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??…
Category Archives: College Math…
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??…
Day #14: Cocktails = Combinatorics!
Q: Suppose you will spend a 3dayssommerweekend 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
Day #12: Buffon’s Needle Problem or – not exactly – how much is the chance you don´t lose your needle when sewing on the terrace??… (Assume the chance you´re sewing is not zero)

Q: Suppose we have a floor made of parallel strips of wood, each the same width, and we drop a needle onto the floor. What is the probability that the needle will lie across a line between two strips?
#9: Pure Awesomeness of the Fundamental Theorems of Mathematics
Q: In your opinion, which fundamental theorem is incredibly missing??…
Fundamental Theorem of Arithmetics
Fundamental Theorem of Algebra
First Fundamental Theorem of Calculus
Day #8:: Hanging Around on a Möbius Stripe
Little balls on the edge of a Möbius stripe change sides!
What do you really know about it??…
Day #3: Visual Worlds, Visual Proofs
Q: Can you write the statement that the above image is proving??…