711 words)

  
 Gasket: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-14)
A gasket is a mechanical seal[for more facts and a summary of this subject, click this link] that serves to fill the space between two objects, Exception Handler: No article summary found.
Gaskets are commonly produced by cutting from sheet materials, Exception Handler: No article summary found.
It is usually desirable that the gasket be made from a compressible or slightly compressible material such that it tightly fills the space it is designed for, Exception Handler: No article summary found.
www.absoluteastronomy.com /ref/gasket   (827 words)

  
 id:A090551 - OEIS Search Results   (Site not responding. Last check: 2007-10-14)
Decimal expansion of the real number quantifying the area of the Apollonian gasket of three congruent circles of radius 1.
The closed form for the area of this Apollonian gasket is 3^(1/2) - (pi/2).
General solution: This constant is the ratio of r^2, where r is the radius of three congruent circles forming a Apollonian gasket, to the area of that Apollonian gasket.
www.research.att.com:9000 /~njas/sequences/A090551   (127 words)

  
 [No title]   (Site not responding. Last check: 2007-10-14)
The fractal is implicitly contained within a modified version of the "Apollonian gasket" generated by a distribution of hexagons shown in Fig.
The hexagonal version of the Apollonian gasket is meant as an approximation for a model structure generated in a neuronal substrate coping with fractality as well as coherence.
The two downscaling pathways merge to the same coherent structure with a fractal imprint indicated by a hexagonal tiling according to a modification of the Apollonian gasket (B).
cogprints.org /79/00/struc2.htm   (6435 words)

  
 Gasket, industrial gasket, hoosier gasket   (Site not responding. Last check: 2007-10-14)
Gasket how much to repair a leaking head gasket 1997 grand caravan - Q&A, industrial gasket, hoosier gasket..
Imagine that you have made a Sierpinski Gasket by beginning with a large white triangle and gluing smaller...
In many joints the bolt spacing is dictated by the gasket pressure mid-way between bolts.
www.commercialfaq.com /gasket.html   (309 words)

  
 Tangencies: Apollonian Circles   (Site not responding. Last check: 2007-10-14)
These green lines cut their circles in two more points, which are the points of tangency of the Apollonian circles.
Once these three points on each Apollonian circle are known, the circles themselves are easily constructed.
The result of this iteration is called the Apollonian gasket.
www.ics.uci.edu /~eppstein/junkyard/tangencies/apollonian.html   (413 words)

  
 Gasket - Gasket   (Site not responding. Last check: 2007-10-14)
The issue is the intake manifold gasket in some GM vehicles.
Only trouble is that I blew a head gasket on my bike so it's out of commission for almost a good week.
The Sierpinski Gasket is similar, but opposite in the sense that you remove things rather than add them.
fast-cash.fact-about.be /Biodiesel/Gasket   (565 words)

  
 Gasket - Don't Blow A Gasket   (Site not responding. Last check: 2007-10-14)
Infinity and the Area of a Sierpinski Gasket.
Gasket Industries, one of the leading manufacturers and exporters of A spiral wound gasket is manufactured by spirally winding a preformed metal strip
There are also other gasket applications where temperature plays a role.
hxof.com /?q=gasket   (308 words)

  
 [No title]   (Site not responding. Last check: 2007-10-14)
I shall discuss the harmonic analysis on three examples of fractal sets: Sierpin\'nski gasket, Apollonian gasket and Farey series.
It turns out that such non-commutative system can be used to write explicitly harmonic functions on the Sierpin\'nski gasket and general terms of the Farey series.
These problems were the subject of my SYM = Seminar for Young Mathematicians which I run last year at Penn.
www.math.wisc.edu /~xxchen/abstracts/kirillov.html   (157 words)

  
 Fix it Up   (Site not responding. Last check: 2007-10-14)
Gaskets and Seals - Garlock Gasket com High Temper...
Gaskets and Seals - Garage Door Seals Overhead doo...
Gaskets and Seals - Garage Door Seal Broten Garage...
fixrup.blogspot.com /2005/07/gaskets-and-seals-gasket-learn-how-to.html   (335 words)

