Abstract
From prehistoric paintings on cave walls to modern flat panel displays, plane media have always been a versatile means for showing projected images of three-dimensional objects. If dimensional analogy is correct, one may suppose that stereoscopic displays could be used to represent the projection into three dimensions of objects from a four-dimensional world. Adding one more dimension will bring various benefits. For instance, it is well known that the calculation of total circuit impedance can be simplified by using complex number representation. However, it is generally not easy for us, living in three-dimensional space, to use our intuitive imagination to understand the four-dimensional world. A story about a square that lives in a two-dimensional world, which was narrated by Edwin Abbott Abbott in the book "Flatland," is almost the only glimpse for non-mathematicians of a shift into higher dimensions. In 1982, the author attempted to graph complex functions by superimposing graphs of the functions that map a real part of a complex number to a complex number. By making the most of today's advances in stereoscopic systems, we can understand the projection of a one-dimensional complex manifold more intuitively. The purpose of this paper is to introduce some studies relating to the visualization of a one-dimensional complex manifold, and to discuss analytical approaches and methodologies. Using recent stereoscopic systems to gain another view of classical mathematics may contribute to educational improvement.
