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Purpose Beautiful and simple curves are most commonly employed in apparel design since they can not only simplify the manufacture process, but also significantly beautify the breast profile of customers. However, it is regularly difficult to choose the most suitable curve when producing the strip costume; this is due to the fact that the curve is a kind of aesthetics without any laws. The quantification and standardization to curves are necessary for fashion design. The purpose of this paper is to investigate the relationship between the stripe of costumes and the breast profiles of wearers. Design/methodology/approach Seven curves drawn derived from the Hogarth theory (Hogarth curves) were firstly diagrammatized by the central line technology using CorelDraw, and the format of bitmaps and quadratic functions of these selected curves were obtained respectively. Simulating formulas were subsequently used to interpret these curves. The standard of curves for apparel design was finally established after being evaluated by comparison between the different types of female breasts and the curves on the costumes. Findings The established models indicated that the fourth Hogarth curves was the most attractive one that combining the static state and the dynamic beauty, which could also help females to highlight the beautiful breast shapes. Originality/value This work provided the fundamentally understanding of the application of Hogarth curves in fashion design and the improvement on the effectiveness of the garment industry.

Purpose Curves with various profiles have been demonstrated to be more attractive and decorative than the straight lines by William Hogarth. Among all kinds of curves, Hogarth proposed seven serpentine lines as the most beautiful curves, i.e., Hogarth curves. Those seven Hogarth curves are subsequently applied in a wide range of fields, e.g., sculpture, painting, architecture and fashion design, indicating their significance to the development of the formal beauty. Recently, the beauty of Hogarth curves has been suspected to be induced by their special-designed curvature, which could have the potential relationship with the Golden Ratio. The purpose of this paper is to explore the relationship between the Hogarth curves and golden ratio by comparing the curvature of curves with the Fibonacci sequence. Design/methodology/approach Each of the Hogarth curves was fully restored and divided into two parts according to the turning point of the curvature; the ratios of span, curvature and angles between these two parts were compared with the Fibonacci sequence. Findings The experimental results disclosed that the ratio of the fourth Hogarth curve, which was considered as the most beautiful line by Hogarth, was infinitely approaching the golden ratio. Based on the relationship between the fourth Hogarth curve and the golden ratio, the ratios of each curve were employed to define and normalize these curves, providing a quantitative way to redraw the Hogarth curves. Originality/value This research work unlocked the information of the relationship between the Hogarth curves and golden ratio, and proposed an effective and convenient mathematic way to quantify the Hogarth curves. The experimental findings disclosed the underlying mechanisms of the beauty of the forth Hogarth curves. Such a fundamental study will promote the establishment of the normalized methods for evaluating the beauty of arts and provide novel ideas for researchers and industrial technologists to use the Hogarth curves.

A graded-index (GI) polymer rod was prepared by interfacial-gel polymerization, in which polymerization was performed in a PMMA tube and bromobenzene (BB) was used as a higher refractive index molecules. By using the new technology, a GI polymer rod without any defect of void or bubble was made. A detailed mechanism and simulation of graded-index formation were given according to the Vrentas-Duda free volume theory.