bonanova 83 Report post Posted December 14, 2017 The area of the triangle is 1. What is the area of the white portion? Quote Share this post Link to post Share on other sites
1 ThunderCloud 5 Report post Posted December 15, 2017 Spoiler This looks like a Sierpinski triangle. It can be defined iteratively by removing the "middle triangle" from the figure, then the "middle triangles" of the remaining 3 triangles, then the middles of those... At each step, the shaded portion is 3/4 of what it was before. So the area of the remaining shaded portion after N steps is (3/4)^{N}. If continued ad infinitum, the limit is zero. Therefore the area of the shaded portion is zero, and the white portion must then be 1. Quote Share this post Link to post Share on other sites
0 Donald Cartmill 2 Report post Posted December 26, 2017 Area of white to 3 places is = 0.763 Quote Share this post Link to post Share on other sites
0 Donald Cartmill 2 Report post Posted December 26, 2017 Area of the white is = 1 (1/4) + 9(1/4 x 1/4 ) + 27 ( 1/4 x 1/4 x 1/4) + 81 ( 1/4 x 1/4 x 1/4 x 1/4 ) The lowest common multiple of all of the divisors is 1024 or 4 x 4 x 4 x 4 Area of the white is = 256/1024 + 192 / 1024 +144/1024 +108/1024 + 81/1024; Totaling these =781 / 1024 then dividing 1024 into 781 you get 0,762695313 rounding off to 3 places = 0.763 Quote Share this post Link to post Share on other sites
The area of the triangle is 1. What is the area of the white portion?
Share this post
Link to post
Share on other sites