Career
He was a student of Carl Gustav Jacob Jacobi. He was promoted in 1831 at the Philosophical Faculty of the University of Königsberg with a dissertation on the division of the circle into 257 equal parts (see references) and was a professor there. Richelot authored numerous publications in German, French and Latin, among them — with his 1832 dissertation — the first known guide to the Euclidean construction of the regular 257-gon with compass and straightedge.
In 1825 he joined the Corps Masovia.
He died in Königsberg in 1875. Friedrich Julius Richelot: De resolutione algebraica aequationis x257 = 1, sive de divisione circuli per bisectionem anguli septies repetitam in partes 257 inter se aequales commentatio coronata.
In: Journal für die reine und angewandte Mathematik. Near 9, 1832, South. 1–26, 146–161, 209–230, und 337–358.