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简单代数方程,丢番图数与大自然的花样
2016-08-25  【 】【打印】【关闭

Institute of Theoretical Physics

Key Laboratory of Theoretical Physics

  Chinese Academy of Sciences

Colloquium

Title

题目

简单代数方程,丢番图数与大自然的花样

Speaker

报告人

曹则贤 研究员

Affiliation

所在单位

中国科学院物理研究所

 

Date

日期

2016年8月25日(周四)下午3:00

Venue

地点

理论物理所新楼6620报告厅

Abstract

摘要

A Simple Algebraic Equation, Diophantine Numbers and Patterns of Nature
Even an algebraic equation as simple as x2+ax+b=0 unfolds many interesting stories. The solutions of this equation for some specific coefficients are referred to the golden ratio, the silver ratio and the platinum ratio, which are further related to the 10-fold, 8-fold and 12-fold quasiperiodic structures, respectively. They make their presence in many patterns in nature, and even in physics problems such the Ising model, the hard hexagon model, the Hardy’s test of Bell’s inequality, etc. By stress engineering we achieved the growth of microscopic Fibonacci parastichous spirals, leading us to a deep understanding of phyllotaxis. Furthermore, by playing with the function , where x as parameter is the silver ratio or platinum ratio, and n the integer as variable, 8-fold and 12-fold quasiperiodical patterns, in a loose sense, can be generated, resulting in the discovery of directional scaling symmetry in square and triangular lattices—a problem that had frustrated Galileo long long ago. With the aid of Gauss and Eisenstein integers, it can be proven that there are infinitely many possibilities of scale symmetry for square lattice, of which one is also related to the golden ratio. Such discoveries are very interesting and can be arrived at only in a serendipitous fashion.
 

Contact person

所内合作者

蔡荣根

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