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What is cutting edge maths? - Mathematics Stack Exchange To come back to your question, the cutting edge is often in the refinement and well considered combination of equations, 'paragraphs' in this metaphor Where the metaphor differs is that the english language allows for endless break down of the rules, such that hundreds of paragraphs can be written quickly, whereas a single mathematical
combinatorics - Let G be a connected graph in which every vertex has . . . $\begingroup$ Two edge-disjoint paths need not form a cycle, because they might not be vertex-disjoint The point of the 3-regular condition here is that for 3-regular graphs, the lack of a cut edge will imply the lack of a cut vertex, but you should actually prove this $\endgroup$ –
Finding the spherical coordinates for the edge obtained by cutting a . . . What I am now interested in is finding the parametrization of the cutting edge, however not as parametrization of a circle, but instead in spherical coordinates of the sphere This means I want to find the coordinates of every point on the cut, expressed in the spherical coordinate system
What is a proper face of a graph? - Mathematics Stack Exchange The paper On the Cutting Edge: Simplified O(n) Planarity by Edge Addition by John Boyer and Wendy Myrvold uses the term quot;proper face quot; I do not know what this term means At a guess, perh
Why can algebraic geometry be applied into theoretical physics? As I progressed in math graduate school specializing in number theory and algebraic geometry, it was astounding to discover a certain class of researchers who were doing very serious and nontrivial cutting-edge stuff connecting algebraic geometry and mathematical physics
general topology - Examples of the difference between Topological . . . There is apparently cutting-edge research by Dustin Clausen Peter Scholze (and probably others) under the name Condensed Mathematics, which is meant to show that the notion of Topological Space is not so well-chosen, and that Condensed Sets lead to better behaved structures What is a simple low-tech example to see the difference?
Cutting a cube with a plane - Mathematics Stack Exchange What you considered seems to be the shape of the face after the cut That would be the same as just cutting a square with a line What the questions asks for, is the shape of the two new internal faces that appears after the cut For example, if you cut along an edge to the opposite edge, you would get a rectangle of dimensions $1\times\sqrt2
Minimum Spanning Tree (MST): Cut property direct proof I'm trying to fully understand the cut property in the concept of minimum spanning trees (MST) in graph theory and graph algorithms It seems that all the literature out there proves this theorem via