Hi PF! A friend asked me to look at a problem, said it was on his mind. Rather than restate it here (since a picture helps) please check out the attachment. I drew a picture in tikZ and gave my attempt at a solution, but something in my gut feels the answer is infinite. I'd love to talk with someone about it after you look over my work. My question is, is the sum of all the triangles really infinite? If so, what's wrong with my reasoning on the attachment? Thanks!