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Golden mean to 5000 digits

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The golden episode is a line segment divided into two conferring to the golden ratio. The entire length a+b is to the lengthier segment a as a is to the lesser segment b. In mathematics and the arts, two numbers are in the golden ratio if the ratio of the sum of those numbers and the bigger one is similar as the ratio of the bigger one and the lesser one. The golden ratio is a mathematical invariable, around 1.6180339887….

In some measure, in the time past the Renaissance, several artists and architects have rounded their works to almost the golden ratio, specifically in the method of the golden rectangle, in which the ratio of the bigger side to the smaller is the golden ratio. Assuming this degree to be visually agreeable. Mathematicians have learned the golden ratio for its unequal and appealing aspects.

A few of the best mathematicians of every age, from Pythagoras and Euclid in olden Greece, throughout the primeval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to modern scientific personas including Oxford physicist Roger Penrose, have spent limitless hours for this common ratio and its properties. But the enthrallment with the Golden Ratio is not compassed only to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and swamis as well have deliberated and argued the foundation of its pervasiveness and influence. Indeed, it is perhaps proper to state that the Golden Ratio has motivated thinkers of all fields of study like no other numeral in the history of mathematics.

Antiquated Greek mathematicians mainly researched on what we learn today as the golden ratio for its regular materialization in geometry. The distribution of a line into “extreme and mean ratio” (the golden section) is vital in the geometry of regular pentagrams and pentagons. Euclid’s Elements offers the first plainly scribed explanation of what we perceive today as the golden ratio.
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