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Topic: Sierpinski

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1882

	Waclaw Sierpinski
		Sierpinski graduated in 1904 and worked for a while as a school teacher of mathematics and physics in a girls school in Warsaw.
		From this period Sierpinski worked mostly is in the area of set theory but also on point set topology and functions of a real variable.
		Sierpinski continued working in the "Underground Warsaw University" while his official job was a clerk in the council offices in Warsaw.
	www.stetson.edu /~efriedma/periodictable/html/Si.html (611 words)

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		Sierpinski was lucky for the lector changed the mark on his Russian language course to 'good' so that he could take his degree.
		Sierpinski spoke of the tragic events of the war during a lecture he gave at the Jagiellonian University in Kraków (Cracow) in 1945.
		Sinkiewicz, On the collaboration of Waclaw Sierpinski and Nikolai Luzin (Polish), Kwart.
	www.angelfire.com /scifi2/rsolecki/waclaw_sierpinski.html (1580 words)

	The Geometry Junkyard: Sierpinski Tetrahedra
		Rainbow Sierpinski tetrahedron by Aécio de Féo Flora Neto.
		Sierpinski gaskets and variations rendered by D. Hepting.
		Sierpinski triangle reptile based on a complex binary number system, R. Gosper.
	www.ics.uci.edu /~eppstein/junkyard/sierpinski.html (493 words)

	Sierpinski biography
		Sierpinski began to study set theory and in 1909 he gave the first ever lecture course devoted entirely to set theory.
		Sierpinski continued working in the 'Underground Warsaw University' while his official job was a clerk in the council offices in Warsaw.
		Sierpinski spoke of the tragic events of the war during a lecture he gave at the Jagiellonian University in Krakóv in 1945 (see [Acta Arithmetica 21 (1972), 7-13.',13)" onmouseover="window.status='Click to see reference';return true">13]).
	www-history.mcs.st-andrews.ac.uk /Biographies/Sierpinski.html (1798 words)

	Fractals: Sierpinski Objects
		Intuitively, the length of the Sierpinski gasket is the total of the length of all the segments required to draw the object.
		This was a period of Russian occupation of Poland and despite the difficulties, Sierpinski entered the Department of Mathematics and Physics of the University of Warsaw in 1899.
		In 1903 Sierpinski was awarded the gold medal for an essay on Voronoy's contribution to number theory.
	users.swing.be /TGMSoft/curvesierpinskiobj.htm (1475 words)

	Famous Fractals - Sierpinski Triangle (Site not responding. Last check: )
		Sierpinski Triangle is one of the most famous fractals.
		The Sierpinski triangle is a fractal cluster, which is formed by cutting out pieces of a triangle.
		The fractal dimension of the Sierpinski Triangle can be easily found using the similarity method.
	library.thinkquest.org /26242/full/fm/fm31.html (213 words)

	Sierpinski Carpet (Site not responding. Last check: )
		The Sierpinski carpet is the intersection of all the sets in this sequence, that is, the set of points that remain after this construction is repeated infintely often.
		Sierpinski used the carpet to catalogue all compact one-dimensional objects in the plane (from a topological point of view).
		So the Sierpinski carpet was actually invented by Stefan Mazurkiewicz, who in 1913 wrote his Ph.D. thesis under the supervision of Sierpinski on curves filling a square.
	ecademy.agnesscott.edu /~lriddle/ifs/carpet/carpet.htm (523 words)

	Sierpinski Tautology Map
		In the case of 'and' the persistent image of the Sierpinski gasket appears in the upper left as a value pattern for contradiction; in the case of 'or' it appears in the lower right as a value pattern for tautology.
		The initially startling appearance of the Sierpinski gasket as a map of tautologies under the Sheffer stroke can thus be understood in terms of (i) what a binary representation of values means and (ii) a corresponding rendering of the familiar 'doubling the distance from the nearest vertex' route to the Sierpinski in terms of binaries.
		It is well known that the points constitutive of the Sierpinski gasket within a continuous unit square are infinitely many, but nonetheless 'very few' in the sense that a random selection of points has a probability approaching zero of hitting such a point.
	www.sunysb.edu /philosophy/fractal/Sierpins.html (2671 words)

