# math – update

## #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

## Day #19:: In or Out of a Little Klein Bottle

#### Time evolution of a Klein figure in xyzt-space

Q: What do you really understand of it??… Continue reading

## 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??…

## #17: How many people do I need to have at my birthday party so that there is a better-than-even chance that one of them will share my birthday i.e. 17/12??…

Q: How many people do I need to have at my birthday party so that there is a better-than-even chance that one of them will share My birthday??… Continue reading

## Day #14: Cocktails = Combinatorics!

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