This document shows a different way of adding lists of numbers to find a way of getting general formulae for figurate numbers and use Gauss?s method to check it.

In this note we give closed forms for a class of logarithmic integrals in terms of Bernoulli polynomials. This provides a method for unifying a large class of definite integrals.

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but…

Everyone is familiar with the concept that the cube and octahedron, dodecahedron and icosahedron are dual pairs, with the tetrahedron being self-dual. On the face of it, the concept seems straightforward; however, in all but the most symmetrical cases it is far from clear. By using the computer and three-dimensional graphics programs, it is…