Feigenbaum constant and golden ratio

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A modified and simple method for the drawing of the golden ratio is given in my article Golden ratio and the angle turn/10 (updated 2020-07-22). Golden ratio and the angle turn/10. • Angle unit degree is defined as 1° = 1 turn/360. Can we have a better definition of the angle unit? Protractor with the angle unit turn/240 . function constant(m,n,c) is used in the function delta(N) (in the line 8). The constant function calculates the roots (vector c) of the iteration function x^2-c and hence dx is the derivative of the iteration function. The delta function calculates the ratio of the roots which should be the delta d. Jul 16, 2018 · The golden ratio, ϕ = 1.61803…, has often been found in connection with biological phenomena, ranging from spirals in sunflowers to gene frequency. One example where the golden ratio often arises is in self-replication, having its mathematical origins in Fibonacci’s sequence for “rabbit reproduction”. Buy Now on Amazon. The Golden Section number for phi (φ) is 0.61803 39887…, which correlates to the ratio calculated when one divides a number in the Fibonacci series by its successive number, e.g. 34/55, and is also the number obtained when dividing the extreme portion of a line to the whole. Sep 06, 2020 · The Golden Ratio defines the ideal result as roughly 1.6, which means a beautiful person's face is about 1 1/2 times longer than it is wide. 3. The next stage is to measure the distance between ... Jul 15, 2015 · What is this Golden ratio?It is the Phi Constant- 1.618.Phi is a superior design number of mathematics. The Creator has always used the very same number in numerous events in the universe; in our heart pulses, in the aspect ratio of DNA spiral, in the special design of the universe called dodecehadron, in the leaf array rules of plants called phylotaxy, in the snow flake crystals, in the ... function constant(m,n,c) is used in the function delta(N) (in the line 8). The constant function calculates the roots (vector c) of the iteration function x^2-c and hence dx is the derivative of the iteration function. The delta function calculates the ratio of the roots which should be the delta d. Dec 21, 2012 · They are a constant and the roots to these the higher dimensions can be translated to any unit of measure by using a conversion ratio. We are dealing with whole number solutions and the ratio Phi is only a derived number, in the natural system you can refer this to the root numbers in Fibonacci series, where the oscillation about the Phi point ... Fibonacci numbers follow a second degree recurrence with asymptotics driven by a quadratic irationnal (the Golden ratio). Feigenbaum constant is conjecturally transcendental and governs more ... The problem I encounter is that a piece of furniture's intended use usually dictates either a height, width or depth requirement. I know one or two of these dimensional requirements, and would appreciate a formula that supplies me with a 'golden' aspect when either height or width is known." A. (Ellis Walentine) "The golden ratio is a constant ... On June 26th 2007 Owen Hacket from Nottingham U.K. wrote: The more i have looked into the concept of PHI the more i have come to realise that any thing can be related to it and that it must be the signature of God, the formula for all creation the way physical things behave from waves in the sea to spiral galaxy formations, the easiest way for plants to grow and the way hairs grow around the ... May 17, 2019 · Constants database¶. In addition to the above variables, scipy.constants also contains the 2014 CODATA recommended values [Rc437f0a4090e-CODATA2014] database containing more physical constants. Apr 15, 2020 · Feignenbaum’s constant isn’t 1.61803398875 (golden radio) because the golden ratio is 3D, it is getting skewed/stretched to 4.669 After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. Did I find the Feigenbaum constant (4.699) in depicting cycles as circles and then sub circles of the first cycle? Maybe the golden ratio (1.61803398875) gets mixed in somehow? Does this lead to an explanation to 3.57 cycles being chaos? “The conclusion that the Egyptians of the Old Kingdom were