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What is cutting edge maths? - Mathematics Stack Exchange It's always better to translate sentences than individual words 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
Cut vertices and cut edges - did I answer these correctly? Problem Find the cut vertices and cut edges for the following graphs My understanding of the definitions: A cut vertex is a vertex that when removed (with its boundary edges) from a graph creates more components than previously in the graph
Cutting a Möbius strip down the middle - Mathematics Stack Exchange During this process, the Möbius strip loses its non-orientability Make two Möbius strips with paper and some tape Cut one and leave the other uncut Now take each and draw a line down the middle The line will come back and meet itself on the Möbius strip; on the cut Möbius strip, it won't Share
Cut edge proof for graph theory - Mathematics Stack Exchange Cut edge proof for graph theory In an undirected connected simple graph G = (V, E), an edge e ∈ E is called a cut edge if G − e has at least two nonempty connected components Prove: An edge e is a cut edge in G if and only if e does not belong to any simple circuit in G This needs to be proved in each direction
difference between minimal and minimum edge cuts. An edge cut is a set of edges that, if removed from a connected graph, will disconnect the graph A minimal edge cut is an edge cut such that if any edge is put back in the graph, the graph will be reconnected A minimum edge cut is an edge cut such that there is no other edge cut containing fewer edges A minimum edge cut is always minimal
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
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
linear algebra - Minimal edge cut - Mathematics Stack Exchange First, connect the three components with two edges Then you can delete either edge and get a pair of components Now, connect them with three or more (N) edges Now, you can choose a subset of (N - 1) edges such that one of the components is disconnected I tried drawing various convoluted graphs with chiral C3 symmetry, but none quite worked
combinatorics - A visual solution to the cube cutting problem . . . r(t):= (1 − t)r0 + tr1 (0 ≤ t ≤ 1) then has the same coordinate order for all t ∈ [0, 1]; hence the segment [r0,r1] does not intersect one of the cutting planes It follows that r0 and r1 belong to the same piece of the partition Since there are 3! = 6 possible orders among different numbers x, y, z we have six different pieces
geometry - Cutting figures into parts of equal size and form . . . How to cut figures 4 and 5 into 2 parts of the same sizes and forms? Cutting is allowed by drawing lines along sides or diagonals only, as demonstrated by the example below Example of cutting into 2 parts In figure 4, each part must have 24 2 = 12 squares In figure 5, each part must have 22 2 = 11 squares Solved it by using shape clues