Re:Gabriel's Horn
by davidrusu on Tuesday June 16, 2015 @11:31PM
(#9729942)
This reminds me of a Putnam problem from a few years back, was something along the lines of:
Construct a set of discs in R^2 s.t. no infinite straight line can be drawn without intersecting at least one disc, and the sum of the areas of all the discs is finite.
Re:Gabriel's Horn
by cousin_it on Wednesday June 17, 2015 @03:32AM
(#9730458)
Take a set of discs with radii 1/n. Their total area is finite but the sum of radii is infinite, so we can just use them to cover the X and Y axes. Yeah, this is pretty similar to Gabriel's horn.
Construct a set of discs in R^2 s.t. no infinite straight line can be drawn without intersecting at least one disc, and the sum of the areas of all the discs is finite.