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The Golden Ratio (Phi) – original contributions & new discoveries (ebook)
The Golden Ratio (Phi) – original contributions & new discoveries (ebook)
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The Golden Ratio (PHI) (aka “golden mean”, “golden section” or “divine section”: standardly denoted with the capital Greek letter PHI) is the only positive (irrational) quadratic solution of the (minimal polynomial) equation x^2-x-1=0, so that PHI=[sqrt(5)+1]/2.
The purpose of this paper is to demonstrate some aspects recently discovered by the author of this paper:
(1) a recursive geometrical method for constructing PHI (inspired by the Taoist religious iconography) which is more simple and elegant than Odom’s method;
(2) an occurrence of PHI in the water molecule geometry;
(3) a quasi-Pythagorean property of the (PHI, e, PI) triad;
(4) some other interesting quasi-exact relations between the elements of the (PHI, e, PI) triad;
(5) the tendency of the human systolic/diastolic blood pressure different (combinational) ratios to stabilize (with age) to values close to PHI;
The purpose of this paper is to demonstrate some aspects recently discovered by the author of this paper:
(1) a recursive geometrical method for constructing PHI (inspired by the Taoist religious iconography) which is more simple and elegant than Odom’s method;
(2) an occurrence of PHI in the water molecule geometry;
(3) a quasi-Pythagorean property of the (PHI, e, PI) triad;
(4) some other interesting quasi-exact relations between the elements of the (PHI, e, PI) triad;
(5) the tendency of the human systolic/diastolic blood pressure different (combinational) ratios to stabilize (with age) to values close to PHI;
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