This work demonstrates in practical terms the evolutionary concepts and computational applications of Parametric Curves. Specific cases were drawn from higher order parametric Bezier curves of degrees 2 and above. Bezier curves find real life applications in diverse areas of Engineering and Computer Science, such as computer graphics, robotics, animations, virtual reality, among others. Some of the evolutionary issues explored in this work are in the areas of parametric equations derivations, proof of related theorems, first and second order calculus related computations, among others. A Practical case is demonstrated using a graphical design, physical hand sketching, and programmatic implementation of two opposite-faced handless cups, all evolved using quadratic Bezier curves. The actual drawing was realized using web graphics canvas programming based on HTML 5 and JavaScript. This work will no doubt find relevance in computational researches in the areas of graphics, web programming, automated theorem proofs, robotic motions, among others.

Knowledge propagation is a necessity, both in academics and in the industry. The focus of this work is on how to achieve rapid knowledge propagation using collaborative study groups. The practice of knowledge sharing in study groups finds relevance in conferences, workshops, and class rooms. Unfortunately, there appears to be only few researches on empirical best practices and techniques on study groups formation, especially for achieving rapid knowledge propagation. This work bridges this gap by presenting a workflow driven computational algorithm for autonomous and unbiased formation of study groups. The system workflow consists of a chronology of stages, each made of distinct steps. Two of the most important steps, subsumed within the algorithmic stage, are the algorithms that resolve the decisional problem of number of study groups to be formed, as well as the most effective permutation of the study group participants to form collaborative pairs. This work contributes a number of new algorithmic concepts, such as autonomous and unbiased matching, exhaustive multiplication technique, twisted round-robin transversal, equilibrium summation, among others. The concept of autonomous and unbiased matching is centered on the constitution of study groups and pairs purely based on the participants' performances in an examination, rather than through any external process. As part of practical demonstration of this work, study group formation as well as unbiased pairing were fully demonstrated for a collaborative learning size of forty (40) participants, and partially for study groups of 50, 60 and 80 participants. The quantitative proof of this work was done through the technique called equilibrium summation, as well as the calculation of inter-study group Pearson Correlation Coefficients, which resulted in values higher than 0.9 in all cases. Real life experimentation