Golden Proportion as the main mathematical constant of Harmony Mathematics The Pythagorean mathematicians by means of discovery of "Incommensurable Line Segments" made the most essential contribution to development of the concept of As is well known a number of irrational numbers is limitless. However, some of them occupy the special place in the history of mathematics, moreover in the history of material and spiritual culture. Their importance consists of the fact that they express some relations, which have a universal character and appear in the most unexpected applications. The first of them is the irrational number , which equals to the ratio of the diagonal to the side of the square. The discovery of the incommensurable line segments and the history of the most dramatic period of the antique mathematics is immediately connected to this irrational number. Eventually this result brought into the elaboration of the irrational number theory and into the creation of modern "continues" mathematics. The p-number and Euler's number of The where is the "imaginary unit", one more unexpected creation of mathematical thought. The p- and
The trigonometric functions are connected to the exponential function with the help of Euler's formulas: The trigonometric functions and the exponential function play a special part in differential and integral calculus because they are invariants of integration and differentiation, i.e.
The trigonometric functions and the exponential function play a special part in differential and integral calculus because they are invariants of integration and differentiation, i.e. p- and The "Golden Section" is one more fundamental irrational number. The latter entered science in the ancient period along with the p-number. Hence, dating back from the ancient Egyptian period in the mathematical science of nature there came into being two trends of the science progress based on different ideas as to the Universe harmony, viz. the trend of the p- In the course of historical progress there occurred a separation of the said two trends of the mathematized nature science progress. The p-number trend added in the 16th century, after the discovery of logarithms, by the But just as Kepler's investigations aimed at finding the principles of the Universe harmony (culminating in the discovery of planets' movements laws) eventually resulted in the emergence of Newton's gravitation theory and of the classical mathematical analysis (differential and integral calculus), adapted optimally for the description of the mechanical processes, the modern investigations in the field of the systems harmony can bring finally into the In the recent years a number of new mathematical findings of fundamental importance have been obtained within the framework of the "harmonious" trend, which may well initiate the Harmony Mathematics development. Those are It follows from this consideration the idea to single out the mathematics part connected to Fibonacci numbers and the Golden Section under the common title of "Harmony Mathematics". First this idea was stated in the lecture "The Golden Section and Modern Harmony Mathematics" delivered by Prof. Stakhov on the 7th International Conference on Fibonacci Numbers and Their Applications (Austria, Graz, 1996). And we will tell about the contents of this lecture at the next pages of out Museum. Follow us! |