I've encountered a problem which I have some idea of solving but am befuddled on how to proceed. Here is the full problem:
Suppose that you wish to cover a 1-km radius, spherical planet with Wi-Fi signal. In order to do this, you have an unlimited number of antennae that cover circular, 35-meter radii areas and transmit signal between themselves as long as the intersection of their areas is equal to or greater than 10m^2. What is the minimum amount of antennae needed to completely cover the planet with Wi-Fi?
So far, I've reasoned that the problem basically boils down to finding an algorithm that will minimise the number of circular areas needed to completely cover the sphere, as long as each circle intersects another with an area of at least 10m^2. However, this resembles nothing I've been currently studying, so I have no idea where to start. I'm assuming integrals must somehow come into play, but have no idea how that logic would go.