【摘要】 黄金分割在自然和社会中有着广泛的意义,从古到今始终被美学家作为形式美的一条法则。黄金分割是人们熟悉的一种数学比例关系,但它的意义却并非如此简单,其中自然有着深奥的机理。黄金分割和斐波那契数列自问世以来,不断显示出它们在数学理论和应用上的重要作用。从黄金分割与Fibonacci数列的联系入手,运用几何方法,确定出黄金分割点,在此基础上建立了一种新的分割,即白金分割。通过Fibonacci数列的递推公式与黄金分割的联系,依据已求得的白金分割,推导出了雅森数列的递推公式。经过深入研究,证明了雅森数列所具有的一些性质。更多还原

【Abstract】 Golden section has a broad significance in nature and society,it has seen as a rule of beauty by esthetician since ancient times.Golden Section is a familiar ratio relationship in mathematics,but the significance is not so simple that it has a profound mechanism,naturally.Since Golden Section and Fibonacci series has been found,it constantly shows their important role in mathematical theories and applications.In this paper,we starting form the relationship between Golden section and Fibonacci series,make good use of geometric methods to determine the golden section point.On this basis,we established a new division,which is called Whitten section.By analyzing the contact of recurrence formula of Fibonacci series and Golden section,and according to the Whitten section which has been obtained,we derived recurrence formula of Jassen series.After intensive research,some properties of Jassen series has been proved.更多还原