摘要
以《黄金率与五重对称》为开端,《物体的形状与黄金率》进一步阐述了现实生活中多边形结构占主要形式的理由(层次结构定理),如,黄金率出现在许多建筑物和绘画作品中(美学定理)等。本文是前述研究的延续,目的在于揭示关于金字塔和其他神圣建筑物数据方面的许多错误推测。这里我们以同样的思想来诠释关于或者黄金率或者等极其美好的数据的错误推测。研究的成功在于仔细探求了许多金字塔的数据,而不只是研究最大的一个金字塔的数据。前半部分是不关联数,后半部分我们致力于二次域上的黄金分割率,并以一种简单易懂的方式,给出了许多代数数论中的记号和结果。我们认为读者具备(代数)数论的初步知识。有关这方面的详细内容,读者可参阅即将出版的书《数论与代数》。
This is a continuation of the researches that we started in S.kanemitsu and de-veloped in K.chakraborty, where we clarified the reason why the pentagonal form is prevailing in living organisms （Hierarchical over structure theorem）, and as a result, the golden ratio appeared in a great number of artful works including ancient buildings and paintings （Aesthetic theorem）. The objective was to debunk the wrong numerological speculations on the size of the Great Pyramid （relinquishing pyramidiots） and other ＂holy＂ constructions.We keep the same spirit here and debunk the wrong association of some fabulous numbers as 1r or the golden ratio r or p, thus the part of title：non-associated numbers, in the first half of the paper. The success of the research depends on scrutinization of data on many pyramids, not only the Great one. In the second half, we will devote ourselves to genuine mathematics surrounding the quadratic field of the golden section unit, where we present many important notions and results from algebraic number theory in such a way that even beginners can grasp the meaning. We refer the reader to a forth coming book for details on this subject. We assume the reader is familiar with some rudiments of （algebraic） number theory.
出处
《商洛学院学报》
2010年第2期3-11,共9页
Journal of Shangluo University
基金
supported in part by Grant in-aid for Scientific Research No. 17540050
关键词
黄金率
金字塔
二次域
伽罗华群
不关联数
golden ratio
pyramid
quadratic field
dihedral group
Galois group