  
 Andart: November 2005 Archives   (Site not responding. Last check: 2007-10-14)
As K is changed the inversions may cause them to be mapped across each other, producing messier attractor setss.
Here I'm not sure whether they correspond to an union of gaskets or form a dense set (that does not correspond to a discrete group).
When K approaches 1/sqrt(3) the attractor definitely seems to become a dense covering of the sphere meeting the other spheres othogonally.
www.aleph.se /andart/archives/2005/11   (2428 words)

  
 The Geometry Junkyard: 2D Geometry   (Site not responding. Last check: 2007-10-14)
Apollonian Gasket, a fractal circle packing formed by packing smaller circles into each triangular gap formed by three larger circles.
Dearing provides formulae for the radii of Apollonian circles, and analogous three-dimensional problems.
Thrackles are graphs embedded as a set of curves in the plane that cross each other exactly once; Conway has conjectured that an n-vertex thrackle has at most n edges.
www.cecs.uci.edu /~eppstein/junkyard/2d.html   (5405 words)

  
 [No title]   (Site not responding. Last check: 2007-10-14)
Subject: Re: Most Dense Sphere Package Date: Fri, 23 Apr 1999 07:55:35 -0700 (PDT) Newsgroups: sci.math,alt.math.moderated Keywords: Apollonian gasket In article
After the third step or so, the speres of any step are not all the same size.
In 2 dimensions (packing circles) this is called (following Mandelbrot) the Appolonian gasket.
www.math.niu.edu /~rusin/known-math/99/gasket   (218 words)

  
 [No title]   (Site not responding. Last check: 2007-10-14)
Hebrew University Basic Notions Following the colloquium on Thursday, June 3rd at 5:15, in Ulam 2, A. Kirillov will give a talk on Analysis and geometry on Fractals.
Abstract: We consider self-similar fractals, such as Cantor set or Sierpinski and Apollonian gaskets.
The study of the Apollonian gasket is related with some discrete subgroups in O(1,3), the Diophantine equation $x^2-y^2-z^2=1+t^2$ and geometry of De Sitter space.
www.math.technion.ac.il /~techm/20040603171520040603kir   (115 words)

  
 Wacky Neighbor: Flaunt it Baby!: Things I learned yesterday:
The Apollonian Gasket is geometric figure consisting of recursed inner soddy circles, and looks exactly like the front panel of a thong bikini.
Posted by condour at May 6, 2004 03:30 AM May 06, 2004 (perm)
Said Soddy wrote a poem about his circles, entitled "The Kiss Precise."
www.wackyneighbor.com /archives/2004/05/things_i_learne.php   (164 words)

  
 CMS Winter 2004 Meeting
The Apollonian gasket is an ancient object, consisting of infinitely many non-overlapping circles packed inside an enclosing circle.
I will review how there are Apollonian gaskets that are integral in a strong sense and then I will construct the Apollonian supergasket, which contains all strongly integral Apollonian gaskets, in a very beautiful structure.
The talk will be elementary and there will be pictures.
www.cms.math.ca /Events/winter04/res/dg?nomenu=1   (2005 words)

  
 the ellipse and its evolute and the distance problem   (Site not responding. Last check: 2007-10-14)
Apollonius' Problem: A Study of Solutions and Their Relations
[Advanced -- MetaPost construction of the "Apollonian gasket" of tangent circles]
For a complete study of the evolutes of the graphs of polynomials, see
www.math.villanova.edu /archives/maple/misc/ellipse   (78 words)

  
 Diary for karlberry
Older diary entries for karlberry (starting at number 36):
TUGboat: edited a short paper by Anita Schwartz on problem solving in LaTeX, and a MetaPost paper by Denis Roegel on kissing circles (the Apollonian gasket, pretty fun).
TeX Live: installed small fix to dvips to avoid embedding of arbitrary files (from Yukata Oiwa), and to afm2tfm to ignore WY elements for vertical spacing (from Werner Lemberg).
www.advogato.org /person/karlberry/diary.html?start=36   (770 words)

  
 UC Berkeley Mathematics   (Site not responding. Last check: 2007-10-14)
The physical notion of a fractal set and its mathematical counterparts.
Two examples: Sierpinski gasket S and Apollonian gasket A. Harmonic functions on S and generalized numerical systems.
What is and what can be a numerical system?
math.berkeley.edu /index.php?module=calendar&calendar[view]=event&id=735   (138 words)

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