2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154291We reconsider the Euclidean version of the photon number integral introduced in ref 1. This integral is well defined for any smooth non-self-intersecting curve in $\R^N$. Besides studying general features of this integral (including it s conformal invariance), we evaluate it explicitly for the ellipse. The result is $n_{ellipse}=(ξ^{-1}+ξ)π^2$, where $ξ$ is the ratio of the minor and major axes. This is in agreement with the previous result $n_{circle}=2π^2$ and also with the conjecture that the minimum value of $n$ for any plane curve occurs for the circle.13 pages including one figureMathematical Physicstext