物体形状与黄金率(英文)

Shapes of Objects and the Golden Ratio

文献[Kanem]对第一手(初等)数学资料进行了诠释,但在现实生活中,五边形形状普遍存在。通过对巨大建筑物如埃及胡夫大金字塔(法老胡夫)中是否使用了黄金率的验证,旨在消除误解,给予有兴趣的业余爱好者提供自我思考其真实与否的一些材料,如果不是真实的,为什么不是真实的。基于同样的原则,关于Fibonacci数,还存在一些更为复杂的研究课题,如黄金率扩展等需要研究。文中部分材料来自Walser,Thomson等,但已被资深专家再加工。

This is a continuation of the researches that we started in [Kanem], where we had rendered visible, appealing to the minimum raw material of （elementary） mathematics, why the pentagonal form is prevailing in living organisms,and verified whether the golden ratio had been used in colossal constructions such as the great pyramid of Cheops （the pharao Khufu） in Egypt. The objective was to debunk the wrong speculations on one hand, and to give interested amateurs some material for self-thinking whether they are really true or not, and if not, why they not, on the other. This principle being the same, we are going to provide some more advanced topics on Fibonacei i numbers, the golden ratio expansion, etc., which may be pursued by aspirant students who aresaiming at degrees. Part of material is taken from Walser, Thomson etc. but is cooked by mastery hands. 2000 Mathematics Subject Classification： 11F66, 11M26, 11M41.