It's my birthday tomorrow and my friend mathematics wishes me mathematically in many ways:-

1) I'm 19 years now. 
The no. 19 is a happy prime.i.e. it is a prime and satisfies  the following property.

1|9     : (1)^2  + (9)^2 = 82
8|2     ;  (8)^2 + (2)^2 = 68
6|8     :  (6)^2 + (8)^2 = 100
1|0|0  : (1)^2 + (0)^2 + (0)^2 = 1! 
( Source: http://en.wikipedia.org/wiki/Happy_number)

2) ஓட்ட  வடை(Sambhar Vadai)  my  favorite dish:
I remember asking my mom to prepare Sambhar Vadai for my birthday which is inauspicious to prepare on occasions which are good such as birthdays but now I realize that as a wholly different thing,

It reminds me, the structure of a torus which topologically speaking is a product of two circles S X S in C^2.
 This has a consequence that topologically a coffee mug and Sambhar Vadai(Torus) a similar  as they are homoemorphic .Since the latter is my favorite the former is also my favorite drink. :)


3) The birthday problem :
" In a set of "n" randomly chosen people what is the probability that a pair of them will have the same birthday."
(Assuming the year is non leap year i.e. contains 365 days)
( As a budding Mathematician I wanted to study the generalized birthday problem but since the Density of my social network is tending to zero(to know more click here),it's better I stick on to the trivial case.:) )

Its clear that for n>365 probability that a pair will have same birthday is 1.

Solution:-
Let
n : Event that a pair of people will have the same birthday.
n# : Event that a pair of people will not have the same birthday.
P(A) denotes the probability of occurrence of event A.
_
P(A) denotes the probability of not occurring of event A(=P(n#) here)

we must have P(n) + P(n#) = 1

Since it's easier to compute P(E#) in this case we have

P(E) = 1 - P(E#) 

So,the required result is 
             _
p(E)=1-p(n)

In my case as the density of social network is low, it's guaranteed that p (E) will be low but let me wait till tomorrow and see.

4) Cake cutting Algorithm: 
I may or may not cut a cake for my birthday also I don't eat cake much ,maybe I  have nothing to say, but here's a video on how to mathematically cut a cake the right way:

An equation means nothing to me unless it expresses a thought of God.                                                                                    - Srinivasa Aiyangar Ramanujan.