Overview of the triangle of knowledge: a driving force for sustainable growth in less developed nations

Today’s challenging and critical world economic and political situation is briefly reviewed in this article. Mathematical and geometrical approaches to the knowledge triangle (KT) concept are outlined and analyzed. The triptych: Education + Research + Innovation has been used in the definition of the KT. The European Institute of Technology is briefly mentioned which also uses the KT but in addition is taking into consideration the important component of Entrepreneurship. A new approach to explore an expanded triptych of KT, by adding the Entrepreneurship-Business component (K-E + R-I + E-B), is attempted, and a new definition is developed by exploring better the geometric triangle schema and the expanded triptych. The new term introduced for first time is the triangle of knowledge (ToK). It is fully explained and justified for this new approach using the expanded (K-E + R-I + E-B) fundamental concepts. The ToK guarantees the full and dynamic interaction between all components needed for the sustainable development and growth of a region or country. The different funding schemes are considered, and the pyramid for sustainable development is presented for the first time. This new approach seems to address better many fundamental issues and problems of the knowledge-based society. In addition, the proposed ToK is used for first time to study the problem of the sustainable growth of a region and/or a nation. The important role that control can play in the further development and mathematical study of the newly proposed concept for the ToK is briefly formulated and analyzed. Future research directions for the proposed new approaches are presented and discussed.