Quadratic Funding
Quadratic funding is a system used for situations where you have a large pool of money and want to allocate that to various public goods projects in the most "optimal" way (optimized wrt some "it's an economics paper, fine, assume homo economicus" assumptions, and calculus)
This is a decent overview of it: https://vitalik.eth.limo/general/2019/12/07/quadratic.html, but it does not explain exactly why the equation is the way it is. It has been hard to find good explanations, because in the original paper it very much reads as the result of some calculus.
If you'd like to read the original paper it's here https://www.radicalxchange.org/media/papers/liberal-radicalism.pdf. The derivation is written somewhat unintuitively.
Implementation differences
All existing Quadratic Funding implementations differ some amount from the original paper. It is the opinion of the main author of this page (archipelago) that these differences are small enough that existing implementations are still useful, but may require some caution to use effectively.
(to be continued)