Problem of the Week 992

Looking Down the Road

Imagine a straight road with some uniformly spaced telephone poles alongside the road. If a photograph is taken looking straight down the road or even if one just looks down the road, the two edges of the road will converge (in the image) to a single point, and the telephone poles too will converge to that point. This means that, in the image, the spacings between the poles form a convergent infinite series. What convergent series is it?

Marc Frantz, Mathematics Magazine, Oct. 1998, 71:4 313-314.

© Copyright 2003 Stan Wagon. Reproduced with permission.

9 October 2003