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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
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
Mathematics Stack Exchange Q A for people studying math at any level and professionals in related fields
an optimisation problem folding paper - Mathematics Stack Exchange A standard $8 5$ inches by $11$ inches piece of paper is folded so that one corner touches the opposite long side and the crease runs from the adjacent short side to the other long side, as shown i
How to find the line that splits the area into two equal parts? Let R R be the region bounded by the graphs of y = cos(πx2) y = cos (π x 2) and y =x2 − 1 y = x 2 − 1 The line y = k y = k splits the region R R into two equal parts Find the value of k k First find the area
Calculus proof for the area of a circle - Mathematics Stack Exchange I was looking for proofs using Calculus for the area of a circle and come across this one $$\\int 2 \\pi r \\, dr = 2\\pi \\frac {r^2}{2} = \\pi r^2$$ and it struck me as being particularly easy The only
right circular cylinder inscribed in a sphere So I quickly drew a cylinder inscribed in a sphere in MS paint for you, in case you needed more help setting up the problem (mvw's 3D plot is also very helpful for the intuition! Compare our pictures to get a feel for how everything goes together) I wasn't sure how to draw just part of the circles dotted as they technically should be, but this should help show what you need to do
Difference between ≈, ≃, and ≅ - Mathematics Stack Exchange In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical Operators B