Maximum number of triangles
Feb. 26th, 2015 12:44 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackIn Ingress, you get points for linking portals together to form triangles covering an area of the city. You contribute to your overall faction's score (ie. satisfaction but no personal benefit) according to total size, but get points for the number of triangles.
I brought this question to mathsjam, given a certain amount of resources invested in creating the links, what's the maximum number of triangles? If you ignore triangles composed of smaller triangles, someone helpfully figured out the only thing to look at is, if you make as many triangles as possible from N portals, the thing that determines how many is just, how many points are on the border, and how many are inside? So N points in a rough polygon suck for this. But N points where three of them form a triangle round all the others give you the most points for the number of portals you use.
The other question is, if you count triangles inside other triangles, what do you get? It's a common Ingress tip that if you make a small number of fields, don't bother making individual fields, wait until you find three points with another inside the triangle, and then you can get four fields from four portals (if you join all the possible links, but it only counts if you make one of the interior links last, which must be from the edge into the middle not the reverse iirc). If you're making a larger contiguous set of fields, I think it's worth creating "four portal four fields" when you can, but since you'd get three of them anyway, it's less important. And I think (not sure) things are rarely arranged so you can get multiple "four portals four fields" unless the portals are really dense (?)
I brought this question to mathsjam, given a certain amount of resources invested in creating the links, what's the maximum number of triangles? If you ignore triangles composed of smaller triangles, someone helpfully figured out the only thing to look at is, if you make as many triangles as possible from N portals, the thing that determines how many is just, how many points are on the border, and how many are inside? So N points in a rough polygon suck for this. But N points where three of them form a triangle round all the others give you the most points for the number of portals you use.
The other question is, if you count triangles inside other triangles, what do you get? It's a common Ingress tip that if you make a small number of fields, don't bother making individual fields, wait until you find three points with another inside the triangle, and then you can get four fields from four portals (if you join all the possible links, but it only counts if you make one of the interior links last, which must be from the edge into the middle not the reverse iirc). If you're making a larger contiguous set of fields, I think it's worth creating "four portal four fields" when you can, but since you'd get three of them anyway, it's less important. And I think (not sure) things are rarely arranged so you can get multiple "four portals four fields" unless the portals are really dense (?)