Take the remaining squares. Take the remaining squares. Divide it into 9 equal-sized squares. It can be constructed using string rewriting beginning with a cell and iterating the rules (1) Students might not realize that the last figure is the same size as the others, just zoomed in to better see the details. If they haven't, part (d) will be very challenging. Divide each one into 9 equal squares. You keep doing it as many times as you want. So the area of the figure is $$\frac{8^2}{9^2}=\frac{64}{81}$$When we divide each square of the figure in part (b) into 9 smaller, equal-sized squares, each new square will have area $\frac19$ of the area the square it was made from, which is $\frac{1}{9^2}$. So the area of the figure is $$\frac89$$When we divide the smaller squares each into 9 new (even smaller), equal-sized squares, each of the new squares will have area $\frac19$ of the area of the square it was made from (which also happens to be $\frac19$). Sierpinski carpet is a fractal that consists of rectangular shapes javascript webgl canvas graphics computer-graphics shader fractal sierpinski sierpinski-carpet Updated on May 10, 2018 Remove the middle one. Given the complexity of the task, this would be a good activity for students to work on in groups. So the area of the figure is $$\frac{8^3}{9^3}=\frac{512}{729}$$Take a square with area 1.
If we remove one, there will be 8 left. $$4+\frac43+8\cdot\frac49+64\cdot\frac{4}{27}$$ In this project, I wrote a shader-based WebGL program which will generate Sierpinski carpet. There are $8\cdot8\cdot8=8^3 = 512$ of these squares ($8 \cdot 8$ is the number of squares being subdivided and the other factor of 8 is the number of new squares these are divided into). Produce a graphical or ASCII-art representation of a Sierpinski carpetof order N. For example, the Sierpinski carpet of order 3 should look like this: The use of the # character is not rigidly required for ASCII art. Sierpiński, W. "On Curves Which Contain the Image of Any Given Curve." So the area of these even smaller squares is $\frac19\cdot\frac{1}{9^2}=\frac{1}{9^3}=\frac{1}{729}$. Fractal Squares.svg 320 × 320; 2 KB. Remove the middle one from each group of 9. Allouche, J.-P. and Shallit, J. Divide each one into 9 equal squares. Because students are most likely to find an answer to part (d) by noting that at each step all squares are replaced by 8 squares that are $\frac19$ as big, this task naturally engages students in MP8, Look for and express regularity in repeated reasoning. Another solution approach students might take is to subtract the "holes" left by removing squares from 1, and it would be instructive for students who approach this task in different ways to compare their solutions to verify they give the same results.The figures students are generating at each step are the figures whose limit is called "Sierpinski's carpet." A very challenging extension is to ask students to find the perimeter of each figure in the task. Divide it into 9 equal-sized squares. Note that the perimeter includes the lengths of the edges of the "holes" that are left by removing the "middle square in each group of 9." Divide each one into 9 equal squares. The purpose of this task is to help motivate the usefulness of exponential notation in a geometric context and to give students an opportunity to see that sometimes it is easier to write a number as a numeric expression rather than evaluating the expression, which is an important facet of MP7, Look for and make use of structure. Es ist verwandt mit dem Sierpinski-Dreieck und dem Menger-Schwamm. Divide each one into 9 equal squares. Engage your students with effective distance learning resources. Catifa Sierpinski.png 462 × 461; 4 KB. Take the remaining 8 squares.