The most valuable part of AMM mathematics is seeing (x \times y = k) as an invariant rather than a formula to memorize. Once the marginal price (y/x) is compared with the average execution price calculated from reserve changes, slippage and price impact become much easier to understand. A useful follow-up could extend the derivation to include swap fees, explain how arbitrage brings the pool price back toward the external market price, and derive liquidity-provider returns versus simply holding the two assets. Connecting the invariant’s curvature to capital efficiency would make the mechanics even more intuitive.