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What is cutting edge maths? - Mathematics Stack Exchange My maths teacher always keeps telling me about this 'cutting edge maths' that is going on in the world, amazing maths research, etc A lot of the google searches I've done for 'Cutting Edge Mathematics' hasn't returned much useful information, so I've taken to mathematics stack exchange
When you randomly shuffle a deck of cards, what is the probability that . . . The situation is not the same as in the birthday paradox The birthday paradox works because the two identical birthdays may appear between any two of the persons However, in your experiment, you demand that you are one of the two persons involved in the same card deck A situation analogous to the birthday paradox would be given by the question "what is the chance that over the last 600
Cut vertices and cut edges - did I answer these correctly? A cut edge is an edge that when removed (the vertices stay in place) from a graph creates more components than previously in the graph My Answers 31) The cut vertex is c c There are no cut edges 32) The cut vertices are c c and d d The cut edge is (c, d) (c, d) 33) The cut vertices are b, c, d b, c, d and i i
Why is the volume of a sphere $\\frac{4}{3}\\pi r^3$? Another such line is parallel to the diameter edge, 4r 3π away from it (verification of this is left as an exercise for the reader) When revolved about the diameter edge of the semicircle, the centroid travels 2π ⋅ 4r 3π = 8 3 ⋅ r, so the volume of the sphere is 1 2πr2 ⋅ 8 3 ⋅ r = 4 3πr3
Prove that the chromatic index of a - Mathematics Stack Exchange Let G G be a (finite) k k -regular graph with a cut vertex v v, and assume for a contradiction that G G admits a proper edge coloring with k k colors Fix such a coloring; each vertex of G G is incident with one edge of each color
Cutting the Cake Problem - Mathematics Stack Exchange Therefore we can apply "you cut, I choose" method to the leaving 2 pieces Edit: This problem can be solved with arbitrary number of children using the algorithm for finding maximum matching in a bipartite graph Suppose, number of children is n Cutting the cake algorithm is the following 1 Let (1) divide cake into three equal pieces 2
Understanding the Equation of a Möbius Strip So the edge of the Mobius strip is given by the equation above for s = w 2 s = w 2 as a parametric equation only in t t Of course s = 0 s = 0 produces the circle of support (base)
Probability question - Mathematics Stack Exchange A large white cube is painted red, and then cut into 27 identical smaller cubes These smaller cubes are shuffled randomly A blind man (who also cannot feel the paint) reassembles the small cubes
Online tool for making graphs (vertices and edges)? Grouping vertices Changing style of nodes and edges (color, shape, thickness of edge, line style, node size) Bending edges Shortcuts support Displaying the last action with possibility to undo Copying, cutting, pasting of nodes and edges Support for mobile and touch devices
Finding the Center of Mass of a disk when a part of it is cut out. From a uniform disk of radius R a circular disk of radius R 2 is being cut out The center of the "cut out" disk is at R 2 from the venter of the original disk We have to find the center of mass of leftover body I thought that we should set up a coordinate system with the center of original disk as the origin The formula for center of mass is →RCM = 1 Mtot∫→r dm