Points in 3D space (Related to Calculus)

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Discussion Overview

The discussion revolves around determining the number of possible connections between points in 3D space, drawing a parallel to a known formula for 2D space. Participants explore the concept of "connections" and the implications of dimensionality on combinatorial calculations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes that the equation for connections in 3D space might be the integral of the 2D formula.
  • Another participant clarifies that "connections" refers to the maximum number of straight line paths between distinct points, providing an example with 4 points in 2D.
  • A participant identifies the problem as a standard combinatorial issue, explaining that the number of ways to choose 2 points from n is given by the combination formula nC2.
  • There is a challenge regarding the terminology of "3D plane," with a participant noting that a plane is inherently two-dimensional, suggesting a need for clearer definitions.

Areas of Agreement / Disagreement

Participants express differing views on the definition of connections and the dimensionality of the problem. There is no consensus on the correct approach to extend the 2D formula to 3D space.

Contextual Notes

Participants have not fully resolved the implications of dimensionality on the combinatorial problem, and there are assumptions about the definitions of connections and planes that remain unaddressed.

Vodkacannon
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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)?
 
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Hey Vodkacannon and welcome to the forums.

What do you mean by a connection?
 
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.)
 
Last edited:
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
 
Vodkacannon said:
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.
 

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