81. Fractals: Sierpinski Objects All pictures from WinCrv, Introduction, waclaw sierpinski, a polish mathematician,and his collegues devised several curves that all bear his name. http://users.swing.be/TGMSoft/curvesierpinskiobj.htm

DisplayHeader( "Geometric Fractals", "The Sierpinski Objects", 0, "main_fractals.htm", "Back to Fractals Main Page"); Content Introduction Construction Properties Variations Author Biography All pictures from WinCrv Introduction Waclaw Sierpinski, a polish mathematician, and his collegues devised several curves that all bear his name. The most famous one, the Sierpinski Gasket, is dated back around 1916. These curves are based on different geometrical basis but share the same construction principle. Here they are: the Sierpinksi Gasket or Sierpinski Triangle the Sierpinski Carpet or Sierpinski Rectangle the Sierpinski Pentagon the Sierpinski Hexagon Construction Two drawing methods are available: Geometric Method Triangle The starting point is a triangle. Divide its three sides in two segments of equal length. Connect the midpoints to get four inner triangles and paint the three external ones. Apply the same process to the inner triangles but the middle one. The first iterations give the following pictures: Rectangle Take a rectangle. Divide the four sides in three segments of equal length. From the midpoints, drawn the lines to get the nine inner rectangles. Paint all the inner rectangles but the middle one.

82. Sierpinski Projects practical number theory. waclaw sierpinski (18821969). The main pagefor sierpinski problem conducted by Wilfrid Keller and Ray Ballinger. http://sierpinski.insider.com/

some Sierpinski problem related projects in practical number theory Waclaw Sierpinski (1882-1969) The main page for Sierpinski problem conducted by Wilfrid Keller and Ray Ballinger The dual sierpinski project The smallest Sierpinski candidate k=4847 ... The smallest Mixed Sierpinski candidate k=19249 More projects to be defined Dual Riesel Dual Base3+ Mixed Base3+ Dual Breyer Dual Base3- Mixed Base3- Dual Cullen Dual Woodal This Page is maintained by Payam samidoost

83. Waclaw Sierpinski Article on waclaw sierpinski from WorldHistory.com, licensed fromWikipedia, the free encyclopedia. Return Index waclaw sierpinski. http://www.worldhistory.com/wiki/W/Waclaw-Sierpinski.htm

World History (home) Encyclopedia Index Localities Companies Surnames ... This Week in History Waclaw Sierpinski Waclaw Franciszek Sierpinski , Polish spelling March 14 October 21 ) was a Polish mathematician, known for outstanding contributions to set theory (research on the axiom of choice and the continuum hypothesis number theory , theory of functions and topology He was born in Warsaw. Two well-known fractal s are named after him (the Sierpinski triangle and the Sierpinski carpet ), as are Sierpinski number s and the associated Sierpinski problem. Waclaw Sierpinski is interred in the Powazki Cemetery , Warsaw, Poland. Sponsored Links Advertisements Harry Potter and the Prisoner of Azkaban unabridged on CD DVD New Releases ... at DVDPlanet Find lost family and friends This article is licensed under the GNU Free Documentation License You may copy and modify it as long as the entire work (including additions) remains under this license. You must provide a link to http://www.gnu.org/copyleft/fdl.html To view or edit this article at Wikipedia, follow this link World History How to cite this page Encyclopedia Index ... Contact Us

84. Vortrag Index Translate this page freuen. sternemann@t-online.de. Literatur sierpinski, waclaw. Surune courbe dont tout point est un point de ramification. Comptes http://www.canisianum.de/bisher/projekte/fraktale/VortragMuenster/

Anmerkung zum Titel Inhalt 1. Sierpinskitetraeder und Mengerschwamm, zwei klassische platonische Fraktale 1.1. Zur Mathematikgeschichte 1.2. Existenz der Grenzfigur 1.3. Fraktale Dimension 1.4. Zu Querverbindungen 2. Aktuelle Experimente mit "Platonischen Fraktalen" in der Schule 2.3. Anwendung auf das Oktaeder 2.4. Anwendung auf das Ikosaeder 2.5. Anwendung auf das Dodekaeder 2.6. Angaben zur konkreten Herstellung unserer Modelle 3. Literatur Anmerkung: (Offizielles Thema:) von Wilhelm Sternemann sternemann@t-online.de Literatur Sierpinski, Waclaw. Sur une courbe dont tout point est un point de ramification. Menger, Karl " und Menger, Karl. Proceedings Academie Amsterdam 29, S. 1124ff, 1923 Blumenthal, Leonhard M./ Menger Karl. Studies in Geometry. W. H. Freeman and Company Sanfrancisco 1970 Fraktale Geometrie der Natur 1987 (engl. Orig. 1977) Les objets fractals: forme, hasard et dimension In: Flammarion. Paris 1975 Urysohn, M. P. "Les multiplicites cantoriennes" M. Komorek/ R. Duit/ M. Schnegelberger (Hrsg.). Fraktale im Unterricht.

