41. Sierpinski Triangle waclaw sierpinski (1882 1969 ). World War I totally disrupted the mathematicalcommunities of eastern Europe. Rather than try to re-build comprehensive http://curvebank.calstatela.edu/sierpinski/sierpinski.htm

Back to . . . Curve Bank Home NCB Deposit #2 Sierpinski Triangles This requires JAVA 1.2 or better. If you have a Mac, the operating system must be OS X or newer. Using the mouse, click on any three points in the box. NCB Deposit # 2 The National Curve Bank welcomes the Sierpinski Triangle animation of Kathleen Shannon and Michael Bardzell Dept. of Mathematics and Computer Science Salisbury University, Salisbury, MD. NCB Deposit #3 A Sample of recursion equations: For a definition click here: Click on the stamp to see an enlargement. Click on the Mandelbrot Set to read more about fractals. Waclaw Sierpinski World War I totally disrupted the mathematical communities of eastern Europe. Rather than try to re-build comprehensive university programs in several areas of research, Sierpinski, Kuratowski, Banach and others decided to work together in the emerging field of abstract spaces. They soon became known as the "Polish School." Their first international recognition came from publishing a new journal, Fundamenta Mathematicae (1920), devoted to set theory and related topics, and not to their work in topology. Indeed, the publication of Banach's dissertation in 1922 has been called the birth of functional analysis.

42. Area Of A Circle Animation sierpinski, waclaw, Pythagorean Triangles, Scripta Mathematica Studies Number Nine.(This is a translation by A. Sharma of a work by the well known http://curvebank.calstatela.edu/circle/circle.htm

Back to . . . . Curve Bank Home Page NCB Deposit # 17 Tom Richmond Bettina Richmond Western Kentucky University 1 Big Red Way Bowling Green, KY 42101 tom.richmond@wku.edu bettina.richmond@wku.edu Animations of Two Classics: Derivation of the Formula for the Area of a Circle and the Pythagorean Theorem From ( I, 47) of the Elements. From the first page of the first printed edition of Euclid's Elements, Venice, 1482. Scholars name this the Ratdolt edition in honor of the printer and publisher. It is not known how the figures were printed in the text. Before leaving the above images, we invite the viewer to consider the following: In the upper right hand corner is the ( I, 47 ) proof of the Pythagorean Theorem from one of the world's oldest hand written copies of Euclid's Elements. To the above right are figures taken from the first printed edition. Now, on the left, we see the contribution of animation, the gift of our generation, to these famous mathematical concepts. The circle, ellipse, parabola and hyperbola are "sections" of a cone. Recall the study of cones dates to Apollnius (262-190 BC) and other early Greeks.

43. Prominent Poles E. Marczewski, On the works of waclaw sierpinski Main trends of his works onset theory. Publications of waclaw sierpinski in the theory of numbers, http://www.angelfire.com/scifi2/rsolecki/waclaw_sierpinski.html

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "angelfire.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Angelfire Murderball Share This Page Report Abuse Edit your Site ... Next Prominent Poles Waclaw Sierpinski, mathematician Born: March 14, 1882, in Warszawa (Warsaw), Russia occupied Poland (now Poland) Died: October 21, 1969, in Warsaw, Poland The early days. Son of Waclaw Sierpinski's a medical doctor. He attended school in Warsaw where his talent for mathematics was quickly spotted by his first mathematics teacher. Higher education. Appointment at the Lwow University. Professorship in Warsaw. In 1919 he was promoted to professor at Warsaw and he spent the rest of his life there. Founding Fundamenta Mathematica. In 1920 Sierpinski, together with his former student Mazurkiewicz, founded the important mathematics journal Fundamenta Mathematica. Sierpinski edited the journal which specialized in papers on set theory. From this period Sierpinski worked mostly is in the area of set theory but also on general topology and on functions of a real variable. Sierpinski was also highly involved with the development of mathematics in Poland. Honors.

