The purpose of this paper is to develop a novel method for establishing the mathematical link between the restored Hogarth curve and the golden ratio, and to advance the potential application of the Hogarth curves in standardization of the garment pattern design by using this method.,The Hogarth curve was fully restored by using the plant design system (PDS) software package and divided the restored curve into two fragments based on the intersection point between the curve and the straight line joining the curve endpoints. The ratios between two fragments of curves and straight lines were calculated and compared with the golden ratio, respectively, which was set as a normalized value. The potential application of the restored Hogarth curves in the normalization of the garment pattern design was therefore studied by using the standard mannequins.,The ratio in the most beautiful curve, i.e., the fourth Hogarth curve, was found to be infinitely approaching to the golden ratio. Furthermore, the incorporation of the Hogarth curves into the garment pattern design demonstrated that the fourth Hogarth curve was the most aesthetic line.,This work offered a novel method for bridging the gaps between arts and maths, i.e., the mathematical relation between the Hogarth curves and the golden ratio. Such a method will provide the protocol to promote the potential applications of the Hogarth curves in the garment pattern design and the human body decoration.

中文翻译：

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Hogarth 曲线在现代服装中的潜在应用

本文的目的是开发一种新的方法来建立恢复的 Hogarth 曲线和黄金分割率之间的数学联系，并通过使用这种方法推进 Hogarth 曲线在服装图案设计标准化中的潜在应用。使用工厂设计系统（PDS）软件包完全恢复Hogarth曲线，并根据曲线与连接曲线端点的直线之间的交点将恢复的曲线分成两个片段。计算曲线和直线的两个片段之间的比例，并分别与黄金比例进行比较，黄金比例设为归一化值。因此，通过使用标准人体模型研究了恢复的 Hogarth 曲线在服装图案设计规范化中的潜在应用。最美丽的曲线，即第四条霍加斯曲线中的比例，被发现无限接近黄金比例。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 此外，将霍加斯曲线纳入服装图案设计表明第四霍加斯曲线是最美观的线条。这项工作为弥合艺术与数学之间的鸿沟提供了一种新方法，即霍加斯曲线之间的数学关系和黄金比例。这种方法将为促进霍加斯曲线在服装图案设计和人体装饰中的潜在应用提供协议。将霍加斯曲线纳入服装图案设计表明第四霍加斯曲线是最具美感的线条。这项工作为弥合艺术与数学之间的鸿沟提供了一种新方法，即霍加斯曲线与黄金比例。这种方法将为促进霍加斯曲线在服装图案设计和人体装饰中的潜在应用提供协议。将霍加斯曲线纳入服装图案设计表明第四霍加斯曲线是最具美感的线条。这项工作为弥合艺术与数学之间的鸿沟提供了一种新方法，即霍加斯曲线与黄金比例。这种方法将为促进霍加斯曲线在服装图案设计和人体装饰中的潜在应用提供协议。