We study Lagrange spectra arising from intrinsic Diophantine approximation of circles and spheres. More precisely, we consider three circles embedded in $\mathbb{ R}^2$ or $\mathbb{ R}^3$ and three spheres embedded in $\mathbb{ R}^3$ or $\mathbb{ R}^4$. We present a unified framework to connect the Lagrange spectra of these six spaces with the spectra of $\mathbb{ R}$ and $\mathbb{ C}$. Thanks to prior work of Asmus L.~Schmidt on the spectra of $\mathbb{ R}$ and $\mathbb{ C}$, we obtain as a corollary, for each of the six spectra, the smallest accumulation point and the initial discrete part leading up to it completely.
Categories: math.NT math.DS