acquainted with both the Fibonacci series and the Golden Section, says Stecchini, is so startling in relation to current assumptions about the level of Egyptian mathematics that it could hardly have been accepted on the basis of Herodotus' statement alone, or on the fact that the phi [golden] proportion happens to be incorporated in ... Euclid originally determined phi, or the golden ratio, as a means to calculate line segments and relationships between shapes. The golden ratio is common in biological relationships. For example, the length of your forearm divided by the length your hand results in a number close to 1.618, or phi. Golden ratio‎ (1 C, 21 P) P ... Favard constant; Feigenbaum constants; Feller–Tornier constant; Feller's coin-tossing constants; Foias constant; May 17, 2019 · Constants database¶. In addition to the above variables, scipy.constants also contains the 2014 CODATA recommended values [Rc437f0a4090e-CODATA2014] database containing more physical constants. This paper will combine information entropy with symbolic dynamics to demonstrate how period doubling can be defined using these tools alone. In addition, the technique allows us to uncover some unexpected, simple estimates for Feigenbaum's constants which relate them to log 2 and the golden ratio, φ, as well as to each other. Maybe the golden ratio (1.61803398875) gets mixed in somehow?Does this lead to an explanation to 3.57 cycles being chaos? [The Golden Ratio is a universal law] in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which ... The quantum ratio (elementary charge / Planck constant> as quantum-ratio. Standard acceleration due to gravity as standard-acceleration-gravity or g. Vacuum electrical permittivity as vacuum-permittivity or ε0. Mathematical constants. Golden ratio as phi or φ. Feigenbaum constants as alpha-feigenbaum-constant and delta-feigenbaum-constant or δ. Jul 15, 2015 · What is this Golden ratio?It is the Phi Constant- 1.618.Phi is a superior design number of mathematics. The Creator has always used the very same number in numerous events in the universe; in our heart pulses, in the aspect ratio of DNA spiral, in the special design of the universe called dodecehadron, in the leaf array rules of plants called phylotaxy, in the snow flake crystals, in the ... “The conclusion that the Egyptians of the Old Kingdom were acquainted with both the Fibonacci series and the Golden Section, says Stecchini, is so startling in relation to current assumptions about the level of Egyptian mathematics that it could hardly have been accepted on the basis of Herodotus' statement alone, or on the fact that the phi [golden] proportion happens to be incorporated in ... The ratio of the square of the charge of an electron to that quantity is a pure dimensionless number known as Sommerfeld's constant or the fine-structure constant : a = m 0 c e 2 / 2h = e 2 / 2hc e 0 = 1 / 137.035999... Aug 20, 2019 · This is what is called the “Golden Ratio” symbolized by the Greek letter Φ which has a constant value of Phi=1.618. Leonardo da Vinci used the ratio to define a symmetry in structures ... And the ratio between the values where the period doubles ends up approaching the Feigenbaum constant, approximately 4.669. So, should we celebrate Feigenbaum Constant Day on April 6th or 7th? Embree-Trefethen constant[?] NuT : δ ≈ 4.66920 16091 02990 67185 32038 20466 20161 : Feigenbaum constant: ChT : α ≈ 2.50290 78750 95892 82228 39028 73218 21578 : Feigenbaum constant: ChT : C 2 ≈ 0.66016 18158 46869 57392 78121 10014 55577 : Twin prime constant: NuT : 5,020 : M 1 ≈ 0.26149 72128 47642 78375 54268 38608 69585 : Meissel ... 0x9e3779b9 is the integral part of the Golden Ratio's fractional part 0.61803398875… (sqrt(5)-1)/2, multiplied by 2^32. Hence, if φ = (sqrt(5)+1)/2 = 1.61803398875 is the Golden Ratio, the hash function calculates the fractional part of n * φ, which has nice scattering properties. The quantum ratio (elementary charge / Planck constant> as quantum-ratio. Standard acceleration due to gravity as standard-acceleration-gravity or g. Vacuum electrical permittivity as vacuum-permittivity or ε0. Mathematical constants. Golden ratio as phi or φ. Feigenbaum constants as alpha-feigenbaum-constant and delta-feigenbaum-constant or δ.