44. Wacław Sierpiński - Netlexikon waclaw sierpinski Bücher zum Stichwort waclaw sierpinski bei Amazon.de http://www.lexikon-definition.de/Waclaw-Sierpinski.html

von mehr Info Mitglied werden Suche: Wacław Sierpiński Article in English: Waclaw Sierpinski Article en fran§ais: Wacław Sierpiński Fehlendes Bild Sierpinski_square.jpg Das Sierpiński Quadrat Wacław Franciszek Sierpiński 14. M¤rz in Warschau 21. Oktober in Warschau ) war ein polnischer Mathematiker. Er studierte am Institut f¼r Mathematik und Physik an der Warschauer Universit¤t. 1908 wurde er Dozent und 1910 schlieŸlich Professor an der Universit¤t von Lw³w Er war bekannt f¼r seine herausragenden Beitr¤ge zur Mengenlehre (Untersuchungen zum Auswahlaxiom und zur Kontinuumshypothese), Zahlentheorie Funktionentheorie und Topologie Zwei wohlbekannte Fraktale - das Sierpinski-Dreieck und der Sierpinski-Teppich - sind nach ihm benannt, genauso das Sierpinski-Problem und die Sierpinski-Zahl Personendaten NAME Sierpiński, Wacław Franciszek ALTERNATIVNAMEN Sierpiński, Wacław KURZBESCHREIBUNG polnischer Mathematiker GEBURTSDATUM 14. M¤rz GEBURTSORT Warschau , Polen STERBEDATUM 21. Oktober STERBEORT Warschau , Polen Seitenkategorien: Mann Mathematiker Pole Amazon.de

45. Mehr Zu "Waclaw Sierpinski Born On March 14" Bei Metando waclaw sierpinski waclaw Franciszek sierpinski, was born on March 14. http://www.metando.de/search_Waclaw Sierpinski born on March 14_0.html

Waclaw Sierpinski born on March 14 Suchbegriff eingeben: Gesponsorte Ergebnisse für den Suchbegriff Waclaw Sierpinski born on March 14 Ergebnis bis von ingesamt für den Suchbegriff Waclaw Sierpinski born on March 14 Impressum Preisvergleich Fußballtrikots Fussball Bundesliga ... Z Suchworte Websuche: Diplomarbeiten Agentur Kirchhausen Zuben-el-Akrab Springende Gene ... Peter Johann Beckx var et_easy = 1; var et_ssl = 0; var et_pagename = ""; var et_areas = ""; var et_ilevel = 0;

46. Mehr Zu "Waclaw Sierpinski" Bei Metando Translate this page Gesponsorte Ergebnisse für den Suchbegriff waclaw sierpinski Bücher zum Themawaclaw sierpinski..Dieser Artikel von Wikipedia ..Foren..Dienstag, 15. http://www.metando.de/search_Waclaw Sierpinski_0.html

Waclaw Sierpinski Suchbegriff eingeben: Ergebnis aus unserem Lexikon für Waclaw Sierpinski Das Sierpiński Quadrat Wacław Franciszek Sierpiński in Warschau 21. Oktober in Warschau ) war ein polnischer Mathematiker Lw³w Mengenlehre (Untersuchungen zum Auswahlaxiom und zur Kontinuumshypothese), Zahlentheorie Funktionentheorie und Topologie Drei wohlbekannte Fraktale , das Sierpinski-Dreieck , der Sierpinski-Teppich und die Sierpiński-Kurve , sind nach ihm benannt, genauso das (Weiter lesen) Gesponsorte Ergebnisse für den Suchbegriff Waclaw Sierpinski Ergebnis bis von ingesamt für den Suchbegriff Waclaw Sierpinski Meinten Sie: Wa claw Sierpinski Verwandte Suchbegriffe Waclaw Franciszek Sierpinski Wac aw Sierpi ski Sierpinski-Problem Polish spelling ... Sierpinski ...http://www.uni-protokolle.de/Lexikon/ Waclaw Sierpinski Waclaw Sierpinski Sierpinski -Problem. Bücher zum Thema Waclaw Sierpinski ..Dieser Artikel von Wikipedia.....Foren..Dienstag, 15. Februar 2005 .. Waclaw Sierpinski .. Diese Seite benötigt.. www.uni-protokolle.de/Lexikon/Waclaw_Sierpinski.html Sierpinski ...Biography of Waclaw Sierpinski Waclaw Sierpinski .....Main index .. Version for printing .. Waclaw Sierpinski 's father was a doctor. He.....References (18 books/articles) A Poster of

