Points in 3D space (Related to Calculus)

[Vodkacannon]

The equation for the number of possible connections between n points on a 2D plane is (n-1)*(n/2).
What is the equation for the number of possible connections between n points on a 3D plane?
Is it the intregal of (n-1)*(n/2)?

 

[chiro]

Hey Vodkacannon and welcome to the forums.

What do you mean by a connection?

 

[Vodkacannon]

Hi. I hope to add good questions and discussions to this web site.

What I mean by "how many connections" is the maximum possible number of straight line paths between two different points.

Essentially you are creating a network of points.

For example, given 4 points on a plane p (that do not lie directly on top of each other by the way), the number of straight lines that can connect from one point to another is 6.
(4-1)*(4/2) = 6

(I'm sorry this probably is in the wrong forum after all.)

 

[chiro]

Well this is a standard combinatoric problem: you have n things in total and want to find the number of ways you can choose 2 things from those n.

Combinations do not care about order (i.e {1,2} is the same as {2,1}) which is the property required for your lines (you don't care about the start and end points, just the connection itself) and this is given by nC2 or

nC2
= n!/2!(n-2)!
= n(n-1)(n-2)!/2!*(n-2)!
= n*(n-1)/2

 

[Mark44]

The equation for the number of possible connections between n points on a 2D plane is (n-1)*(n/2).
What is the equation for the number of possible connections between n points on a 3D plane?

What do you mean by a "3D plane"? A plane is a two-dimensional object. You can have a plane in three-dimensional space, but it is still a plane.