# Stable Math

First introduced by Curve, the Stableswap is a hybrid algorithm, to bring solution to the problems of slippage and fixed liquidity. The Stableswap hybrid combines both

**Constant Product**and**Constant Sum**models, and the following chart shows the Stableswap algorithm in relation to constant product and constant sum invariants.The

*amplification parameter*,$A$

, defines the degree to which the Stable Math curve approximates the Constant Product curve (when $A=0$

), or the Constant Sum curve (when $A\rightarrow \infty$

). **Constant Sum:**When the liquidity pool portfolio is balanced, the algorithm functions as a Constant Sum formula;**x + y = k**. You can observe the StableSwapstaying close to the Constant Sum*blue line*, and the price is stable.*red line***Constant Product:**As the liquidity pool portfolio becomes imbalanced, the StableSwap algorithm functions as a Constant Product formula;**x * y = k**. You can observe the StableSwapnow resembling the Constant Product*blue line*, and the price becoming expensive.*purple line*

Since the Stable Math equation is quite complex, determining the invariant,

$D$

, is typically done iteratively.$A \cdot n^n \cdot \sum{x_i} +D = A \cdot D \cdot n^n + { \frac{D^{n+1}}{{n}^{n}\cdot \prod{x_i} } }$

Where:

- $n$is the number of tokens
- $x_i$is is balance of token$i$
- $A$is the amplification parameter

Last modified 1yr ago