On the Nine-Palace Arithmetic -- A New Method of Mental Calculation

Abstract

Based on the nine-palace diagram, we establish the systematical geometric theory of arithmetic, which can realize the arithmetical addition, subtraction, multiplication, division and other operations thoroughly in the mind. In this paper, we give a brief introduction to this theory, including the rotation invariance theorem, the vector addition and the lattice addition, the summation by the center of gravity, the law of multiplication ones and carries on the nine-palace diagram, the counting method, and so on. This systematical arithmetic can be viewed as the mathematics based on the Chinese Luoshu Diagram so that it is not only of mathematical significance, but also of philosophical significance.