N 阶斐波那契数列和阶黄金分割及其应用

摘要

The golden section method is an important application of the Fibonacci sequence ,with beautiful Propor-tional ,artistry and harmony ,contains rich aesthetic value ,reveals the nature of the laws of science . To generalized N -order Fibonacci sequence to deduce the N th-order golden section ,which second-order gold section and filling theory of mixtures dense gradation in terms of the principle is the same ,to common combination ratio of cement concrete ,ce-ment gradation macadam and bituminous concrete mixture with specific examples and second -order gold section are in good agreement ,with a view to the second-order gold section principle found the optimal ratio of cement concrete ,ce-ment gradation macadam and Bituminous concrete mixture or by golden section method for fast or reduced with than the number of trials and effectively improve the quality of the mixtures material structure engineering .%黄金分割法是斐波那契数列的一个重要应用，具有优美的比例性、艺术性、和谐性，蕴藏着丰富的美学价值，揭示了自然界的一些科学规律。以广义的阶斐波那契数列推演出阶黄金分割，其中二阶黄金分割与混合料密级配填充理论在原理方面是相同的，以常用的水泥混凝土、水泥级配碎石和沥青混凝土混合料配合比的实例说明与二阶黄金分割吻合较好，以期通过二阶黄金分割原理找到水泥混凝土、水泥级配碎石和沥青混凝土混合料的最优配合比或通过黄金分割的方法快速或减少配合比试验次数，有效提高混合料结构的工程质量。