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.
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.