2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/49988We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Apéry sums). The study of non-alternating sums leads to an investigation of different types of sums which we call multiple Clausen values. The study of alternating sums leads to a tower of experimental results involving polylogarithms in the golden ratio. In the non-alternating case, there is a strong connection to polylogarithms of the sixth root of unity, encountered in the 3-loop Feynman diagrams of {\tt hep-th/9803091} and subsequently in hep-ph/9910223, hep-ph/9910224, cond-mat/9911452 and hep-th/0004010.17 pages, LaTeX, with use of amsmath and amssymb packages, to appear in Journal of Experimental MathematicsHigh Energy Physics - TheoryClassical Analysis and ODEstext