Scientific computing over the Web in various programming languages: Solving problems in Fortran, C, and Octave

Scientific computing over the Web is presented to solve two problems in various programming languages, classical (Fortran 90, and C), and modern (Octave). The problems, with surprising results, are applications of numerical computation, so as to be adequate to all these languages: a certain simple series, with a mathematical conjecture on its limit; and the distance to random points in a circle. The objective of this work is twofold: to emphasize the pertinence of the Web for scientific computing, and to illustrate the productiveness of the modern languages. The authors' opinion is that scientific computing over the Web has lagged behind most of its other uses, and is particularly recommended, namely, in academy, in industry, and in their connection.