47. MathematikerInnen - Mandelbrot und Sierpinski Translate this page waclaw sierpinski. Mandelbrot und sierpinski sind beide Mathematiker, waclaw sierpinski lebte von 1882 bis 1969. Er war einer der berühmtesten http://mathematica.ludibunda.ch/mathematicians-de12.html

Intro Leonhard Euler Pierre de Fermat Carl Friedrich Gauss ... Bertrand Russell Mandelbrot und Sierpinski Thales von Milet Spiel Spielplatz Rapunzel ... MathematikerInnen Benoit B. Mandelbrot und Waclaw Sierpinski Das Sierpinski Dreieck hat die Eigenschaften der Fraktale: Dieses Sierepinski Dreieck ist aber nur ein "Vorfraktal", da es nicht wirklich selbstähnlich ist; wenn du es auch nur etwa fünfmal vergrösserst, siehst du keine Selbstähnlichkeit mehr, sondern nur noch grosse Flächen. Um aus diesem "Vorfraktal" ein echtes Fraktal zu erhalten, müsste es noch durch unendlich viele Iterationen gehen. Mandelbrot Menge Probieren wir nun noch eine kleine Variation dazu aus: Wenn wir die beiden Katheten bei jeder Runde von neuem vertauschen, so entsteht ein Satz des Pythagoras Weiter Kontakt Diese Seite auf Englisch

48. Serendip Search This design is called sierpinski s Triangle (or gasket), after the Polishmathematician waclaw sierpinski who described some of its interesting properties 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

49. Machu Picchu & The Sierpinski Triangle. Puzzle. Antonio Gutierrez The Polish mathematician waclaw sierpinski (18821969) introduced his fractal in1916. See alsoThe sierpinski Triangle Machu Picchu Fractal illustration http://agutie.homestead.com/files/Puzzle_Sierpinski_Machu.htm

T he Sierpinski triangle is a fractal whose envelope is an equilateral triangle and which is composed of three half-sized Sierpinski triangles. A fractal is a geometric shape which is self-similar and has fractional dimension. The Polish mathematician Waclaw Sierpinski (1882-1969) introduced his fractal in 1916. See also Fractal illustration with animation. Machu Picchu and Geometric Art Solve the puzzle. Click with your mouse to move the pieces. (The puzzle requires Java enable browser.) More puzzles Nazca Lines: Condor Nazca Lines: The Monkey Nazca Lines: The Spider Machu Picchu ... Newton's Theorem Your browser does not support Scripting! Home Email Last updated: August 5, 2005

50. Golem.de - Lexikon sierpinskisquare.jpg Das sierpinski Quadrat. waclaw Franciszek sierpinski (* 14. http://lexikon.golem.de/Waclaw_Sierpinski

News Forum Archiv Markt ... Impressum Lexikon-Suche Lizenz Dieser Artikel basiert auf dem Artikel Wacław Sierpiński aus der freien Enzyklopädie Wikipedia und steht unter der GNU Lizenz für freie Dokumentation . In der Wikipedia ist eine Liste der Autoren verfügbar, dort kann man den Artikel bearbeiten Letzte Meldungen IFA: Veranstalter und Aussteller hochzufrieden Sanyo-Projektor PLV-Z4: Leise und kontraststark ... Originalartikel Weitergeleitet von Bild: Sierpinski square.jpg in Warschau 21. Oktober in Warschau ) war ein polnischer Mathematiker. Mengenlehre (Untersuchungen zum Auswahlaxiom und zur Kontinuumshypothese), Zahlentheorie Funktionentheorie und Topologie Drei wohlbekannte Fraktale - das Sierpinski-Dreieck , der Sierpinski-Teppich und die Sierpinski-Kurve - sind nach ihm benannt, genauso das Sierpinski-Problem und die Sierpinski-Zahl Personendaten NAME ALTERNATIVNAMEN KURZBESCHREIBUNG polnischer Mathematiker GEBURTSDATUM GEBURTSORT Warschau , Polen STERBEDATUM 21. Oktober STERBEORT Warschau , Polen Englische Wikipedia: Waclaw Sierpinski Die Inhalte unter lexikon.golem.de

