Recently the Spanish government announced its goal that the national high-speed railroad network (AVE) be developed so that every town in Spain is within 50 km from an AVE station. On the other hand, the estimations by the government itself are that the AVE network total length will reach 2,230 km by 2010. Are these statements compatible?
Ignoring the boundary effects, an hexagonal grid is the most efficient way to distribute points on the plane so as to maximize the area covered by circles with a fixed radius centered at the points.
R = 50 km,
r = ((√3)/2) R = 43.30 km,
A = (3(√3)/2) R2 = 6,495 km2.
L = 2r(n-1) = 6,495 km,