Topology

This word is derived from the Greek word topos&sbquo which means "place" or "location." German mathematician J. B. Listing used this word for the first time in his book Vorstudien zur Topologie (The Basics of Topology) published in 1847. Mathematical interpretation of topology was established by the French mathematician Henri Poincare who called it "analysis situs" (location analysis). The word topology became widely used after German mathematician S. Lefschetz published a book titled Topology in 1930. Since that time it has been able to represent mathematical structures by defining the concepts of limit and continuity&sbquo and adopting them to group theory. It further enabled the physical interpretation of variables in time and spatial process for cyclic phenomena such as oscillation and wave movement. Owing to these mathematical and physical contents and methodologies&sbquo it has become possible to clarify the location and characteristics of the shape of the subject figure and even the continuity of dots that compose the figure. Owing to these concepts and definitions of topology&sbquo it is deemed possible to geometrically make use of figures&sbquo forms&sbquo space and even processes of material change. In other words&sbquo it is possible to part from Euclidean geometry and make formal and spatial designs with topology. In specific terms&sbquo it will be possible to create topological spaces and forms with 3D and even 4D CAD on the computer&sbquo and revolutionize the design method that has been bound by the concepts and interpretation of Euclidean geometry. Topology has already made it possible to apply compact spatial definitions and catastrophe theory as clues to design artificial objects. It means liberation from conceptualizing and expressing within the realm of graphics. Even for virtual topologic forms&sbquo it has become possible to realize tangible shape-recognition due to interlocked methods with rapid prototyping such as the optical fabrication system. Introducing topology as a method of design is a revolution in design methodology.

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