51. Efg's Fractals And Chaos -- Sierpinski Triangle Lab Report Polish mathematician waclaw sierpinski introduced the sierpinski Gasket in 1915.Starting with a triangle, recursively cut the triangle formed by the http://www.efg2.com/Lab/FractalsAndChaos/SierpinskiTriangle.htm

Fractals and Chaos Sierpinski Triangle Lab Report Create a Sierpinkski "Gasket" By Cutting Holes in a Triangle Purpose The purpose of this project is to show how to create a Sierpinksi gasket, a "holey" triangle, by recursively cutting holes in a triangle. Mathematical Background Polish mathematician Waclaw Sierpinski introduced the "Sierpinski Gasket" in 1915. Starting with a triangle, recursively cut the triangle formed by the midpoints of each side: The single equilateral triangle in Step 0, is divided into four equal-area equilateral triangles in Step 2. The "middle" triangle is colored differently to indicate it has been "cut" from the object. This same "rule" is applied an infinite number of times. Here are the next two steps: Let's analyze what's happening. Consider the perimeter of the red triangles: Step Triangles 3 sides/triangle Length of Side Total Length a a/2 a/4 k k a/2 k k+1 a/2 k As k approaches infinity, the perimeter of all the red triangles approaches infinity. The area of an equilateral triangle with each side length a is . (See the von Koch Curve Lab Report for details.) For further computations here, we'll make computations as a fraction of A

52. Math Lessons - Waclaw Sierpinski Math Lessons waclaw sierpinski. waclaw sierpinski. waclaw Franciszeksierpinski, was born on March 14, 1882 in Warsaw and died on October 21, http://www.mathdaily.com/lessons/Waclaw_Sierpinski

Search Mathematics Encyclopedia and Lessons Lessons Popular Subjects algebra arithmetic calculus equations ... more References applied mathematics mathematical games mathematicians more Waclaw Sierpinski , was born on March 14 in Warsaw and died on October 21 in Warsaw . He 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 published over 700 papers and 50 books (two of which, "Introduction to General Topology" ( ) and "General Topology" ( ) were later translated into English by the Canadian mathematician Cecilia Krieger ). Two well-known fractals are named after him (the Sierpinski triangle and the Sierpinski carpet ), as are Sierpinski numbers and the associated Sierpinski problem. Education Sierpinski enrolled in the Department of Mathematics and Physics at the University of Warsaw in and graduated four years later. In , while still at the University of Warsaw, the Department of Mathematics and Physics offered a prize for the best essay from a student on Voronoy 's contribution to number theory. Sierpinski was awarded a gold medal for his essay, thus laying the foundation for his first major mathematical contribution. Unwilling for his work to be published in Russian , he withheld it until , when it was published in Samuel Dickstein 's mathematical magazine 'The Works of Mathematics and Physics'.