	Sierpinski Gasket (Site not responding. Last check: )
		The Sierpinski gasket, also known as the Sierpinski triangle, is the intersection of all the sets in this sequence, that is, the set of points that remain after this construction is repeated infinitely often.
		The Sierpinski gasket is also referred to as the Sierpinski triangle or as the Sierpinski triangle curve.
		It apparently was Mandelbrot who first gave it the name "Sierpinski's gasket." Sierpinski described the construction to give an example of "a curve simultaneously Cantorian and Jordanian, of which every point is a point of ramification." Basically, this means that it is a curve that crosses itself at every point.
	ecademy.agnesscott.edu /~lriddle/ifs/siertri/siertri.htm (818 words)

	Pictorial Gazette - Sierpinski comes up big against Portland
		Sierpinski scored eight of his 16 points in a three-minute span of the fourth quarter, Riordan buried a big 3-pointer with four minutes to play, and Pratt tossed in 22 points to lead the Cougars past the Highlanders, 63-53.
		Riordan followed with a clutch 3-pointer but Schroll answered with a pull-up jumper in traffic and, after a Sierpinski bucket, a 3-pointer to close the deficit to 52-48 with 3:53 left.
		Sierpinski, however, was in the right place again, corralling a Cougars 3-point miss for a putback that extended the lead to 54-48.
	www.zwire.com /site/news.cfm?newsid=15885844&BRD=1631&PAG=461&dept_id=31538&rfi=6 (803 words)

	Sierpinski Fractals
		Sierpinski Gaskets, Sierpinski Pentagons, and a Menger Sponge.
		This is a Sierpinski Pentagon and a snowflake derived from it by selectively filling the shapes which are left white in the first one.
		The normal Sierpinski Pentagon was made in postscript and the snowflake thing in metapost.
	ungwe.org:30000 /art/sierpinski (312 words)

	Sierpinski Fractals (Site not responding. Last check: )
		Sierpinski Gaskets, Sierpinski Pentagons, and a Menger Sponge.
		This is a Sierpinski Pentagon and a snowflake derived from it by selectively filling the shapes which are left white in the first one.
		The normal Sierpinski Pentagon was made in postscript and the snowflake thing in metapost.
	ungwe.org /art/sierpinski (312 words)

	Programmed DNA forms fractal TRN 040605
		A Sierpinski triangle is a type of crystal, or structure that regularly repeats.
		The DNA Sierpinski triangles show that there is no theoretical barrier to using molecular self-assembly to carry out any kind of computing and nanoscale fabrication, according to Winfree.
		In the case of a Sierpinski pattern, the molecules are directing the process of self-assembly, he said.
	www.trnmag.com /Stories/2005/040605/Programmed_DNA_forms_fractal_040605.html (990 words)

	Sierpinski Curve (Site not responding. Last check: )
		While the Hilbert curve is an open curve, the Sierpinski curve is closed; it bounds an area that is 5/12 that of the square it fills.
		The Sierpinski curve consists of four open curves linked together by line segments located in the outer corners.
		Like the Hilbert curve, the Sierpinski curve is also the limit of an infinite series of curves.
	home.comcast.net /~davebowser/fractals/sierpinski.html (383 words)

	Sierpinski Pyramid
		Sierpinski pyramids, or gaskets, are equilateral triangular pyramids formed by joining 4 smaller pyramids together in such a way that the larger pyramid is similar in shape to the original smaller pyramids.
		Sierpinski pyramids serve as an introduction to the study of fractals, and are useful in exploring the concepts of similarity and iteration which are significant in art, math and science.
		The Sierpinski pyramid has a hollow region at its center.
	www.newtrier.k12.il.us /academics/math/Connections/patterns/sierpyr.htm (319 words)

