This paper, the second of a two part article, expands on an idea that appeared in literature in the 1950s to show that by restricting the domain to those complex numbers that map onto real numbers, representations of functions other than the ones in the real plane are obtained. In other words, the well-known curves in the real plane only depict…

This paper, the first of a two-part article, follows the trail in history of the development of a graphical representation of the complex roots of a function. Root calculation and root representation are traced through millennia, including the development of the notion of complex numbers and subsequent graphical representation thereof. The…

Quadrature methods for approximating the definite integral of a function f(t) over an interval [a,b] are in common use. Examples of such methods are the Newton-Cotes formulas (midpoint, trapezoidal and Simpson methods etc.) and the Gauss-Legendre quadrature rules, to name two types of quadrature. Error bounds for these approximations involve…