Posted by **JOE** on Wednesday, February 10, 2010 at 8:54pm.

Hello,

Here is a question with something i've never heard of.

These are the first two stages of a fractal known as the Sierpinski carpet. The carpet begins with a square (stage 1). The square is cut into 9 congruent squares and the middle square is removed (stage 2).

Draw stage 3 using the method described to get from stage 1 to stage 2.

To the nearest whole percent, what percent of the original square remains in stage 3? Show your work and explain your answer.

- math -
**JOE**, Wednesday, February 10, 2010 at 9:17pm
ok, I realize that I should cut each remaining square into 9 quadrants leaving the middle open of each of them.

Now, I just dont know how to get the percent of the original square that remains in stage 3.

- math -
**Damon**, Wednesday, February 10, 2010 at 9:17pm
In stage one say the square is 9 units by 9 units thus 81 square units in area.

Then we cut it into 9 units each 3 units by three units so each 9 square units in area. We remove one so we only have 8 left each 9 square units in area.

Now for stage 3 we split each of those 8 squares into 9 squares each one unit by one unit or one unit square. We now divide one of those 1 by 1 squares into 9 squares each 1/3 by 1/3 so we can remove the middle one. The area left is 1 minus the middle which is 1/3*1/3 = 1/9 so it is 8/9

so we started with a square of 9 by 9 or 81 square units and now we have a little square with area of 8/9 square units so

(8/9)/81 is the ratio of area of one of the final little carpets to the original carpet.

- math -
**Damon**, Wednesday, February 10, 2010 at 9:20pm
Remember you have 8 of those little carpets.

- math -
**Damon**, Wednesday, February 10, 2010 at 9:25pm
This might help, nice drawing of it.

(Broken Link Removed)

## Answer This Question

## Related Questions

- Math - Carpet plus installs carpet for $100 plus $8 per square yard of carpet. ...
- geometry - you plan to carpet 468ft of space. carpet costs $26.75 per square ...
- math - A simple fractal tree Grows in stages. A each new stage, two new line ...
- Math - Mr. Carpenter sent his wife to the store to buy 200 square feet (A) of ...
- Math - LeAnn is a carpet layer. She has agreed to carpet a house for $18 per ...
- maths - The Park's are buying new carpet for their house.They need about 1,175 ...
- Math - A contractor buys 14 yd of nylon carpet and 20 yd of wool carpet for $...
- math - . A respondent tells you she just bought living room carpet which is 20 ...
- geometry - FredFred wants to carpet his room that measures 12ft by 15ft. The ...
- math - Ramon is to carpet the bedroom and the living rpom of his apartment. Find...

More Related Questions