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. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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