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...

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.

and saw that their graphs were parabolas. Since this shape was so different from a circle, with what did not appear to me to be an enormous difference in mathematical form, I wondered what other curves of the form x + y = 1 would look like. Fortunately, I have an Atari 800 computer at home which allows me the opportunity to make such an investigation relatively simple. Eventually, I became bore...

The golden ratio has fascinated people of diverse interests for at least 2,400 years (see e.g. [24]). In mathematics (and the arts) two quantities a and b are in the golden ratio if the ratio of the sum of the quantities a+b to the larger quantity a is equal to the ratio of the larger quantity a to the smaller quantity b . This amounts to setting (a+b)/a = a/b =: φ and solving φ2−φ−1 = 0 which ...

BACKGROUND The maxillary anterior teeth are important in achieving pleasing dental aesthetics. Various methods are used to measure the size and form of them, including the golden proportion between their perceived widths, and the width-to-height ratio, referred to as the golden standard. The purpose of this study was conducted to evaluate whether consistent relationships exist between tooth wid...