Asymptotes rhymes with:
anecdotes, banknotes, booknotes, euronotes, ferryboats, footnotes, gunboats, houseboats, keynotes, lifeboats, overcoats, petticoats, raincoat's, raincoats, redcoats, riverboat's, riverboats, sailboats, scapegoats, showboat's, speedboats, steamboats, tugboats