Sierpinski Triangle: Equilateral or Isosceles?

  • Thread starter omega-centauri
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In summary, a Sierpinski Triangle is a fractal shape that is created by dividing an equilateral or isosceles triangle into smaller triangles and removing the middle triangle. It can be either equilateral or isosceles, depending on the starting triangle. Some properties of a Sierpinski Triangle include an infinite perimeter and a finite area, as well as self-similarity at any level of magnification. This shape is created by repeatedly dividing and removing triangles, and it can be found in nature and used in computer graphics as a representation of chaos and self-similarity in mathematics and physics.
  • #1
omega-centauri
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Is the Sierpinski triangle composed of equilateral or isosceles triangles? I've seen references for both but I have a student asking which one it is... any help is here greatly appreciated.

Isosceles example: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=5524998&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F5492939%2F5524731%2F05524998.pdf%3Farnumber%3D5524998

Thanks in advance!
 
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  • #2
Doesn't matter, all kind of triangles can be used.
 
  • #3
Visual comfort and readability would correlate with isosceles. Bilateral symmetry is important. Equilateral also would work well.
 

1. What is a Sierpinski Triangle?

A Sierpinski Triangle is a fractal shape that is created by repeatedly dividing an equilateral or isosceles triangle into smaller triangles and removing the middle triangle.

2. Is a Sierpinski Triangle always equilateral or isosceles?

No, a Sierpinski Triangle can be either equilateral or isosceles depending on the starting triangle used. If the starting triangle is equilateral, then the resulting fractal will also be equilateral. If the starting triangle is isosceles, then the resulting fractal will also be isosceles.

3. What are the properties of a Sierpinski Triangle?

A Sierpinski Triangle has an infinite perimeter and a finite area. It is also self-similar, meaning that at any level of magnification, the smaller triangles within the fractal will look similar to the larger triangle.

4. How is a Sierpinski Triangle created?

A Sierpinski Triangle is created by dividing a triangle into smaller triangles and then removing the middle triangle. This process is repeated for each remaining triangle, resulting in a fractal pattern.

5. What are some real-world applications of Sierpinski Triangles?

Sierpinski Triangles can be found in nature, such as in the formation of coastlines and mountain ranges. They are also used in computer graphics and as a visual representation of chaos and self-similarity in mathematics and physics.

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