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Paper Abstract and Keywords
Presentation 2013-03-15 16:50
Shapes of the Imaginariness
Atsushi Miyazawa, Itsuha Sakurai (Tokyo Polytechnic Univ.), Ko Hayashi (Klon)
Abstract (in Japanese) (See Japanese page) 
(in English) 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.
Keyword (in Japanese) (See Japanese page) 
(in English) Complex manifold / Visualization / Complex analysis / Four-dimensional space / / / /  
Reference Info. ITE Tech. Rep., vol. 37, no. 17, AIT2013-95, pp. 193-196, March 2013.
Paper # AIT2013-95 
Date of Issue 2013-03-08 (AIT) 
ISSN Print edition: ISSN 1342-6893
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Conference Information
Committee AIT IIEEJ AS  
Conference Date 2013-03-15 - 2013-03-15 
Place (in Japanese) (See Japanese page) 
Place (in English) Keio Univ. 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To AIT 
Conference Code 2013-03-AIT-IIEEJ-AS 
Language Japanese 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Shapes of the Imaginariness 
Sub Title (in English)  
Keyword(1) Complex manifold  
Keyword(2) Visualization  
Keyword(3) Complex analysis  
Keyword(4) Four-dimensional space  
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1st Author's Name Atsushi Miyazawa  
1st Author's Affiliation Tokyo Polytechnic University (Tokyo Polytechnic Univ.)
2nd Author's Name Itsuha Sakurai  
2nd Author's Affiliation Tokyo Polytechnic University (Tokyo Polytechnic Univ.)
3rd Author's Name Ko Hayashi  
3rd Author's Affiliation Klon Co.,Ltd. (Klon)
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Speaker Author-1 
Date Time 2013-03-15 16:50:00 
Presentation Time 90 minutes 
Registration for AIT 
Paper # AIT2013-95 
Volume (vol) vol.37 
Number (no) no.17 
Page pp.193-196 
#Pages
Date of Issue 2013-03-08 (AIT) 


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