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SIERPINSKI TRIANGLE

SIERPINSKI TRIANGLE. This design is called Sierpinski triangle (or gasket ), after the Polish mathematican Wacław Sierpinski who described some of its interesting properties in 1916.Among these is its fractal or self-similar character.

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SIERPINSKI TRIANGLE

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  1. SIERPINSKI TRIANGLE This design iscalledSierpinski triangle (orgasket), afterthePolishmathematican Wacław Sierpinskiwhodescribedsome of itsinterestingproperties in 1916.Among theseisitsfractalorself-similarcharacter.

  2. The arearemainingaftereach step is ¾ of the areafromtheprevious step, and an infinitenumber of stepsresultsis zero. So we cansay the area of Sierpinski triangle is zero.

  3. Construction: step one Draw an equilateral triangle with sides of 2 triangle lengths each. Connect the midpoints of each side. You have four equilateral triangles now. Cut out the triangle in the center.

  4. Step two Draw another equilateral triangle with sides of 4 triangle lengths each. Connect the midpoints of the sides and cut out the triangle in the center as before. Cut out the three small triangels in each of the three triangles On each corner – three more holes.

  5. Step three Draw an equilateral triangle with sides of 8 triangle lengths each. Follow the same procedure as before, making sure to follow the cutting pattern.

  6. References:http://serendip.brynmawr.edu/playground/sierpinski.htmlhttp://math.rice.edu/~lanius/fractals/http://pl.wikipedia.org/wiki/Tr%C3%B3jk%C4%85t_Sierpi%C5%84skiegoReferences:http://serendip.brynmawr.edu/playground/sierpinski.htmlhttp://math.rice.edu/~lanius/fractals/http://pl.wikipedia.org/wiki/Tr%C3%B3jk%C4%85t_Sierpi%C5%84skiego E-twinning project „TRIANGLES ARE EVERYWHERE” Primary School no 26 in Wrocław Adam W., Bartosz C., Tymon P.

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