Square in Square in Square

Geometry Level 4

Consider a sequence of squares inscribed within each other to infinity. The squares are alternatively colored blue and yellow.

What proportion of the figure will be colored blue?

4 5 \frac{4}{5} 3 4 \frac{3}{4} 2 3 \frac{2}{3} 1 2 \frac{1}{2}

Chung Kevin by Chung Kevin , 46, Australia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Archit Agrawal
Sep 30, 2016

Take the big sq of 1*1. Then the area of blue sq will be 1-1/2+1/4-1/8..... =1/2+1/8+1/32..... =1/2(1+1/4+1/16.....) =1/2(1/(1-1/4)) =1/2×4/3 =2/3

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you do it without considering an infinite series?

Use the fact that the picture is self-similar.

Chung Kevin - 4 years, 8 months ago

Log in to reply

Let the bigger square be 1 1. Let fraction of blue area of bigger sq be a=a 1, so similarly fraction of are of yellow sq of just smaller sq will be a=a*1/2. So a+a/2=1 a=2/3.

Archit Agrawal - 4 years, 8 months ago

Log in to reply

Not are, it's area. And its 1*1 not 11.

Archit Agrawal - 4 years, 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...