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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
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 1 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
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
Cutting the corners of a cube - Mathematics Stack Exchange 0 You can cut the corners of a cube by another concentric and congruent cube: taking it in random orientation, it will in most cases not contain any of the corners, thereby "cutting them all off" But the corners will never be cut off regularly in this case for a simple reason: the cutting is done by the faces of a cube of which there are 6 6
linear algebra - Minimal edge cut - Mathematics Stack Exchange It sounds like you're right ! Suppose that C C is a minimal edge cut that yields at least 3 components Call G′ G ′ the graph obtained after removing C C from G G Put back any edge e ∈ C e ∈ C in G′ G ′ The two endpoints of e e belong to at most 2 of the components, so adding e e can only reduce the number of components of G′ G
cutting a cake without destroying the toppings If it crosses no more than N 2 toppings, then we are done Otherwise, make a vertical cut between two of the crossed rectangles This vertical cut does not cross any rectangle crossed by the horizontal cut, therefore it crosses at most N 2 toppings Lower bound N 4: In the following cake, with 4 toppings, every cut must cross at least 1 topping:
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