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Successive points dividing a

**golden**rectangle into squares lie on a logarithmic**spiral**(Wells 1991, p. 39; Livio 2002, p. 119) which is sometimes known as the**golden****spiral**. ...The logarithmic

**spiral**is a**spiral**whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...A

**section**of a solid is the plane figure cut from the solid by passing a plane through it (Kern and Bland 1948, p. 18).The

**golden**ratio, also known as the divine proportion,**golden**mean, or**golden****section**, is a number often encountered when taking the ratios of distances in simple geometric ...The

**Fibonacci**numbers are the sequence of numbers {F_n}_(n=1)^infty defined by the linear recurrence equation F_n=F_(n-1)+F_(n-2) (1) with F_1=F_2=1. As a result of the ...The

**golden**triangle, sometimes also called the sublime triangle, is an isosceles triangle such that the ratio of the hypotenuse a to base b is equal to the**golden**ratio, ...The

**Fibonacci**chain map is defined as x_(n+1) = -1/(x_n+epsilon+alphasgn[frac(n(phi-1))-(phi-1)]) (1) phi_(n+1) = frac(phi_n+phi-1), (2) where frac(x) is the fractional part, ...The

**golden**ratio conjugate, also called the silver ratio, is the quantity Phi = 1/phi (1) = phi-1 (2) = 2/(1+sqrt(5)) (3) = (sqrt(5)-1)/2 (4) = 0.6180339887... (5) (OEIS ...The

**Fibonacci**factorial constant is the constant appearing in the asymptotic growth of the fibonorials (aka.**Fibonacci**factorials) n!_F. It is given by the infinite product ...Let psi = 1+phi (1) = 1/2(3+sqrt(5)) (2) = 2.618033... (3) (OEIS A104457), where phi is the

**golden**ratio, and alpha = lnphi (4) = 0.4812118 (5) (OEIS A002390). Define the ......