MathDB

In a city, there are some buildings. We say the building

A

is dominant to the building

B

if the line that connects upside of

A

to upside of

B

makes an angle more than

45^{\circ}

with earth. We want to make a building in a given location. Suppose none of the buildings are dominant to each other. Prove that we can make the building with a height such that again, none of the buildings are dominant to each other. (Suppose the city as a horizontal plain and each building as a perpendicular line to the plain.)

Problem Statement