A Journey to a Mathematical Frontier with Multiple Computer Tools

called the Golden Ratio.The goal of this article is to demonstrate how the integration of multiple software toolsinto a familiar educational context of Fibonacci numbers allows for the discovery of newmathematical knowledge. It is a snapshot of the authors’ recent work (Abramovich andLeonov 2008, 2009a, b) on the development of technology-motivated methods of teachingtopics in discrete mathematics at the university level, including programs for secondarymathematics teachers (referred to below as teachers). The snapshot highlights the potentialof the joint use of a spreadsheet and computer algebra systems for the discovery of cycles