The golden section, ϕ = (1 + √5)/2 = 1.618... and its companion ϕ = 1/ϕ = ϕ -1 = 0.618..., are irrational numbers which for centuries were believed to confer aesthetic appeal. In line with the presence of golden sectioning in natural growth patterns, recent EEG recordings show an absence of coherence between brain frequencies related by the golden ratio, suggesting the potential relevance of th...

We discuss the Waring rank of binary forms degree 4 and 5, without multiple factors, point out unexpected relations to harmonic cross-ratio, j-invariants golden ratio. These computations ranks for are used show that combinatorics a line arrangement in complex projective plane does not determine defining equation even very simple situations.

On-line chain partition is a two-player game between Spoiler and Algorithm. Spoiler presents a partially ordered set, point by point. Algorithm assigns incoming points (immediately and irrevocably) to the chains which constitute a chain partition of the order. The value of the game for orders of width w is a minimum number val(w) such that Algorithm has a strategy using at most val(w) chains on...

In this paper we describe the application of the Golden Ratio to three-dimensional facial scans. The Golden Ratio is believed to be a blueprint for facial features that conform to beauty. Faces are scanned using the Minolta VI-700 range data scanner. The acquired 3D meshes are viewed and manipulated using 3DS Max and MAXScript. A Golden Mask, constructed based on the Golden Ratio is used to ind...

Human walking is a complex task which includes hundreds of muscles, bones and joints working together to deliver harmonic movements with the need of finding equilibrium between moving forward and maintaining stability. Many different computational approaches have been used to explain human walking mechanisms, from pendular model to fractal approaches. A new perspective can be gained from using ...

 The paper focuses on some of the biological characteristics of golden grey mullet, Liza aurata in Iranian waters of the Caspian Sea. Samples of commercial catch of mullet obtained by means of beach seine fishing cooperatives along the Iranian coasts of Caspian Sea (2007-2008) as monthly interval. Samples subjected to biometric measurement to specify their biological characteristics. The male/f...

We show that the partitions of an n-element set into k members of a given set family can be counted in time O((2− )), where > 0 depends only on the maximum size among the members of the family. Specifically, we give a simple combinatorial algorithm that counts perfect matchings in a given graph on n vertices in time O(poly(n)φ), where φ = 1.618 . . . is the golden ratio; this improves a previou...

Several sequences of graphs are introduced whose perfect matching numbers, or Kekulé numbers, K(G), are either Fibonacci or Lucas numbers, or their multiples. Since the ratio of the K(G)s of consecutive members converges to the golden ratio, these sequences of graphs belong to another class of golden family graphs.