math – update

blogging & searching for true math …

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#23: The Prime Theorem of Math = The Prime Number Theorem


Q: Did you ever realized that the Prime Number Theorem is equivalent to the statement that the nth prime number pn satisfies

 p_{n}\sim n\log(n) ??… Continue reading

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Day #20: Riding on a Wild Torus


Q1: Say, you are actually riding on the surface of a torus, and say, you´re in a hurry! Could you find the shortest path to follow??…

Q2: And, if the surface of a – flexible – square that generates a Torus is just 1. Could you tell radius of its two generating circles and of its cartesian equation??…

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Day #18: Reaching into Kepler´s Conjecture and Hilbert´s 18th Problem


Q: Imagine a cube of sides L and put 8 – maximal – spheres centered on each vertex. Then calculate the density of this 8/8 spheres inside the cube!!… Now, put a whole sphere in the center of the cube – as dense as it´s possible – and calculate again!!… And now, take away the central sphere, and instead, put central spheres in each of the six faces of the cube – as dense as possible – and calculate again!!… Is this the maximal density of Kepler´s conjecture??…

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