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

TL;DR

This paper introduces a geometric systematical arithmetic method based on the nine-palace diagram, enabling mental calculation of basic operations through a structured mathematical framework rooted in Chinese tradition.

Contribution

It develops a comprehensive geometric theory of arithmetic using the nine-palace diagram, integrating concepts like rotation invariance, vector addition, and multiplication laws.

Findings

Establishes a geometric theory for mental arithmetic operations.

Demonstrates the mathematical and philosophical significance of the nine-palace based system.

Provides methods for addition, subtraction, multiplication, and division in the mental calculation context.

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.