# SIERPINSKI TRIANGLE - PowerPoint PPT Presentation

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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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## SIERPINSKI TRIANGLE

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

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.

### 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.

### 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.

### 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.

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%84skiego

E-twinning project „TRIANGLES ARE EVERYWHERE”

Primary School no 26 in Wrocław

Adam W., Bartosz C., Tymon P.