sum of the areas of the removed squares from 9 squares of unit square
Source: Eotvos 1905 p2
September 6, 2024
geometryareas
Problem Statement
Divide the unit square into equal squares by means of two pairs of lines parallel to the sides (see figure). Now remove the central square. Treat the remaining squares the same way, and repeat the process times.(a) How many squares of side length remain?
(b) What is the sum of the areas of the removed squares as becomes infinite?
https://cdn.artofproblemsolving.com/attachments/7/d/3e6e68559919583c24d4457f946bc4cef3922f.png