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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
Finding the spherical coordinates for the edge obtained by cutting a . . . 1 I am searching the spherical coordinates for the circular edge that are obtained when a sphere is cut at a certain position with a plane The sphere has herby a radius r r and is focused at the center of a coordinate system The plane cut is performed at a certain x, y, x, y, or z z position (see an exemplary cut in the linked image)
number theory - Undergraduate roadmap for Langlands program and its . . . This is like a person who is just learning to count asking for a roadmap to integral calculus Focus on completing the core graduate material in analysis, geometry, and algebra -- the cutting-edge stuff will come in due time
Cutting a cube with a plane - Mathematics Stack Exchange 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 × 2–√ 1 × 2 It is the intersection of the cube and the plane
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
Calculating angles for wood joinery - Mathematics Stack Exchange After the boards are tilted up, B cannot have been cut at 45° if the faces are the join Also, the cut edge is no longer 90° from the face (like the other 3 edges on each board) How do I calculate B and C given an angle A? Essentially, the cut faces need to be parallel to the Z-axis
Prove by induction that a circle cut by $n$ chords can be filled by 2 . . . Let n ∈ N n ∈ N and suppose that n n chords are drawn in a circle, cutting the circle into a number of regions Prove that the regions can be colored with two colors in such a way that adjacent regions (that is, regions that share an edge) are different colors
geometry - What is the result of truncating Platonic solids . . . 0 Truncation need not be to the midpoint of an edge The traditional truncated Platonics have smaller pieces cut off so that the original edges are shortened but remain present These solids are know simply as the "truncated [named Platonic] Cutting back to the midpoint as described is known as rectification