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Sierpinski Triangle

Sierpinski Triangle. Kendal, Matt, Heather, Caitlin. History. Discovered by Waclaw Sierpinski in 1916 Born in 1882, Warsaw, Poland Also known as Sierpinski Gasket Appeared in Italian art in 13 th century. Stage one. Stage five. Stage three. Stage seven. Stage six. Stage two.

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Sierpinski Triangle

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  1. Sierpinski Triangle Kendal, Matt, Heather, Caitlin

  2. History • Discovered by Waclaw Sierpinski in 1916 • Born in 1882, Warsaw, Poland • Also known as Sierpinski Gasket • Appeared in Italian art in 13th century.

  3. Stage one Stage five Stage three Stage seven Stage six Stage two Stage four

  4. Formulas • Number of new holes. • Nn=3n-1 • Number of total holes. ∞ • Nn=Σ3n-1 n=1

  5. Formulas cont. • Length of a side of a triangle. - Ln = (.5s)n • Area of a new hole. • An=(.25an-1)

  6. LIMIT • Area of holes goes towards the area of the 1st iteration • Area of whole triangle goes towards 0

  7. Chaos Game • This will create the sierpinski triangle. • The example

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