53. The Sierpinski Gasket On the left and right, we see a series of sierpinski gaskets (drawn using Fractintand Paint Shop Pro), discovered by waclaw sierpinski. http://www.jimloy.com/fractals/sierpins.htm

Return to my Mathematics pages Go to my home page The Sierpinski Gasket A Sierpinski gasket is also called a Sierpinski sieve. On the left and right, we see a series of Sierpinski gaskets (drawn using Fractint and Paint Shop Pro ), discovered by Waclaw Sierpinski. The first order would just be a straight line segment. Here, I show orders 2 through 7. You should probably see how each new order is built from the previous one. The true Sierpinski gasket is the limit of infinitely many of these steps. Instead of lines, we can also build it with dark triangles (or any other object). The Sierpinski gasket is related to The Yanghui Triangle (usually called Pascal's triangle), below. I have drawn hexagons around the odd numbers. That pattern is identical to that of the Sierpinski gasket, forever. There is an interesting experiment called "the chaos game," in which random (presumably chaotic) chance produces great order. On the left, we see a picture. We draw three (or more) points (the vertices of a triangle, which doesn't have to be equilateral or isosceles), labeled 1, 2, and 3. Then we choose a starting point S, at random (the one I chose is not within the triangle). Then we begin the game. We proceed to choose random numbers, 1, 2, or 3 (with dice or whatever). Each random number defines a new point halfway between the latest point and the point toward which our random number directs us. For example, my first random number was a 1; so I drew a point halfway between S and 1. Then I got another random 1, then 3, 2, 1, and 3. After drawing 6 points, I perceive no obvious pattern. With a computer, it is easier to continue to choose many more points.

54. Todd Wenrich Prof. Daepp Final Exam 12/6/99 Fractal Geometry In waclaw sierpinski was born on March 14, 1882, in Warsaw, Poland. sierpinski attendedthe University of Warsaw in 1899, when all classes were taught in http://www.facstaff.bucknell.edu/udaepp/090/w3/toddw.htm

Todd Wenrich Prof. Daepp Final exam Fractal Geometry Waclaw Sierpinski was born on March 14, 1882, in Warsaw, Poland. Sierpinski attended the University of Warsaw in 1899, when all classes were taught in Russian. He graduated in 1904 and went on to teach mathematics and physics at a girl's school in Warsaw. He left teaching in 1905 to get his doctorate at the Jagiellonian University in Cracow. After receiving his doctorate in 1908, Sierpinski went on to teach at the University of Lvov. During his years at Lvov, he wrote three books and many research papers. These books were The Theory of Irrational numbers Outline of Set Theory (1912), and The Theory of Numbers (1912). In 1919, Sierpinski accepted a job as a professor at the University of Warsaw, and this is where Waclaw Sierpinski (The Mactutor) he would spend the rest of his life. Throughout his career, Sierpinski wrote 724 papers and an amazing 50 books. Sierpinski studied many areas of mathematics, including, irrational numbers, set theory, fractal geometry, and theory of numbers. Sierpinski is viewed as one of the greatest Polish mathematicians ever. He is noted for his construction of the Sierpinski gasket. (The Mactutor) Sierpinki gasket (The MacTutor) Sierpinski Carpet (Bunde) The Sierpinski carpet for the above example has n = 5 and k = 9. It is possible for the carpets to look different when k is changed. Using the same idea as for the calculation of the dimension of the gasket, we denote by L the length of a square side and by the M mass of the carpet. Considering that n^2 – k smaller squares with side length L/n make up the whole carpet with side length L we get M(L) = (n^2 – k) M (L/n). Combining this with the general formula M = A L^d for some constant A we get (n^2 – k) A (L/n)^d = A L^d which simplifies to n^2 – k = n^d. Taking logarithms on both sides and solving for the dimension we get d = log(n^2 –k) / log n. In the example above, the fractal dimension is log(16) / log(5) = 1.7227 .(Daepp)

55. Biblio: Fundamenta Mathematicae (55) By Janiszewski, Zygmunt, Stefan Mazurkiewic Zygmunt, Stefan Mazurkiewicz and waclaw sierpinski Book Item Details. Janiszewski, Zygmunt, Stefan Mazurkiewicz and waclaw sierpinski Fundamenta http://www.biblio.com/books/40814290.html

