Radical insight into how and why Gauss nodes work using alternative non-polynomial vectors presented in a simple argument. In fact, the Runge-vector solution (arguably the most important solution presented in GNR), is fully accessible to high school mathematics. And conventional Gauss-Legendre nodes generate as one of an infinite number of approaches to the Runge-vector solution.

Radical insight into how and why Gauss nodes work using alternative non-polynomial vectors presented in a simple argument. In fact, the Runge-vector solution (arguably the most important solution presented in GNR), is fully accessible to high school mathematics. And conventional Gauss-Legendre nodes generate as one of an infinite number of approaches to the Runge-vector solution.