	Sierpinski triangle Summary
		The Sierpinski triangle has Hausdorff dimension log(3)/log(2) ≈ 1.585, which follows from the fact that it is a union of three copies of itself, each scaled by a factor of 1/2.
		The area of a Sierpinski triangle is zero (in Lebesgue measure).
		The tetrix is the three-dimensional analog of the Sierpinski triangle, formed by repeatedly shrinking a regular tetrahedron to one half its original height, putting together four copies of this tetrahedron with corners touching, and then repeating the process.
	www.bookrags.com /Sierpinski_triangle (1681 words)

	The Sierpinski Gallery (Site not responding. Last check: )
		The underlying framework is that of the delta stitch, with five Sierpinski triangles incorporated radially.
		A very early proof-of-concept design, this is a single relief-work Sierpinski triangle, done in gray acrylic with back-and-forth crochet, so the relief stitches are both front-post and back-post on alternating rows.
		Another proof of concept, done in off-white cotton yarn, this is a pair of relief-work Sierpinski triangles worked back-and-forth, one increasing in size with each row, and the other decreasing.
	www.math.ucsd.edu /~dwildstr/crochet/sierpinski/index.html (175 words)

	SierpinskiProblem - SeventeenOrBust
		Most mathematicians believe that 78557 is, indeed, the smallest Sierpinski number.
		Remember, a Sierpinski number is a fixed k such that all n yield composite N.
		Nine of them have now been eliminated by the project, and eight remain to prove that 78557 is the smallest Sierpinski number.
	wiki.seventeenorbust.com /index.php/SierpinskiProblem (355 words)

	PlanetMath: Sierpinski conjecture
		The Sierpinski problem consists in determining the smallest Sierpinski number.
		Cross-references: prime, sufficient, integer, Sierpinski number, property, composite, odd integers
		This is version 4 of Sierpinski conjecture, born on 2003-04-15, modified 2006-10-19.
	planetmath.org /encyclopedia/SierpinskiConjecture.html (91 words)

	NetLogo Models Library: Sierpinski Simple
		Sierpinski was a professor at Lvov and Warsaw.
		The Sierpinski tree is closely related to the class of fractals called Sierpinski Carpets which includes the famous Sierpinski Triangle or as it is usually called The Sierpinski Gasket.
		However connectedness is apparent from the way Sierpinski tree is generated; at each iteration the set is connected.
	ccl.northwestern.edu /netlogo/models/SierpinskiSimple (377 words)

	Science Center :: Sierpinski's Carpet
		Stretched over the bricked floor and patio of the 10,000-square-foot, multilevel Brown Family Courtyard is a very specific geometric pattern known as Sierpinski's Carpet.
		First described by Polish mathematician Warclaw Sierpinski (1882-1969), the pattern is formed by dividing one square into nine congruent squares in a 3-by-3 grid, then removing the center square.
		Sierpinski’s Carpet is classified as a fractal, a shape that appears similar at all levels of magnification.
	www.ups.edu /x11805.xml (159 words)

	Famous Fractals - Sierpinski Pyramid (Site not responding. Last check: )
		Thus, the Sierpinski Pyramid is indeed a fractal, since the fractal dimension is greater than the topological dimension.
		The area of the Sierpinski Triangle is equal to 0.
		Because of this, the surface area of the Sierpinski Pyramid also has to be 0.
	library.thinkquest.org /26242/full/fm/fm32.html (291 words)

	PlanetMath: Sierpinski gasket
		(alternately the intersection of all these sets) is a Sierpinski gasket, also known as a Sierpinski triangle.
		Figure: Sierpinski gasket stage 0, a single triangle, and at stage 1, three triangles
		This is version 19 of Sierpinski gasket, born on 2002-06-02, modified 2005-02-02.
	planetmath.org /encyclopedia/SierpinskiTriangle.html (99 words)

