Abstract
Geometric properties of finite Blaschke products have been intensively studied by many different aspects. In this paper, our aim is to study geometric properties of finite Blaschke products related to the golden ratio $\alpha =\frac{1+\sqrt{5}}{2}$. Mainly, we focus on the relationships between the zeros of canonical finite Blaschke products of lower degree and the golden ratio. We show that the geometric notions such as "golden triangle, "golden ellipse" and "golden rectangle" are closely related to the geometry of finite Blaschke products.
Highlights
We focus on the relationships between the zeros of canonical ...nite Blaschke products of lower degree and the golden ratio
We show that the geometric notions such as "golden triangle, "golden ellipse" and "golden rectangle" are closely related to the geometry of ...nite Blaschke products
In [19], the golden ratio is used in graphs; in [10], it is proved that in any dimension all solutions between unity and the golden ratio to the optimal spherical code problem for N spheres are solutions to the corresponding DLP problem
Summary
It is well-known that the golden ratio is almost everywhere in nature and science [12]. In this paper, we study on the connection between geometric properties of Blaschke products and the golden ratio. Note that the canonical Blaschke products correspond to ...nite Blaschke products vanishing at the origin It is well-known that every Blaschke product B of degree n with B(0) = 0; is associated with a unique Poncelet curve (for more details, see [4], [5] and [8]). We investigate the relationships between the zeros of canonical ...nite Blaschke products of lower degree and the golden ratio. We see that some geometric notions such as "golden triangle, "golden ellipse" and "golden rectangle" are closely related to the geometry of ...nite Blaschke products
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