In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. [1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.

2012年8月25日 · A Golden spiral is very similar to the Fibonacci spiral but is based on a series of identically proportioned golden rectangles, each having a golden ratio of 1.618 of the length of the long side to that of the short side of the rectangle:

2023年8月25日 · The Golden Spiral plays a role in the geometry of fractals, a complex pattern that repeats forever. American mathematician Edmund Harriss became popular for his fractal curve based on the Golden Spiral, now known as the Harriss Spiral.

The Fibonacci spiral approximates the golden spiral in the similar way that the Dürer spiral approximates the Archimedean spiral, with the difference that quarter circles are connected instead of semicircles.

In a golden spiral the distance between the golden spiral coils keeps increasing, growing wider as it moves away from the source or narrower as it moves toward it. The golden spiral is an exponential, logarithmic spiral.

2011年9月4日 · Golden Spiral. The Golden Spiral is a special case of the logarithmic spiral. We can write the general logarithmic spiral as a function in polar coordinates using t as follows: r(t) = ae t cot b. Note: Normally, we use θ for the independent variable, but we often use t as we can think of the spiral being traced out over time. Besides, it's ...

The golden spiral possesses a partial "eadem mutata resurgo" property, namely it is invariant under similarity with centre O, ratio and angle ; therefore, it approximates a true logarithmic spiral where m is defined by , hence with polar equation , passing by the points A , A ', A " etc...

2024年4月13日 · As we know, ϕ can be obtained from the ratio of two successive Fibonacci numbers; the golden ratio forms a spiral pattern. This spiral follows a constant angle close to ϕ and is thus known as the Golden Spiral .

2025年1月31日 · 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.

2020年1月23日 · The spiral pattern created by the way in which the seeds grow out from the center of the seed head approximates the Golden Spiral. This arrangement preserves the most space for an optimal number of seeds.