Leia e aprenda gratuitamente sobre o seguinte artigo. Virtual and manipulative geometrical and topological games. The sierpinski triangle also with the original orthography sierpinski, also called the sierpinski gasket or sierpinski sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. So, in seeking the application of mathematical concepts in fractal geometry, we calculate the area and volume of the sierpinski triangle after n interactions. Mathworld mentions a broader context for why binary logic can be used in the construction of the sierpinski triangle. With and the method given above is only one of the very many ways to draw sierpinski triangles. In fact we give a characterization of the apollonian gasket. Even the binomial coefficient has factorials which are recursively defined.
Sierpinski graduated from warsaw university in 1904, and in 1908 he became. The sierpinski triangle also with the original orthography sierpinski, also called the sierpinski gasket or sierpinski sieve, is a fractal attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. The sierpinski triangle is a fascinating design in mathematics. Sierpinskimesh is also known as sierpinski triangle and sierpinski sponge. This page was last edited on 9 december 2015, at 16. We present a topological characterization of the sierpinski triangle. Begin with a solid equilateral triangle, and remove the triangle formed by connecting the midpoints of each side. Pdf on dec 1, 2010, ismary lavandera and others published diseno. Sierpinskimesh takes the same options as meshregion, with the following additions. It is named for polish mathematician waclaw franciszek sierpinski who studied its mathematical properties, but has been used as a decorative pattern for centuries.
The sierpinski triangle cannotbe wrought without heed to the creeping tendrils of recursion. Originally constructed as a curve, this is one of the basic examples of selfsimilar setsthat is, it is a mathematically. Sierpinski picture showing fractal structure 640x480, 9. No applet seguinte podemos visualizar os primeiros sete passos da sua construcao carregando nos botoes previous stage e next stage. A topological characterization of the sierpinski triangle. All structured data from the file and property namespaces is available under the creative commons cc0 license. The sierpinski triangle page to end most sierpinski triangle pages, tan exhaustiva como definitiva y bella. This lesson will define the sierpinski triangle, observe its construction, discuss some of the patterns it contains, and take a.
Waclaw franciszek sierpinskis famous fractal forms the central point, framed by triangular side parts, which end up in a border of triangular structures. He was known for contributions to set theory research on the axiom of choice and the continuum hypothesis, number theory, theory of functions and topology. If you take of a pixel the xcoordinate as an integer, and the ycoordinate as an integer, and use the and operator on them, if the result is 0, draw a pixel of one color, otherwise another. Consequently we show that any subcontinuum of the apollonian gasket, whose boundary consists of three. Files are available under licenses specified on their description page. Polish mathematician waclaw sierpinski described the fractal that bears his name in 1915, although the design as an art motif dates at least to thcentury italy.