So it looks like people can't sit in a circle,....
Ha ha ha ha ha. The hilarity never ends on ELU. You see, it's funny because, well, never mind.
Obviously what's required is the development of a theory of circle sitting or circumsituation, if you will.
Axiom 1: Two people can't sit in a circle.
Now, for this metaphor to make sense, the circle must be of sufficient diameter:
Axiom 2: For people to sit in a circle, the circle must have a minimum radius r.
If a circle is too small, then the people will just be seen as a bunch or crowd. We'll leave r unspecified, but for purposes of estimation, let's say that r = A*m/2*π, where m is the minimum number of circumsituents anyone could propose, and A represents a reasonable arm's length between circumsituents.
Theorem 1: There is some number of people who can sit in a circle. Proof: Take a circle of radius at least r and add people to the circumference until each person's shoulders touch another person.
Definition 1. An even number of people are sitting in a circle C of radius at least r, if every circumsituent sits on the circumference of C equidistant in arc length on C from his neighbors, and his line of sight through the center of C includes another circumsituent.
Definition 2. An odd number N of people are sitting in a circle C of radius at least r, if N-1 people can sit in the circle C.
Theorem 2: 3 people cannot sit in a circle.
The proof is left as an exercise for the reader. Hint: Apply Definition 2.