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Anonymous
I made a new field of mathematics
2016-01-07 17:13:06 Post No. 7767891
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I made a new field of mathematics
Anonymous
2016-01-07 17:13:06
Post No. 7767891
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Is this a thing already?
I call it pipe theory, or fat-graph theory. Its 1 dimension up from normal, 'thin' graph theory. As seen in 1a, the vertices become 2D smooth, non intersecting curves, and the edges become surfaces with boundaries only on the curves in 1b. All the fat graphs drew here are 'volumetric' graphs, the equivalent of planar thin graphs. meaning the surfaces do not intersect each other. The process of 'fattening up' a planar graph to a volumetric is however not just redrawing all the lines as surfaces, as seen in 3, fattening up a thin graph requires a different configuration than the thin graph to make the graph representation volumetric.
I have shown in 4 that any planar thin graph can be fattened up by rotating the graph around a vector not intersecting the graph.
I have a conjecture that i have not been able to prove. First lets define some termsWhen you thin down a fat graph, you get the corresponding thin graph A volumetric fat graph is 'genetically fat' if they can not be thinned down. My conjecture is that no genetically fat graphs exists.
Another conjecture is that the number of volumes separated by surfaces in a fat graph is equal to the number of areas separated by edges in the thinned down graph (given by Eulers formula)
The stronger form of the conjectures is that all of fat-graph theory is equivalent to graph theory on the thinned down graphs, in other words, this new fields yields nothing new to mathematics.
Anyone wiling to help me prove this?