Complex Numbers contd. . .

What are complex numbers? Can you give an analogy?
Money involved here. As the explanation can be quite expensive. Ambani is not sitting idle just to thwart flies.
Any way, I will give.
2 = 1 + (i squared) 1. Doubling is natural. When you break it becomes two.
And so 4 = 2 + (i squared) 2.
i squared in both the above is +1.
Consider, i squared as -1. Let us see what happens. This is risky. But a calculated one. On the strength of my education am I taking this risk.
So,
2 = 1 + (i squared) 1. Is that true No it isn't. Because 2 is not equal to zero. It may hurt dvaita philosophers, but not advaita philosophers. They may say 2 is indeed zero. There is no two.
So, what happens when i squared is -1 is that philosophy of one two arises.
Mathematicians thought, let us not waste time. Let us make i squared equal to -1. It will not be wrong also as i squared equal to +1 already exists.
So they decided on complex number i.

Magudanchavadi - A Short Story

Sekhar was trying to get some sleep in his berth in 2nd AC. He was on his way to visit a retired professor who was known to be staying in a place which the train will reach the next morning. It was evening 8 pm and Sekhar had nothing better to do. But try and relax.
Sekhar was a post graduate student in Physics. He was pursuing particle physics and was brilliant in it. The retired professor he wanted to meet was an expert in relativity and was acknowledged to have better theories than even Einstein. The retired professor was ignored by most of the Indian scientists and professors and was leading a sad life in one corner of a place. A place Sekhar was about to visit. He came to know the retired professor was staying at that particular place from a magazine which carried the article of the dejected retired professor.
Sekhar was brilliant in particle physics. He always stood second in his exams. The first position went to Tarun who was hard working and had great memory power. He never blamed Tarun for anything. He did not criticise him for using memory rather than inspiration and methods. Sekhar prided in being balanced and was supportive of even his rivals. Sekhar told himself, Tarun has his own methods of studying; I have my own; Both matters and both are following their  own ways.
Sekhar had a friend in Yakub. Yakub was a school friend of Sekhar. Yakub made it big in Gulf. He had his own business and was earning in crores. Sekhar's father would often compare Sekhar with Yakub. He would say how practical Yakub is and he made crores of money while Sekhar was pursuing theories. Sekhar refused to learn a lesson from his father. He maintained that Yakub is fine in his own way. And he is fine in his own way. Both matters and both are following their own ways.
Robert was another schoolmate of Sekhar and he made it big in pop music. Robert was young and his songs were continuously in the top charts for the last five years. Sekhar's sister would often tease Sekhar and would compare Sekhar with Robert. Sekhar did not allow himself to be affected by this comparison. He maintained that Robert is fine in his own way. And he is in his own way. Both matters and both are following their own ways.
Sekhar was thinking deeply in all these issues. He felt that the AC was not effective. But then he told himself, that's how it is. He felt that the train was slow. But then he told himself, that's how the trains move here. The food was cold. But then, he cannot expect steaming hot curries and rotis in train.
Suddenly the train stopped. Possibly for signal. Sekhar looked out of the window. It was Magudanchavadi. A small village or town.
Sekhar decided to get down and breathe in natural air. He got up from his berth and moved towards the door. There was a railway police personnel who stopped him. The railway police personnel was rather harsh and told Sekhar that he must be mad to get down here for the train will move any instant.
Sekhar was hurt by the word mad. But then he remembered. He was mildly schizophrenic and was taking medicines for it.
He went back to his berth. He opened his bag. He took out a tablet and popped in his mouth and drank water. Then, he decided.
Sekhar decided that he will not meet the dejected retired professor. There was no point. He will instead get down at the next big station. And return back to college. He promised himself that he will get well.
The railway police personnel at Magudanchavadi had saved him !!

My favorite Delhi Street Foods

My favorite Delhi foods are :-

1. Chole Bhature from BTW, Dwarka
2. Papri Chaat from the shop near UPSC
3. Aloo Tikki from Bengali Sweets, South Extension
4. Kulcha Chana from Haldiram's, Dwarka
5. Rabri Faluda from Giani's

I have never been to Parathe wali gali in Chandni Chowk area.

#PythaShastri post

About # PythaShastri

Corrected expressions
Given below are corrected expressions of phi and pi.

Questions to #PythaShastri.
1. What is the philosophy behind the term #PythaShastri?
Kirtivasan (I) is # PythaShastri. There were mad inspiration in me. I wanted to go closer to mathematical truth. So I decided to use the term #PythaShastri.
2. Has #PythaShastri reached the truth?
Yes. The above two are giving me the satisfaction of truth.
3. Why so much of fuss over numbers, #PythaShastri?
Numbers are not easy. We count with fingers. We go on, one the thumb, two the pointing finger. But someone exceptionally bright would say the thumb is different and the middle finger is. So two is not there. He may argue that no two things are exactly the same. Only some factors make the two things same.
4. The above expressions and so are many in the blog are not precise. Why publish them, # PythaShastri?
There are many accurate expressions too. When the focus is on one thing, the expression is accurate. When focus is on two are more things, the expression is not accurate. Measuring behavior is accurate and focus is on one thing. Becoming extroverted is focusing on two or three things and expression is not accurate.

#PythaShastri expression

I was wondering for last many years, how to handle  root 2, root 3, 2, root 5 etc. as a series. I was unable to get an expression.
Yesterday, I was thinking about the circle I get with a A4 sheet by tearing method. And I was thinking of half, quarter, one-eighth etc. as a series.
Then an idea struck me. Multiply half with one; quarter with one by root 2; one-eighth with one by root 3 and so on. This was what I seemed to be doing in circle from A4 by tearing.
What was the result in multiplying half with one; quarter with one by root 2; one-eighth with one by root 3 and so on?
The result till 1/(16384×root 14) was 0.80610075. Phi by two? Half of golden ratio?
Possibly. The curiosity of years got some peace as now I am able to understand root 2, root 3, 2, root 5 series. Multiply and invert with 4, 8, 16 etc.

Wolfram results do not support #PythaShastri claims. 0.806 it is till 1000. Not 0.808. But peace of mind has indeed been obtained, with this.

Is it the fastest nature Pi formula?#PythaShastri

Pi formulas exist in nature. Then there are formulas by Ramanujan, Chudnovsky and possibly others which are faster.
The Wikipedia formula of k!/(2k+1)!! is fast. This is nature. This is what I claim as Measuring Behaviour equation. It exists in nature.
Then there is another formula(2^n)/(comb(2n,n)). This too is nature. This was discovered by #PythaShastri. This is also Measuring Behaviour equation. It exists in nature.
The expression k!/(2k+1)!! gives pi to 6 places in 25 steps in Microsoft Excel.
The expression (2^n)/(comb(2n,n)) gives pi by 2 to 7 places in 25 steps in Microsoft Excel.
The second expression may be a little faster. Of course, Ramanujan expressions or Chudnovsky expressions are very fast. But this expression of (2^n)/(comb(2n,n)) will possibly come in top ten fast expressions of the world, if not the top five.
Also the two expressions are of nature.