math – update

blogging & searching for true math …


Leave a comment

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

pnt-1

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
Advertisements


Leave a comment

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

kc-3

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??…

Continue reading


Leave a comment

Day #14: Cocktails = Combinatorics!

l-g-c2
Rosé Champagner

Q: Suppose you will spend a 3-days-sommer-weekend at some warm & wonderful place – like Garda Lake (Italy), or Venice  Beach (Miami), or Pucon (Chile), … – . And say, you want to drink – only – 2 cocktails each and every of the 3 days you´ll be there! Now, if you choose your cocktails among those you think are your 7 favorite ones, and you don´t repeat drinks, can you tell in how many – different – ways you could enjoy them??… Hint: There are at least three ways to understand the question! Continue reading


Leave a comment

Day # 13: Fibonacci Numbers – From 0 and 1 to Unbounded Imagination

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …
Animated GIF showing successive tilings with squares whose side lengths are successive Fibonacci numbers  +  a graph of approximations to the Golden Ratio calculated by the sequence of ratios   1/1, 2/1, 3/2, 5/3, 8/5, 13/8, ……. , 89/55, 144/89   given by pairs of consecutive Fibonacci numbers.

Continue reading