View cart Search for Books By author: By title: By keyword or ISBN: Advanced booksearch Search for multiple books @Biblio Home Search for books Books by subject Rare book room ... Contact us Books by subject Arts Biography Books on Books Gardening ... More subjects Janiszewski, Zygmunt, Stefan Mazurkiewicz and Waclaw Sierpinski: Fundamenta Mathematicae (55) Format : Hardcover Warsaw: , 1964. VG++. 308 pp. Text in English. Green boards with gilt lettering on spine.. Add to cart Shipping rates Seller information Ask seller a question ... Printable version More information Seller Inventory # Format : Hardcover Publisher : Warsaw: , 1964 Offered for sale by [Back to top] bookworm bookstore 4335 crestview road harrisburg, Pennsylvania 17112 United States Visa, Mastercard, American Express, Discover, Check/Cheque or Money Order, PayPal Bookseller terms of sale: all books may be returned within 10 days of sale, as stated on our web site. Member Login Email address: Password: Don't have an account? Register free! 3 items in your cart Checkout now Home Search for books ... Contact us

56. Wacław Sierpiński - Wikipedia Translate this page Das sierpinski Quadrat. waclaw Franciszek sierpinski (* 14. NAME, sierpinski,waclaw Franciszek. ALTERNATIVNAMEN, sierpinski, waclaw http://de.wikipedia.org/wiki/Wacław_Sierpiński

Es ist geschafft - unser Spendenziel von 200.000$ ist erreicht . Herzlichen Dank an alle Spender. Wacław Sierpiński aus Wikipedia, der freien Enzyklop¤die Das Sierpiński Quadrat Wacław Franciszek Sierpiński 14. M¤rz in Warschau 21. Oktober in Warschau ) war ein polnischer Mathematiker Er studierte am Institut f¼r Mathematik und Physik an der Warschauer Universit¤t. 1908 wurde er Dozent und 1910 schlieŸlich Professor an der Universit¤t von Lw³w Er war bekannt f¼r seine herausragenden Beitr¤ge zur Mengenlehre (Untersuchungen zum Auswahlaxiom und zur Kontinuumshypothese), Zahlentheorie Funktionentheorie und Topologie Drei wohlbekannte Fraktale , das Sierpinski-Dreieck , der Sierpinski-Teppich und die Sierpiński-Kurve , sind nach ihm benannt, genauso das Sierpinski-Problem und die Sierpinski-Zahl Personendaten NAME Sierpiński, Wacław Franciszek ALTERNATIVNAMEN Sierpiński, Wacław KURZBESCHREIBUNG polnischer Mathematiker GEBURTSDATUM 14. M¤rz GEBURTSORT Warschau , Polen STERBEDATUM 21. Oktober STERBEORT Warschau , Polen Von " http://de.wikipedia.org/wiki/Wac%C5%82aw_Sierpi%C5%84ski

57. Sierpinski Curve It has named after the Polish mathematician waclaw sierpinski (18821969), butit was Stefan Mazurkiewicz who found the curve (in 1913). http://www.2dcurves.com/fractal/fractals.html

Sierpinski curve fractal last updated: The Sierpinski curve is a base motif fractal where the base is a square. After subdivision in 3x3 equal squares the motif is to remove the middle square: The curve is also known as the Sierpinski (universal plane) curve, Sierpinski square or the Sierpinski carpet It has named after the Polish mathematician Waclaw Sierpinski (1882-1969), but it was Stefan Mazurkiewicz who found the curve (in 1913). The curve is the only plane locally connected one-dimensional continuum S such that the boundary of each complementary domain of S is a simple closed curve and no two of these complementary domain boundaries intersect. Wow! In other words: the Sierpinski curve contains a topologically equivalent copy of any compact one-dimensional object in the plane. The fractal dimension of the curve is equal to log 8/ log 3, i.e. about 1.8928 The curve is a two-dimensional generalization of the Cantor set Some kind of shells (conus textilus, conus gloriatnatis) have patterns that resemble the Sierpinksi square. Professor Gerda de Vries of the University of Alberta designed a quilt named ´Sierpinksi Meets Mondrian´ notes 1) Fractal dimension = log N / log e, where N is the number of line segments and e the magnification.