85. TeleMath - ÌáèçìáôéêÜ êáé Öéëïôåëéóìüò The summary for this Greek page contains characters that cannot be correctly displayed in this language/character set. http://www.telemath.gr/mathematical_stamps/stamps_mathematicians/persons/sierpin

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86. Serendip This design is called sierpinski s Triangle (or gasket), after the Polish mathematicianWaclaw sierpinski who described some of its interesting properties in http://serendip.brynmawr.edu/playground/sierpinski.html

The Magic Sierpinski Triangle Order dependent on randomness This design is called Sierpinski's Triangle (or gasket), after the Polish mathematician Waclaw Sierpinski who described some of its interesting properties in 1916. Among these is its fractal or self-similar character. 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. Fractals and self-similarity are of considerable interest in their own right, but our interest here is in how to construct Sierpinski's triangle. 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. But there is a more intriguing way to construct Sierpinski's triangle, sometimes called the Chaos Game Lots of interesting questions have probably occurred to you. Does the pattern depend on the particular triangle you start with? Find out by clicking on the Custom button and creating your own triangle. Does the choice of the initial point matter? Try that out too by clicking the Clear button and selecting a new point inside the triangle. How come this construction gives the same (itself rather remarkable) pattern as inscribing triangles? We'll leave that and some other questions to

87. The Magic Sierpinski Triangle This design is called sierpinski s Triangle (or gasket), after the Polish mathematicianWaclaw sierpinski who described some of its interesting properties in http://serendip.brynmawr.edu/serendip/interactive/sierpinski.html

TO PIRELLI REVIEWERS: This exhibit is taken from Serendip's website beginning at http://serendip.brynmawr.edu/playground/sierpinski.html . Amost all links are active; for inactive links go to the URL given. The Magic Sierpinski Triangle Order dependent on randomness This design is called Sierpinski's Triangle (or gasket), after the Polish mathematician Waclaw Sierpinski who described some of its interesting properties in 1916. Among these is its fractal or self-similar character. 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. Fractals and self-similarity are of considerable interest in their own right, but our interest here is in how to construct Sierpinski's triangle. 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. But there is a more intriguing way to construct Sierpinski's triangle, sometimes called the Chaos Game Lots of interesting questions have probably occurred to you. Does the pattern depend on the particular triangle you start with? Find out by clicking on the Custom button and creating your own triangle. Does the choice of the initial point matter? Try that out too by clicking the Clear button and selecting a new point inside the triangle. How come this construction gives the same (itself rather remarkable) pattern as inscribing triangles? We'll leave that and some other questions to

88. Sierpinski's Polygons This fractals were named after the Polish mathematician WaclawSierpinski who described some of theirs interesting properties in 1916....... http://members.lycos.co.uk/ququqa2/fractals/Sierpinski.html

Sierpinski's polygons Instructions: This applet draws n polygons. Each polygon has smaller polygons drawn in its corners. You can specify m number of steps, that are drawn. Description: This fractals were named after the Polish mathematician Waclaw Sierpinski who described some of theirs interesting properties in 1916. The most famous is Sierpinski Triangle that can be generated using different algorithms: chaotic IFS Algorithm or deterministic algorithm based on Pascal Triangle . Here is presented a different way to generate Sierpinski's fractals. Figure is divided into n parts. In each part is drawn a smaller figure. You can follow this proces by choosing step 1 and increasing step using '+' button. The better figure can be seen if we remove long segments Contents Back to main page

89. Sierpinski Triangle sierpinski Triangle. This fractal was named after the Polish mathematician Waclawsierpinski who described some of its interesting properties in 1916. http://members.lycos.co.uk/ququqa2/sierpinskip.php

Sierpinski Triangle Center Left - Bottom Left - Top Right - Bottom Right - Top Sierpinski Triangle. This fractal was named after the Polish mathematician Waclaw Sierpinski who described some of its interesting properties in 1916. Sierpinski Triangle can be generated using different algorithms: chaotic IFS Algorithm or deterministic algorithm based on Pascal Triangle. Using modulus 2 operation on Pascal Triangle we get Sierpinski Triangle. The third algorithm is to draw iteratively smaller triangles. Contents Back to main page

90. Math Forum - Ask Dr. Math Date 01/20/97 at 112636 From Doctor Toby Subject Re sierpinski Triangle Waclawsierpinski invented the triangle (or gasket) named after him in 1916. http://mathforum.org/library/drmath/view/54524.html

Associated Topics Dr. Math Home Search Dr. Math Sierpinski Triangle Date: 01/15/97 at 10:28:11 From: Anonymous Subject: Sierpinski Triangle Hi, My name is Ryan and I would like to ask you a question. What is a Sierpinski Triangle? http://mathforum.org/dr.math/ Associated Topics High School Fractals Search the Dr. Math Library: Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age. all keywords, in any order at least one, that exact phrase parts of words whole words Submit your own question to Dr. Math Math Forum Home Math Library Quick Reference ... Math Forum Search Ask Dr. Math TM http://mathforum.org/dr.math/

