/sci/ - Science & Math

I came up with an interesting math problem.

The idea is that you have a road construction company. The square grid in picrelated represents a grid of cities - each dot in one square is a city. The government asks you to build roads such that the network of roads makes it possible to travel from any city to any other city. But building road costs money. So you want to minimize the amount of road that you must build to connect the cities.

The problem is this. How long is the minimized road for the n:th grid? For example, if n=7, then the number of cities is 49. Also assume that the distance between two adjacent cities (horizontally/vertically) is one unit.

I already put the correctsolution for n=2 where the road is marked with the red line. For n=2 you could solve the length of the road with some basic trigonometry but I have no idea how you would do it for the general case.

I came up with an interesting math problem.

The idea is simply put, that you have a road construction company. The square grid in picrelated represents a grid of cities - each dot in one square is a city. The government asks you to build roads such that the network of roads makes it possible to travel from any city to any other city. But building road costs money. So you want to minimize the amount of road that it takes to connect the cities.

The problem is this. How long is the minimized length of road that you have to make for the n:th city? For example, if n=7, then the number of cities is 49. Also assume that the distance between two adjacent cities (horizontally or vertically) is one unit.