Curvature prevalently exists in the world of carbon materials (e.g, fullerenes, buckyl bowls, carbon nanotubes, and onions), but traditional C2-addition mechanisms fail to elucidate the mechanism responsible for the formation of carbon curvature starting from a pentagonal carbon ring in currently available chemical-physical processes such as combustion. Here, we show a complete series of nascent pentagon-incorporating C-5-C-18 that are online produced in the flame of acetylene cydopentadiene oxygen and in situ captured by C-60 or trapped as polycyclic aromatic hydrocarbons for darifying the growth of the curved subunit of C20H10. A mechanism regarding Cl-substitution and C2-addition has been proposed for understanding the formation of curvature in carbon materials, as exemplified by the typical curved molecule containing a single pentagon completely surrounded by five hexagons. The present mechanism, supported by the intermediates characterized by X-ray crystallography as well as NMR, has been experimentally validated for the rational synthesis of curved molecule in the commercially useful combustion process.