Abstract

The construction of numbers has historically followed the process of recognizing the properties of geometry. The concept of countability is represented by natural numbers(N) on a straight line, while the completeness of real numbers(R) is derived from the continuous property of the number line. A complex number is established on a plane off the number line, and thereafter, the whole number system is completed. When the process of constructing a number with geometric features is investigated from different perspectives, it provides a new insight into the fundamental principle of a number, which leads to a novel methodology in mathematics.