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What I thought as my worst fear was perhaps my most loyal companion. For the better part of the two decades, I remember myself wondering, whining, and crying myself to sleep over not being able to communicate what I felt within me. I wondered why I wasn’t the perfection that my sibling seemed to effortlessly master and contain; pondered over not being fun or frolic like my peers. I was told that this was the way achievers behaved, but I look down at my empty hands sometimes and feel nothing but the sting of remorse and regret. I wanted to laugh. I have tried. But someone always chides me. Maybe that is only because that is how they usually talk. How can I tell them that though I would want to brush it aside and laugh along, I am unintroduced to that luxury I love staring at them when they do that? How do people find it so easy to look so light? Can I too learn that secret? I don’t know who I should ask. I want to tell all of them that I am grateful that they are around. I want to give them a hug sometimes…I want to wink at them…I want to call out their name just to feel that they are around me. And I want to tell them. But what if they don’t like me? I have tried telling people how I feel. I have tried telling them of the things that amuse me, things that make me happy…and things I thought they too would love to see. But there has hardly been a time when I told them and they stayed. They all choose to leave and it is my fault. I am boring…intolerable sometimes. I can only bleed on paper but I cannot tell you how much I want to learn to talk like them, be like them…to smile, to have friends, to hangout, to have secrets to share and inside jokes to laugh at. I know it is stupid. I try to imitate them. I try to learn from them. But when they recoil away from me, I am afraid to call them back. I want to ask them how I can be like them. I want to know if I can be one of them. I want to tell them that it is not that I do not care. Just that I am afraid to accept the fact that I feel lonely mostly. I want to contradict the people around me calling me friendless and arrogant, and for which I must myself firstly believe that I am not scared of this claustrophobic confine and void that looms larger within me…so I pretend to be the one choosing…I pretend that I love who I am; I pretend that I can genuinely spell and paint my loneliness in the brightest shade of wondrous solitude. I must admit I am wrong and the wet pillow on my bed and the pile of patient paper are all that I can bring to you as witnesses to this crumbled me. And yes, I have loved. Whatever else I did half-heartedly, I have loved with all my heart and soul. I have loved like to love was the last of the human freedoms left to me, and I have picked up every piece of me like shards of broken porcelain and tried to lay them in careless fashion for their kind perusal. There was nothing that could interest them there either. But as memoirs penned on sleepless nights, I bequeathed from all the unrequited love a reminiscence that I poured into the open arms of my paper. I have murmured names to empty nights, chanted lines of confidence to memories…but I somehow surely lacked the courage to love myself that way. Had I perchance, I would never had written this to you. But I will continue to love and dream…till whatever last remains of me. If you have read till here, I would like to thank you for bearing with me and I would like to tell you that I indebted for your patient company. I don’t know what else to say but I hope that the above passages – unedited, written in the middle of a sleepless, drowsy night – will tell you all that I wanted to. I have always wanted to tell you how much your presence, every single moment of slightest conversation, a wave across the room, meant for me. I wanted to hold your hand and tell you my fears, thank you for just crossing my path. I wanted to show you a million minute scars. But I was just afraid. All I can tell you is a sorry…for being awkward and stupid sometimes. Good night.

little motivation

few days back i had been working on my PR for some organization , it was about a mathematical entity called the quaternion’s and i did not have any single idea about what quaternion’s are?. so i started learning about that from ground on by myself. Initially i was excited and wanted to learn as quickly as possible.
Later, after some days, then I had some difficulties which I got depressed about. My task was to understand the rotation of the quaternion function at the rate of a vector provided(whaaaaaaaattt??), I believed if I don’t understand the derivation, there is no point to just code that formula without actually understanding it. I did not sleep at all that night, trying to see the clear picture. But no use , I realized it’s the morning already. I made fresh myself, had a bath, went for breakfast and then head to college. I was really sad and was thinking about leaving the idea and doing something else.

Next I entered my class , grabbed my seat , said good morning to my friends, and then looked up to the blackboard. To my surprise there was this great quote written there -“everything you don’t know is something you can learn.”
I was like woooooooooo!!, that was cool, really cool, that line charged me up.

That’s all , I was like I don’t need anything else, no more bad thoughts, no more give up , I did not think about anything but to finished what i had started.

today I have successfully done my PR to the organization and It Is under discussion right now. But I’m not done yet I’m already working on other things(modules) with more energy and now I am not scared of doing something i don’t fully understand, the thing is, If I want, I can learn it!

