This research is concerned with studying the representations of event in drawings ancient civilizations world, and consists two axes, axis theoretical framework, which included (the problem, its aim, limits, definition terminology). The aims to reveal how pattern was formulated by artist on surface his visual achievement, limits search were spatial Iraq, Egypt, Greece Rome, but temporal could n...

Since the time of ancient Greece and India, Pell’s equation, a2 − db2 = 1, has been studied and its solutions sought after. These solutions are significant, because they correspond to the units of the rings Z[ √ d]. Along with prime numbers, units are vital in understanding the structure and especially the factorization within different rings. Dirichlect’s Unit Theorem establishes the structure...