Math

List of all Mathematics posts on wpgaurav

Understanding Poincare Conjecture

In 1904, the french Mathematician Henri Poincaré (en-US: Henri Poincare) posed an epoch-making question, which later came to be termed as Poincare Conjecture, in one of his papers, which asked: If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere? Henri Poincare – 1904 So what does it really mean? How

What is a Prime Number? An integer, say $p$ , [ $\ne {0}$ & $\ne { \pm{1}}$ ] is said to be a prime integer iff its only factors (or divisors) are $\pm{1}$ & $\pm{p}$ . As? Few easy examples are: $\pm{2}, \pm{3}, \pm{5}, Derivative of x squared is 2x or x ? Where is the fallacy? We all know that the derivative of$x^2$is 2x. But what if someone proves it to be just x? Solving Ramanujan’s Puzzling Problem Consider a sequence of functions as follows:-$ f_1 (x) = \sqrt {1+\sqrt {x} }  f_2 (x) = \sqrt{1+ \sqrt {1+2 \sqrt {x} } }  f_3 (x) = \sqrt {1+ \sqrt {1+2 \sqrt {1+3 \sqrt {x} } } } $……and so on to$ f_n (x) = \sqrt {1+\sqrt{1+2 \sqrt

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