The Sierpinski triangle (pictured below) is a fractal image. The original figure is an equilateral triangle. In each step, the computer splits every triangle in the design into 444 congruent equilateral triangles, and removes the center one from the design. The area remaining in a particular design after nnn steps can be shown using the following expression:
\qquad\dfrac{25\sqrt{3}}{2}\cdot\left(\dfrac{3}{4}\right)^n
2
25
3
⋅(
4
3
)
n
start fraction, 25, square root of, 3, end square root, divided by, 2, end fraction, dot, left parenthesis, start fraction, 3, divided by, 4, end fraction, right parenthesis, start superscript, n, end superscript
The image shows 4 triangular figures, which represent the Sierpinski triangle fractal at 0, 1, 2, and 3 iterations.
The original triangular figure is an equilateral triangle which is entirely shaded. The triangular figure labeled n = 1 is formed by subdividing the original triangle into 4 congruent triangles and removing the middle triangle. The triangular figure for n = 2 is formed by subdividing each of the congruent triangles from the figure labeled n = 1 into 4 congruent triangles and removing the middle triangles.
The triangular figure for n = 3 is formed by subdividing each of the congruent triangle from the figure labeled n = 2 into 4 congruent triangles and removing the middle triangles.
The image shows 4 triangular figures, which represent the Sierpinski triangle fractal at 0, 1, 2, and 3 iterations. The original triangular figure is an equilateral triangle which is entirely shaded. The triangular figure labeled n = 1 is formed by subdividing the original triangle into 4 congruent triangles and removing the middle triangle. The triangular figure for n = 2 is formed by subdividing each of the congruent triangles from the figure labeled n = 1 into 4 congruent triangles and removing the middle triangles.
The triangular figure for n = 3 is formed by subdividing each of the congruent triangle from the figure labeled n = 2 into 4 congruent triangles and removing the middle triangles.
What does \dfrac{25\sqrt{3}}{2}
2
25
3
start fraction, 25, square root of, 3, end square root, divided by, 2, end fraction signify in the expression?