91. Fractal Antennas - Front Page The sierpinski Gasket is one of the oldest fractal shapes. It is named afterWaclaw sierpinski, the Polish mathematician that extensively studied it. http://www-tsc.upc.es/eef/research_lines/antennas/fractals/gallery/spk60.html

The Sierpinski Antenna Introduction The Sierpinski Gasket is one of the oldest fractal shapes. It is named after Waclaw Sierpinski, the Polish mathematician that extensively studied it. The fractal form is composed by 3 triangular sets, being each one itself a Sierpinksi Gasket. A classical procedure for constructing it is burning a triangular hole in the central part of a solid triangular shape, and keep iterating the same procedure over each new triangle formed this way. The object has a fractal dimension D and a characteristic scale factor d relating the several gaskets within the structure. Antenna Description The antenna was built by printing a iteration, 8.9 cm tall Sierpinski gasket over a Cuclad 250-GT microwave circuit dielectric substrate. The monopole configuration was chosen first for its simplicity and feeding scheme. The antenna was mounted orthogonally to a 80 cm x 80 cm ground plane and fed through an SMA coaxial connector. Owing to the antenna geometry, one expected current flowing from the feeding vertex to the antenna tips and power becoming radiated, i.e., driven out from the antenna, at those fractal iterations that matched the operating wavelength. Since the antenna contained 5 scale-levels with a characteristic scale-factor of relating all of them, it appeared reasonable to assume that the antenna would perform in a similar way at

92. Fractals: Sierpinski Curve Introduction, The sierpinski curve, named from the polish mathematician Waclawsierpinski who originally devised it around 1912, is much less known than the http://users.swing.be/TGMSoft/curvesierpinski.htm

DisplayHeader( "Geometric Fractals", "The Sierpinski Curve", 0, "main_fractals.htm", "Back to Fractals Main Page"); Content Introduction Construction Properties Variations Author Biography All pictures from WinCrv Introduction The Sierpinski curve, named from the polish mathematician Waclaw Sierpinski who originally devised it around 1912, is much less known than the other fractal objects created by Sierpinski and his co-workers as the Sierpinski gasket or the Sierpinski Carpet However, this curve allows beautiful variations that make it a wonderful candidate for our excursion in the world of fractals ... Construction As most of the fractal curves, the construction of the curve is based on the recursive procedure. The curve grain is obtained by replacing each corner of a square by a small square placed along the diagonal axis. The picture of the first recursion makes it easy to understand. > This process is then repeated for the 4 corners of the figure generated at the previous iteration. The second iteration gives this picture: The third iteration already gives an intricate pattern that require a much larger drawing to follow the construction rule visually. Playing with WinCrv will help learning the construction of this curve ...

93. TeleMath - ÌáèçìáôéêÜ êáé Öéëïôåëéóìüò The summary for this Greek page contains characters that cannot be correctly displayed in this language/character set. http://www.telemath.gr/mathematical_stamps/stamps_mathematicians/

document.writeln(""); ABEL, Niels Henrik. AL-KHOWARIZMI. 'Añáâáò Ìáèçìáôéêüò( 790850 ) ARCHIMEDES. BABBAGE, Charles. BANACH, Stefan. BANACHIEWICZ, Tadeusz. ... KHAYYAM, Omar. 'Añáâáò Ìáèçìáôéêüò( 10481122 ) KIRCHHOFF, Gustav. KOVALEVSKAYA, Sofia. KRYLOV, Aleksei N. LAGRANGE, Joseph-Louis. ... ZAREMBA, Stanislaw.

94. Fundamenta Mathematicae Vol. 33, 1945 http://www.impan.gov.pl/PUBL/Old_Archive/FM/V033.html

Fundamenta Mathematicae Vol. 33, 1945 Waclaw Sierpinski, Un theoreme sur les familles d'ensembles et ses applications. Andrzej Mostowski, Remarques sur la note de M. Sierpinski ``Un theoreme sur les familles d'ensembles et ses applications.'' Waclaw Sierpinski, Sur une suite transfinie d'ensembles de nombres naturels. Anthony P. Morse, John F. Randolph, Gillespie measure. M. H. Stone, On characteristic functions of families of sets. Stefan Kempisty, Sur l'aire des surfaces courbes continues. G. Van-der-Lijn, La definition fonctionnelle des polynomes dans les groupes abeliens. Alfred Tarski, Ideale in vollstandigen Mengenkorpern. II. Bedrich Pospisil, Wesentliche Primideale in vollstandigen Ringen. S. Bergmann, J. Marcinkiewicz, Sur les fonctions analytiques de deux variables complexes. W. L. Ayres, On transformations having periodic properties. Waclaw Sierpinski, Sur une suite infinie de fonctions de classe $1$ dont toute fonction d'accumulation est non mesurable. (Solution d'un probleme de M. S. Banach). A. N. Singh

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