nth fibonacci using goldenratio Algorithm

Other names include extreme and average ratio, medial section, divine proportion (Latin: proportio divina), divine section (Latin: sectio divina), golden proportion, golden cut, and golden number. Mathematicians since Euclid have study the property of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. German mathematician Simon Jacob (d. 1564) noted that consecutive Fibonacci numbers converge to the golden ratio; this was rediscovered by Johannes Kepler in 1608.According to one narrative, 5th-century BC mathematician Hippasus observed that the golden ratio was neither a whole number nor a fraction (an irrational number), surprising Pythagoreans. According to Mario Livio: Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its property....

nth fibonacci using goldenratio source code, pseudocode and analysis