alt Hacker News> together rectangles with height one and width decreasing in geometric progression
The geometric series sums to 2 - your glued together rectangles will have perimeter 2*(1+2) and area 2*1.
> together rectangles with height one and width decreasing in geometric progression
The geometric series sums to 2 - your glued together rectangles will have perimeter 2*(1+2) and area 2*1.
> your glued together rectangles will have perimeter 2*(1+2)
No. You should think through that perimeter calculation one more time, preferably while drawing a picture.
Here's a hint: the perimeter of a rectangle is no less than its height; you can glue so that the perimeter of each rectangle contributes at least 1 to the perimeter of the union.