Center of Mass Operation is Associative

Theorem

Let $S$ denote the set of massy particles in ordinary space.

Let $\circ$ denote the binary operation defined as:

$\forall x, y \in S: x \circ y =$ the center of mass of $x$ and $y$


Then $\circ$ is an associative operation.


Proof


This theorem requires a proof.
In particular: Apparently it's equivalent to Ceva's Theorem.
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Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Ceva's theorem
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Ceva's theorem
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