SMO Senior
The outermost, largest square in the diagram has dimensions 10 x 10. Take the 4 points that each split the sides of this square into the ratio 1:5, and then connect them to get the second largest square inscribed in it.
Then, do the same with the second largest square in order to get the third largest square inscribed in it, and so on.
Continuing on this infinite process of drawing successively smaller squares swirling down into the center of the figure, what is the total area of all the squares?
The answer is 360.
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1 solution
If you work out the relation between square n to n+1, you will get the length to be:
Then you can write this out as a geometric series, as this relation is the same as you go through each square: