We improve the current best bound for distinct distances on non-ruled algebraic surfaces in $${\mathbb {R}}^3$$ . In particular, we show that n points such a surface span $$\Omega (n^{32/39-{\varepsilon }})$$ distances, any $${\varepsilon }>0$$ Our proof adapts of Székely planar case, which is based crossing lemma. As part our surfaces, also obtain new results between circles Consider two point...

Abstract This research concerns the use of warped ruled surfaces in load bearing structures 19th century stone bridges Prague. The descriptions a skew arch used at Negrelli Viaduct and special surface called “corne de vache” Legion Bridge are based not only on historical survey, archival materials period publications, but also contemporary measurements.