SERPINSKI TRIANGLE

Source=http://www.visionol.net/~jy/serp.htm

Next, let's discuss the area of what you have drawn. Let's assume that the area of your original triangle is one unit and the shaded area is that which is left after cutting out the upside-down triangles. Think about how you would complete the table below. Look for a pattern in the numbers.

Area of Serpinski Triangle
Stage	0	1	2	3	4	n
Area Shaded	1	?	?	?	?	?

Now think about what the total area of the shape would be as n goes to infinity. Check if your numbers are getting bigger or smaller.

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PERIMETER

Now let's think about how much the perimeter changes at each stage. Let's assume that each side of our triangle is one unit. Next think about the answers for the below stages. Again, look for a pattern. Is there some number you multiply by each time? How can you symbolize the perimeter of the nth stage?

Perimeter of Serpinski Triangle
Stage	0	1	2	3	4	n
Perimeter of Figure	3	?	?	?	?	?

What happens to the perimeter of the figure as n approaches infinity? Explain why.

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