MathDB

13

Part of 2017 ASDAN Math Tournament

Problems(1)

2017 Guts #13

Source:

11/25/2022
Let S1S_1 be a square of side length 33. For i=2,3,4,…i=2,3,4,\dots, inscribe a square SiS_i inside Si−1S_{i-1} such that the sides of the inner square form four 30∘−60∘−90∘30^\circ-60^\circ-90^\circ triangles with the outer square. Compute the total sum ∑i=1∞area(Si).\sum_{i=1}^\infty\text{area}(S_i).
2017Guts Round