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Infinite carpet square math.
An infinitely recurring square root asked by gopikrishna srinivasan on friday nov 24 1995.
A sierpinksi carpet is one of the more famous fractal objects in mathematics.
These carpet tiles are made from recycled materials are commercially rated and are outdoor approved the installation possibilities are also infinite.
Looking at the carpet.
Infinite carpet tiles are just that infinite possibilities.
What is the sqrt 1 sqrt 1 sqrt 1.
Suppose by contradiction that there is a point p in the interior of the carpet.
Remove the middle one.
My name is krishna.
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The interior of the carpet is empty.
Take a square with area 1.
Start with a square divide it into nine equal squares and remove the central one.
Multi 1 multi 1 facet value.
Then there is a square centered at p which is entirely contained in the carpet.
Before when i was in the math club they posed a question.
The figures students are generating at each step are the figures whose limit is called sierpinski s carpet this is a fractal whose area is 0 and perimeter is infinite.
Creating one is an iterative procedure.
A very challenging extension is to ask students to find the perimeter of each.
Carpet square yardage carpet square footage 9.
The area of the carpet is zero in standard lebesgue measure.
It is constructed by removing the center one ninth of a square of side 1 then removing the centers of the eight smaller remaining squares and so on.
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Also note that the sqrt sign is within the sqrt sign and so on.
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To get the total square yardage divide that number or the total square footage by nine.
The square root is abbreviated with sqrt.
Divide it into 9 equal sized squares.
The figure below shows the first three steps of the construction.