4. A Sierpinski triangle can be created by starting with an equilateral triangle, breaking the triangle into 4 congruent equilateral triangles, and then removing the middle triangle. Starting from a single black equilateral triangle with an area of 256 square inches, here are the first four steps: a. Complete this table showing the number of shaded triangles in each step and the area of each triangle. step number of area of each shaded triangle number shaded triangles in square inches 1 256 192 128 164 81 1 9. 27 81 243 b. Graph the number of shaded triangles as a function of the step number, then separately graph the area of each triangle as a function of the step number. c. How are these graphs the same? How are they different? 3.
4. A Sierpinski triangle can be created by starting with an equilateral triangle, breaking the triangle into 4 congruent equilateral triangles, and then removing the middle triangle. Starting from a single black equilateral triangle with an area of 256 square inches, here are the first four steps: a. Complete this table showing the number of shaded triangles in each step and the area of each triangle. step number of area of each shaded triangle number shaded triangles in square inches 1 256 192 128 164 81 1 9. 27 81 243 b. Graph the number of shaded triangles as a function of the step number, then separately graph the area of each triangle as a function of the step number. c. How are these graphs the same? How are they different? 3.
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.1: Area And Initial Postulates
Problem 3E: Consider the information in Exercise 2, but suppose you know that the area of the region defined by...
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