	Sierpinski Triangle (by Luigi Vigilante)
		Without a doubt, Sierpinski's Triangle is at the same time one of the most interesting and one of the simplest fractal shapes in existence.
		The geometric construction of the Sierpinski triangle is the most intuitive way to generate this fascinating fractal; however, it is only the tip of the Sierpinski iceberg.
		For example, the Sierpinski Triangle is a canonical example of a shape known as a fractal.
	victorian.fortunecity.com /orwell/433/sierpinsky.html (1211 words)

	The Magic Sierpinski Triangle
		This design is called Sierpinski's Triangle (or gasket), after the Polish mathematician Waclaw Sierpinski who described some of its interesting properties in 1916.
		The large blue triangle consists of three smaller blue triangles, each of which itself consists of three smaller blue triangles, each of which..., a process of subdivision which could, with adequate screen resolution, be seen to continue indefinitely.
		One way to do so is to inscribe a second triangle inside the original one, by joining the midpoints of the three sides, and then repeat the process for the resulting three outer triangles, for the three outer triangles that result from that, and so forth.
	serendip.brynmawr.edu /complexity/sierpinski.html (973 words)

	Mathematicians - Mandelbrot and Sierpinski
		Mandelbrot and Sierpinski are two mathematicians who made important contributions in the field of fractals.
		But of course, a Sierpinski triangle drawn to five iterations is no real fractal because when you start to zoom in you'll pretty soon see no more selfsimilarity but just big areas of fl and white.
		From this it's clear that the border of the Sierpinski triangle doesn't have a dimension of one or two, but a non interger dimension somewhere between one and two.
	mathematica.ludibunda.ch /mathematicians12.html (901 words)

	The Prime Glossary: Sierpinski number
		In 1960 Sierpinski showed that there were infinitely many such numbers k (all solutions to a family of congruences), but he did not explicitly give a numerical example.
		The congruences provided a sufficient, but not necessary, condition for an integer to be a Sierpinski number.
		It is conjectured that 78557 is the smallest Sierpinski number becase for most of the smaller numbers we can easily find a prime (in fact, for about 2/3rds of the numbers k there is a prime with n less than 9).
	primes.utm.edu /glossary/page.php?sort=SierpinskiNumber (470 words)

	Sierpinski Pyramid
		The Sierpinski pyramid is inspired by the two dimensional Sierpinski "gasket" described in Chaos and Fractals: New Frontiers of Science by Peitgen, Jurgens and Saupe, Springer Verlag 1992.
		Waclaw Sierpinski (1882-1969) was a professor at Lvov and Warsaw.
		The Sierpinski pyramid is a three dimensional version of the one dimensional Sierpinski gasket.
	www.bearcave.com /dxf/sier.htm (604 words)

	An Example of Using Random Numbers in Java - The Sierpinski Gasket (Site not responding. Last check: )
		The Sierpinski gasket is named after the mathematician Waclaw Sierpinski (1882-1969).
		One way to create the Sierpinski gasket is to start at one of the three corners (read vertices) of an equilateral triangle.
		Now, you should be able to run the Sierpinski gasket program on computers not connected to the Internet through your browser by opening the index.html file in the new folder.
	www.aspire.cs.uah.edu /~lillya/RandomNumbers.html (1383 words)

	MATLAB Central File Exchange - Sierpinski Sponge
		The Sierpinski Sponge is a fractal image based on the Cantor Set.
		The Sierpinski Sponge is the three-dimensional extrapolation of the carpet.
		Like the Sierpinski Gasket, as the level of iterations approaches infinity, the area of the sponge approaches zero, while the perimeter approaches infinity.
	www.mathworks.com /matlabcentral/fileexchange/loadFile.do?objectId=3524&objectType=file (406 words)

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