58. Sierpinski Gasket waclaw sierpinski (18821969), a Polish mathematician, described the constructionto give an example of a curve simultaneously Cantorian and Jordanian, http://www.2dcurves.com/fractal/fractalg.html

Sierpinski gasket fractal last updated: The Sierpinski gasket is a base motif fractal where the base is a triangle. After subdivision in 4 equal triangles the motif is to remove the middle triangle: The curve is also known as the Sierpinski triangle or as the Sierpinski triangle curve . It was Mandelbrot who first gave it the name of the Sierpinski gasket. Waclaw Sierpinski (1882-1969), a Polish mathematician, described the construction to give an example of a curve simultaneously Cantorian and Jordanian, of which every point is a point of ramification. The fractal dimension of the curve is equal to log 3/ log 2, i.e. about 1.58496 A Sierpinski gasket constructed from resistors gives a simple network, that can be used to study electrical conductivity, diffusive transport and thermodynamic properties notes 1) Fractal dimension = log N / log e, where N is the number of line segments and e the magnification. For the Sierpinski gasket: N=3, e=2. 2) W.K. Ching, M. Erickson, P. Garik, P. Hickman, J. Jordan, S. Schwarzer, and L. Shorem Overcoming Resistance with Fractals: A New Way to Teach Elementary Circuits

59. The Cushman Network - Fractals waclaw sierpinski was not the first one to come up with this idea, for thesefigures have been found on patterns drawn on the pulpit of a 12th century http://cushman.net/projects/fractals/

Fractals and Chaos in Nature In the past two decades, scientists and mathematicians have developed a new way of looking at the universe around us, a new science that better describes the irregular shaped objects we find in nature and math. As James Gleick put it, "This new science, called chaos, offers a way of seeing order and pattern where formerly only the random, erratic, the unpredictable - in short, the chaotic - had been observed". Scientists had come upon an important tool in understanding nature. This science, along with the closely related science of fractals, models real-world situations better than anything else before. In 1961 at MIT, Edward Lorenz developed a model for an ideal weather system with few variables. He came up with three equations to reflect the changes on a computerized graph. These equations are defined to be: dx/dt = 10(y-x) dy/dt = xz+28x-y dz/dt = xy-(8/3)z He was studying changes in the weather, but he unknowingly founded the science of chaos. He discovered that small changes in the initial conditions would produce large differences in the long run (Stevens 63) The computer that Lorenz ran his system of equations on would compute the digits out to an accuracy of six decimal places. When Lorenz wanted to re-simulate a section on the graph that was produced, he started the computer over again at the beginning of the section in question, only with three digits of accuracy, instead of six. After a short period of time, Lorenz could see a large difference in the two graphs. This led to the discovery of the Lorenz attractor, a butterfly-shaped graph. When these equations are graphed on a computer, the output is chaotic, but orderly. These equations model such natural phenomena as the flow of fluid, or the movement of a water wheel

60. Sierpinski Problem The sierpinski Problem Definition and Status. In 1960 waclaw sierpinski (18821969)proved the following interesting result. Theorem S. http://www.prothsearch.net/sierp.html

The Sierpinski Problem: Definition and Status In 1960 Waclaw Sierpinski (1882-1969) proved the following interesting result. Theorem [S] There exist infinitely many odd integers k such that k n + 1 is composite for every n A multiplier k with this property is called a Sierpinski number . The Sierpinski problem consists in determining the smallest Sierpinski number. In 1962, John Selfridge discovered the Sierpinski number k = 78557, which is now believed to be in fact the smallest such number. Conjecture. The integer k is the smallest Sierpinski number. To prove the conjecture, it would be sufficient to exhibit a prime k n + 1 for each k Summary of results. This summary describes developments in the computational approach to a possible "solution" of the Sierpinski problem, from the earliest attempts in the late 1970ies until November 2002, and gives a comprehensive status of results known at that point. For more recent information, refer to the distributed computing project Seventeen or Bust . The name of this project indicates that when it was created, only 17 uncertain candidates k were left to be investigated, namely

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