基本数论问题的可视化证明方法研究与实践

Research and Practice on Visual Proof Method of Elementary Number Theory Problems

可视化研究是当前国际上的热点问题,广泛应用于理论数学、物理实验、算法加密等多个领域。基本数论问题是数论研究的基石,对于基本数论问题进行可视化证明的研究具有重要现实意义。本文从毕达哥拉斯游程问题、巴塞尔问题等基本数论问题出发,基于可视化证明所具有的优势与特点,结合基本数论问题特点,提出基本数论问题的可视化证明方法,并实例应用于托勒密定理的可视化证明,可以有效降低托勒密定理的理解难度,对其他数论基本问题的可视化证明有着极大参考价值。

At present,visualization research is a hot issue in international scope,which is widely applied in multiple fields including theoretical mathematics,physical experiment,algorithm encryption,etc.Elementary number theory problem is the cornerstone of number theory research,and performing study on the visual proof of elementary number theory problems has great practical significance.From some elementary number theory problems such as the Pythagorean Length and the Basler Question,based on the advantages and characteristics of the visual proof,in this paper a visual proof method of elementary number theory problems is proposed by combining the characteristics of the elementary number theory problems.In addition,as an application instance,the proposed method is applied to the visual proof of the Ptolemy’s Theorem,which indicates that the proposed method could effectively decrease the difficulty of understanding the Ptolemy’s Theorem and may provide great reference value to the visual proof of other elementary number theory problems.