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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
What is a great book to read about sequences, sums and products? 24 I assume you're asking about real and complex infinite sequences, series and products I don't know of any text which gives anything like a "complete" or even a "cutting-edge" treatment of this topic One reason is that the subject of infinite series was much more mathematically fashionable in the period from, say, 1800 to 1900 than it is now
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
Why is the volume of a sphere $\\frac{4}{3}\\pi r^3$? As the plane cutting through the solids moves, these blue squares will form 4 small pyramids in the corners of the cube with isosceles triangle sides and their apex at the edge of the cube Moving through the whole bicylinder generates a total of 8 pyramids
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
Visually stunning math concepts which are easy to explain Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are easy to understand and explain but are
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
Properties of Equilateral Triangles in Circles Yes If you're familiar with construction using compass and straight edge, one of the easiest ways to construct an equilateral triangle is to draw two circles where each circle's centre lies on the other circle's edge Drawing a line between the two intersection points and then from each intersection point to the point on one circle farthest from the other creates an equilateral triangle You