2. Waclaw Sierpinski Born in Warsaw, Poland in 1882. 1919- promoted to professor at Warsaw in mathematics and physics. 1920- founded math journal- Fundamenta Mathematica– specialized in set theory. Retired in 1960 and was given many awards. Died in 1969.

3. Sierpinski’s Carpet Go to http://www.shodor.or g/interactivate/activiti es/carpet/index.html Go to http://www.shodor.or g/interactivate/activiti es/carpet/index.html http://www.shodor.or g/interactivate/activiti es/carpet/index.html http://www.shodor.or g/interactivate/activiti es/carpet/index.html

4. Side Length & Area of Removed Square After 1 st iteration, what is the length of the removed square? What is the area of this square? After 2 nd iteration, what is the length of removed square? What is the area? After 3 rd,….? See any patterns? Write the formulas for side length & area of a removed square.

5. Number of Removed Squares After 1 st iteration, how many squares have been removed? After 2 nd iteration, how many squares have been removed? After 3 rd iteration, how many squares have been removed? See any patterns? Write down the formula for determining the number of removed squares.

6. Total Area Remaining  With no iterations, what is the area remaining of the figure.  After the 1 st iteration, how would you find the area remaining?  After the 2 nd iteration, what is the area remaining of the figure?  After the 3 rd,…?  What patterns do you see? Write down the explicit formula for the area remaining.

7. Area Removed How would we find the total area of the squares we removed? How would we find the total area of the squares we removed? What relationship is there between the area remaining and the area removed? What relationship is there between the area remaining and the area removed?

8. Limit of the Remaining Area  Using the formula of total area remaining, what is the limit if we send ‘n’ to infinity?

9. The End