Al-Farabi's mathematical legacy and algorithmic approach to resolving problems regarding geometrical constructions in geogebra environment

Abstract

Al-Farabi had left a rich scientific heritage for the succeeding generations including studies in various scientific areas. So far, his proceedings are still valuable being of great interest in the scientific society. The actuality of analyzing the problems with regard to geometric constructions accomplished by Al-Farabi for modern mathematical and engineering education lies in the unique character of Al-Farabi's efforts involving the use of the algorithmic approach for resolving mathematical problems and application-oriented researches. These algorithmic approaches enable the creation of didactic teaching techniques based on the use of information processing technology. One of the main Al-Farabi's principles is to study and consider the mathematics in terms of natural phenomena and processes as well as all types of its practical implementation. This article pursues studying Al- Farabi's mathematical heritage concerning geometrical construction problems as well as the development of their solution methods using modern information technology, in particular, using the GeoGebra dynamic geometry system which is a problem-solving environment designed for studying, conversion and visualization of geometric object models. This scientific article shows examples of resolving geometric construction problems using only a mathematical compass and a ruler by the Al-Farabi's procedures as well as problems for dividing squares and spheres and giving Al-Farabi's visual evidence of proving Ptolemy's theory from trigonometry area. The authors are interested in a targeted audience to familiarize themselves with algorithms developed by Al-Farabi and this software implementation; for this purpose, a scientific-education portal has been designed for the concerned researches and pedagogues may find out a lot of useful and interesting information.