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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
Mathematics Stack Exchange Q A for people studying math at any level and professionals in related fields
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
A double Möbius Strip - Mathematics Stack Exchange 1 Playing with home made Mobius Bands is good fun You can try cutting them down the middle, or one third the way from the edge Do the same with Bands of different numbers of twists See also this presentation
geometry - Compass-and-straightedge construction of the square root of . . . For example, suppose you want to find the square root of 5 Construct a right triangle with side lengths 1 and 2 This can be done with straight edge and compass Then the hypotenuse has length 5–√ 5 (times the unit) The procedure can get more complicated
How can a piece of A4 paper be folded in exactly three equal parts? Bend the paper in half, top to bottom, making crease #1 at the center on one edge of the paper Bend top down to fit in crease #1 to make crease #2 (1 4 distance from the top) Reverse paper (back face), bend so crease #1 and crease #2 align and make crease #3 halfway between them
geometry - Why is the volume of a cone one third of the volume of a . . . The volume of a cone with height h and radius r is 1 3πr2h, which is exactly one third the volume of the smallest cylinder that it fits inside This can be proved easily by considering a cone as a solid of revolution, but I would like to know if it can be proved or at least visual demonstrated without using calculus
arithmetic - Can a piece of A4 paper be folded so that its thick . . . If, however, the pressure created by making the folds (and cutting the paper into tiny rectangles and whatnot) compresses the paper so that it becomes less than ~0 1mm thick, then our exponent will no longer be valid Say that during the cutting process, the cellulose fibers unravel somewhat, leaving only two layers of fiber
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