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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Stefan Mazurkiewicz (September 25, 1888 in Warsaw, then Russian Empire June 19, 1945, Grodzisk Mazowiecki, Poland) was a Polish mathematician who worked in mathematical analysis, topology, and probability. He was a student of Wac aw Sierpi ski and a member of the Polish Academy of Learning (PAU). His students included Karol Borsuk, Bronis aw Knaster, Kazimierz Kuratowski, Stanis aw Saks, and Antoni Zygmund. For a time Mazurkiewicz was a professor ath the University of Paris, however he spent most of his career as a professor at the University of Warsaw.

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High Quality Content by WIKIPEDIA articles! The Sierpinski carpet is a plane fractal first described by Wac aw Sierpi ski in 1916. The carpet is a generalization of the Cantor set to two dimensions (another is Cantor dust). Sierpi ski demonstrated that this fractal is a universal curve, in that any possible one-dimensional graph, projected onto the two-dimensional plane, is homeomorphic to a subset of the Sierpinski carpet. For curves that cannot be drawn on a 2D surface without self-intersections, the corresponding universal curve is the Menger sponge, a higher-dimensional generalization. The technique can be applied to repetitive tiling arrangement, triangle, square, hexagon being the simplest. It would seem impossible to apply it to other than rep-tile arrangements.

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High Quality Content by WIKIPEDIA articles! The Sierpinski triangle, also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal named after the Polish mathematician Wac aw Sierpi ski who described it in 1915. Originally constructed as a curve, this is one of the basic examples of self-similar sets, it is a mathematically generated pattern that can be reproducible at any magnification or reduction.Comparing the Sierpinski triangle or the Sierpinski carpet to equivalent repetitive tiling arrangements, it is evident that similar structures can be built into any rep-tile arrangements.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The Sierpinski triangle (also with the original orthography Sierpi ski), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal named after the Polish mathematician Wac aw Sierpi ski who described it in 1915. Originally constructed as a curve, this is one of the basic examples of self-similar sets, it is a mathematically generated pattern that can be reproducible at any magnification or reduction. Comparing the Sierpinski triangle or the Sierpinski carpet to equivalent repetitive tiling arrangements, it is evident that similar structures can be built into any rep-tile arrangements.

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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Stanis aw Ruziewicz (b. August 29, 1889 in Podstaje - July 12, 1941 in Lviv, Ukraine, then Soviet Union) was a Polish mathematician and one of the founders of the Lviv School of Mathematics. He was a former student of Wac aw Sierpi ski, a professor at the Lviv University and Lviv Academy of Foreign Trade. During the Second World War, he was arrested and murdered by the Gestapo on July 12, 1941 in Lviv, during the Massacre of Lviv professors.

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High Quality Content by WIKIPEDIA articles! Wac aw Franciszek Sierpi ski (Polish pronunciation: [ vatswaf fra t i k r p i sk i]) (March 14, 1882, Warsaw October 21, 1969, Warsaw) was a Polish mathematician. He was 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.Three well-known fractals are named after him (the Sierpinski triangle, the Sierpinski carpet and the Sierpinski curve), as are Sierpinski numbers and the associated Sierpi ski problem.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Sierpi ski space (or the connected two-point set) is a finite topological space with two points, only one of which is closed. It is the smallest example of a topological space which is neither trivial nor discrete. It is named after Wac aw Sierpi ski. The Sierpi ski space has important relations to the theory of computation and semantics.Wac aw Franciszek Sierpi ski (March 14, 1882, Warsaw October 21, 1969, Warsaw) was a Polish mathematician. He was 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.Three well-known fractals are named after him (the Sierpinski triangle, the Sierpinski carpet and the Sierpinski curve), as are Sierpinski numbers and the associated Sierpi ski problem.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Rule 90 is a one-dimensional binary cellular automaton. The Sierpinski triangle (also with the original orthography Sierpi ski), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal named after the Polish mathematician Wac aw Sierpi ski who described it in 1915. Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction. Comparing the Sierpinski triangle or the Sierpinski carpet to equivalent repetitive tiling arrangements, it is evident that similar structures can be built into any rep-tile arrangements.

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High Quality Content by WIKIPEDIA articles! In number theory, a Sierpinski number is an odd natural number k such that integers of the form k2n + 1 are composite (i.e. not prime) for all natural numbers n. In other words, when k is a Sierpinski number, all members of the following set are composite:The number 78,557 was proved to be a Sierpinski number by John Selfridge in 1962, who showed that all numbers of the form 78557·2n+1 have a factor in the covering set {3, 5, 7, 13, 19, 37, 73}. For another known Sierpinski number, 271129, the covering set is {3, 5, 7, 13, 17, 241}. All currently known Sierpinski numbers possess similar covering sets.In 1967, Sierpi ski and Selfridge conjectured that 78,557 is the smallest Sierpinski number, and thus the answer to the Sierpinski problem.

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