Joke time

1. A cafe patron ordered a pastry, then changed his mind and replaced it with a cup of coffee. When he finished his coffee, he started leaving without paying. The waiter approached him:
—You didn't pay for coffee!
—But I had it instead of the pastry.
—You didn't pay for the pastry either!
—But I didn't have the pastry.


2. I bought a book online "How to implement an Internet scam." Somehow, though, it's been a while, and I still haven’t received it.

In search of pattern.

we know that ,
e^x = 1 + x/1! + x^2/2! + x^3/3! +...............ad. inf.

to get the series for a^x where a is any real number,
let e^y = a
thus log(a) = y
therefore a^x = e^(xy)

a^x = 1 + xy/1! + (xy)^2/2! + (xy)^3/3! +......................ad. inf.
a^x = 1 + x[log(a)]/1! +x[log(a)]^2/2! +x[log(a)]^3/3! +...............ad.inf.

now consider a = 1+y
we get,

(1+y)^x = 1 + x[log(1+y)]/1! +x^2.[log(1+y)]^2/2! +x^3.[log(1+y)]^3/3! +...............ad.inf. ---------(1)

also by binomial theorem,
(1+y)^x = 1 + x.y/1! + x.(x-1).y^2/2! + x.(x-1).(x-2).y^3/3! +.....................ad. inf. ----------(2)

from (1) & (2) , it is clear that log(1+y) is the coefficient of x in (2)
thus , log(1+y) = y - y^2/2 + y^3/3 + y^4/4 +..............ad. inf.

but thats not it , we also get to know that [log(1+y)]^2, [log(1+y)]^3, [log(1+y)]^4, and so on are the coefficients of x^2, x^3, x^4 and so on respectively in (2)

thats the thing everyone knows but still no book seem to have those infinite series ,
so i decided to calculate them and try to find some patterns in their coefficients.

log(1+y) = 1 + y/ 1 + y^2/2 + y^3/3 +................ad. inf. (you will find this series in most of the books)

what about raising an infinite series to higher integer power,

[log(1+y)]^2 = 2.[y^2/2! - 3.y^3/3! +11.y^4/4! - 50.y^5/5! + 274.y^6/6! - 1764.y^7/7! + 13068.y^8/8! - 109584.y^9/9! + 1026576.y^10/10! -............ad.inf]

[log(1+y)]^3 = 6.[y^3/3! - 6.y^4! + 35.y^5/5! - 225.y^6/6! + 1624.y^7/7! - 13132.y^8/8! +118124.y^9/9! - 1172700.y^10/10! + ................ad.inf.]

(this is special , you will not find this anywhere but here.

I was also calculating the series for [log(1+y)]^4 , but later i thought this is pointless, so i drop the idea (i was just hoping that maybe i will figure out some interesting things, but anyways i've done this just because i was curious.)


It is easy to see the pattern in the coefficient of the terms in log(1+y) series.
what about [log(1+y)]^2 and [log(1+y)]^3 ?
well i figured this out ,

the coefficient of y^n in the expansion of [log(1+y)]^2 is

2(-1)^n-1/n *(1 + 1/2 + 1/3 + 1/4 +.........1/n-1)

and for [log(1+y)]^3, nth term coeffcient is

(-1)^n+1 *[1 + 1/2 + 1/2^2 + ............ + 1/2^n-2]

My first arduino project (tv-remote controlled car)

more to come....

I made this car during my vacations after i completed robotics with arduino workshop at Makxenia (http://www.makxenia.com/) Nagpur. I really enjoyed that and looking forward to learn more. Unfortunately I've been busy in Gsoc 19 this semester so don't have much time to do more robotics projects.

Happy pi day!

pi is an infinite , non-repeating decimal - meaning that every possible number combinations, all exists somewhere in pi. Converted into ASCII text, somewhere in that infinite string of digits is the name of every person you will ever love, the date , time, and manner of death, and the answers to all the great questions of the universe.
Converted into a bitmap, somewhere in that infinite string of digits is pixel-perfect representation of the first thing you saw on this earth, the last thing you will see before your life leaves you , and all the moments, momentous and mudane, that will occur between those two points.

All information that has ever existed or will ever exist, the DNA of every being in the universe.
EVERYTHING:
all contained in the ratio of a
circumference and a diameter.

-- Anonymous.