  Using Coulomb correlation parameters appropriate for $\pi$-conjugated
polymers (PCPs), and a nearest neighbor hopping integral that is arrived at by
fitting the energy spectra of three zigzag semiconducting single-walled carbon
nanotubes (S-SWCNTs), we are able to determine quantitatively the exciton
energies and exciton binding energies of 29 S-SWCNTs within a semiempirical
$\pi$-electron Hamiltonian that has been widely used for PCPs. Our work
establishes the existence of a deep and fundamental relationship between PCPs
and S-SWCNTs.
