The HGRAM graphical format—its geometrical interpretation and its applications

Abstract

Most deterministic engineering problems could be solved either analytically or graphically. As not all problems could be solved in closed forms, numerical methods have to be used. Analytical methods enable users to manipulate multivariable equations by rote without much insight into the inter‐relations between these variables. Educators who teach matrix methods of solving engineering problems, from structural analysis to state‐space equations, will attest to this unsatisfactory experience. To visualize such inter‐relationships one has to rely on graphical plots. Unfortunately it is difficult to present more than three variables on one graph unless one uses multiple graph plots. Although a graphical method is more visual and intuitive, it cannot be extended to problems with more than three variables. The author solved this problem using a multiaxis graph‐paper called the HGRAM which has no upper limit on the number of variables which could be assigned to the axes [1]. Here are discussed some fundamental aspects of the HGRAM graphical format and shows some applications using it. The author has found a long list of potential applications for the HGRAM [2—4]. Graphical methods, being visual, demand less aptitute in higher mathematics and therefore should be considered by educators when facing a ‘mixed’ class with different levels of mathematical aptitude. This situation is prevalent in most educational institutes other than the handful of premier institutes which can pick and choose their candidates. The author believes that ultimately the HGRAM graphical method will be adopted in the teaching of a wide spectrum of technical subjects.