鸡蛋和数学：介绍鸡蛋形状的通用公式,Annals of the New York Academy of Sciences

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鸡蛋和数学：介绍鸡蛋形状的通用公式
Annals of the New York Academy of Sciences ( IF 4.1 ) Pub Date : 2021-08-23 , DOI: 10.1111/nyas.14680
Valeriy G Narushin _{1,

2} , Michael N Romanov ₃ , Darren K Griffin ₃

Affiliation

鸡蛋作为最传统的食品之一，长期以来从分析的角度引起了数学家、工程师和生物学家的关注。作为卵形学的主要参数，迄今为止，鸟蛋的形状已经逃脱了普遍适用的数学公式。可以使用四个几何图形来分析所有鸡蛋的形状：球形、椭圆形、卵形和梨形（圆锥形或梨形）。前三个有明确的数学定义，每个都源自前一个的表达式，但梨形剖面的公式尚未导出。为了纠正这个问题，我们在卵形公式中引入了一个附加函数。随后的数学模型拟合了一个全新的几何形状，可以表征为球体演化的最后阶段——椭球体——Hügelschäffer的卵形变换，它适用于任何鸡蛋几何形状。所需的测量值是蛋的长度、最大宽度和距离尖端末端的直径。这种数学分析和描述代表了寻求的通用公式，不仅是了解蛋形本身的重要一步，而且是了解它如何以及为什么进化的重要一步，从而使广泛的生物学和技术应用在理论上成为可能。

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Egg and math: introducing a universal formula for egg shape

The egg, as one of the most traditional food products, has long attracted the attention of mathematicians, engineers, and biologists from an analytical point of view. As a main parameter in oomorphology, the shape of a bird's egg has, to date, escaped a universally applicable mathematical formulation. Analysis of all egg shapes can be done using four geometric figures: sphere, ellipsoid, ovoid, and pyriform (conical or pear-shaped). The first three have a clear mathematical definition, each derived from the expression of the previous, but a formula for the pyriform profile has yet to be derived. To rectify this, we introduce an additional function into the ovoid formula. The subsequent mathematical model fits a completely novel geometric shape that can be characterized as the last stage in the evolution of the sphere—ellipsoid—Hügelschäffer's ovoid transformation, and it is applicable to any egg geometry. The required measurements are the egg length, maximum breadth, and diameter at the terminus from the pointed end. This mathematical analysis and description represents the sought-for universal formula and is a significant step in understanding not only the egg shape itself, but also how and why it evolved, thus making widespread biological and technological applications theoretically possible.

更新日期：2021-08-23

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