Aryabhata – I

476 – 550 CE (CE is the same as AD and BCE is the same as BC)

 

“Chaturadhikam Shatamashtagunam Dvashashtistatha Sahasranam

Ayutadvayavi Shkambhasyasanno Vrttaparinahah” – Ganita Pada, 10 – Aryabhatiya.

 

Roughly translated: “Add 4 to 100, multiply by 8 and add to 62000. This is approximately the circumference of a circle whose diameter is 20000”

Implying PI = 62832/20000 = 3.1416

 

• One of his most important legacies is his accurate knowledge of the value of Pi. Especially when Pi could be expressed only as a whole number ratio as there was no system for decimal fractions back then.
• Prior to him, Vedic Sutras had expounded on geometric relationships for religious purposes such as altar construction and keeping track of calendars. Jain mathematicians also excelled at mathematics prior to Aryabhata.
• One of his works, “Aryabhatiya” has survived till today. It was written in Sanskrit and in poetic verse form containing 123 stanzas.
• Aryabhata provides methods to find out square roots and cube roots (Though the square roots have been thought of being found out before him)
•  Since the value of Pi was known to him, he also gave the formulae to calculate the area of a circle and volume of sphere.
• One of his more complicated works was his derivation of the Sine Table. In fact, the modern  trigonometric names ‘Sine’ and ‘Cosine’ are a mis-transcription of the words ‘jya’ and ‘kojya’ as introduced by Aryabhata. These were transcribed as Jiba and KoJiba in Arabic. They were then misinterpreted by Gerard of Cremona while translating an Arabic Geometry text into Latin. He took Jiba to be the Arabic word Jaib, which means fold in a garment, ie. Sinus.
• Aryabhata’s astronomical calculation methods were also very influential. Calendric calculations worked out by Aryabhata and followers have been in continuous use in India for the practical purposes of fixing the Panchangam or the Hindu calendar.
• Aryabhata was the first astronomer to make an attempt at measuring the earth’s circumference accurately. His estimation of 24,835 miles was a deviation of just 0.2% from the actual value.

 

So, the next time you hear the name of the first satellite launched by India to be “Aryabhata”, the Lunar Crater “Aryabhata”, Aryabhata Maths Competition or of the Aryabhata Research Institute of Observational Sciences (Near Nainital), you know who the great person was and why they are all named after him – After all, calculating the value of Pi when there was no decimal fraction system was like thinking of a car when the wheels were not invented!

 

 

Destination Infinity

Thought Provoking Quotes – II

Since by now, you would have known my interest in collecting different quotations which would make you read them once again, here are some more, which I found interesting:

“Fortune does not change men; it unmasks them”

“Fashion is a form of ugliness so intolerable that we have to change it every six months”

“Always forgive your enemies. Nothing annoys them as much”

“It’s human to think wisely but act in an absurd manner”

“The true measure of a man is how he treats someone who can do him absolutely no good”

“Truth, like surgery, may hurt but it cures”

“The greatest good you can do for another is not just to share your riches, but to reveal to him his own”

“Obstacles are those frightful things you see when you take your eyes off your goal”

“You should not bite the hand that feeds you. But maybe you should, if it prevents you from feeding yourself”

“What we are is God’s gift to us. What we become, is our gift to God”

“Insanity in individuals is something rare. But in groups, parties, nations and epochs, it is the rule”

“There are three sides to every argument – Your side, My side and the Right side.”

“Everyone should have a spouse, because there are a number of things that go wrong that one can’t blame the Government”

“Hearing is one of the body’s five senses. But listening is an art”

“Be kind, for everyone you meet is fighting a hard battle”

“The young do not know enough to be prudent, and therefore they attempt the impossible, and achieve it generation after generation”

 

Destination Infinity

Related Reading: Thought Provoking Quotes

You could visit the Quotations and Humour section of this blog for similar articles. 

I am a Hypocrite

 

Rakesh has tagged me. This was the opportunity that I was waiting for!

The Tag: Requires me to post six things that are eccentric attributes of mine.

I choose to describe only one eccentric attribute (trait?) of mine – Hypocrisy. But I would give six instances to showcase it though!

When the match fixing scandal was exposed in Cricket, I thought that it was some kind of a conspiracy to undermine the popularity of the game. Because, even after the exposure, I tend to watch the game with the same passion I had earlier, in any of its forms. What is important for me is the fun I have in cheering for my team and the ‘feeling’ I get after we win a match or a tournament. Even if some people are skeptical about the rival captain’s decision to bowl part time bowlers at a crucial point of a match, I would choose to ignore all that. I am ecstatic because of the fact that we won that match. And that is what matters to me. I don’t really bother when in football, the United States is a a quarter finalist in a world cup hosted by the United states or when Japan and Korea both reach the semi finals of the world cup jointly hosted by them or when Italy wins the world cup just after a huge match fixing scandal breaks out there. What I am more bothered about is that I was not able to watch some of the matches! You could also read a Poem that I wrote on the topic ‘Match Fixing’ some time back!

When I see a bottle in the middle of the road, I curse the person who put it there and would get around it hoping that every one else also would be able to do the same. The idea of stopping my vehicle and removing the bottle from there never crosses my mind. Even if it does after some time (And distance), I would like to think that some one would have removed it by now! When a fellow commuter breaks the traffic signal to attend to some ‘Urgent’ work that he always seems to have, I would abuse him. Or ignore him. Worse, I would even take him as an example and start breaking signals myself, as I think that he was daring, smart and even saved a lot of time by breaking signals!

When Miss My Country wins the Miss Universe or Miss World pageant after giving such a complex and a brilliantly well constructed reply to the question posed by the judges in the final round, I would rejoice even though the sentence seems to be hopelessly memorized (Albeit for a short time, after which that ‘good’ feeling takes over again)!

I sincerely believe that all those film awards are being given to the deserving ‘artistes’ and I fail to understand or even probe why Amir Khan is not present to collect the award for any of his movies. I am happy as long as I am entertained with so many glamorous people all under one roof, and I think why they don’t screen these award functions at the multiplexes!

I believe that education is the key to success in life. So much, that I don’t care to notice how students are admitted into these ‘technical’ institutes, what they are taught there, whether they are able to understand and are able to apply the theoretical concepts to practical applications, how they very often memorize whole pages to just pass the examinations, or even to get university ranks. I just don’t bother about all these trivial things as long as I get admitted in one, manage to pass out with a decent GPA and get a high paying job in a big company. I don’t bother to see if the kind of work I am doing is helping me to achieve quality results and is able to help me take further strides in my career to understand good business practices and acquire skill sets that would reward my company and myself.  All I would be bothered about after joining one would be about the appraisals (Perhaps the lack of it?) and the onsite ‘opportunities’. Of course, I would also be bothered about how much more is my college mate or ex-colleague is earning in his/her big company!

And last but not the least, I really think that Open and Free market strategies and practices are really open and free for everyone and they are the best bet to solve all our economic woes!

I am a hypocrite and a proud one at that. Because, if I was not proud of it, I would have at least attempted to change myself! I guess I share a lot with my fellow citizens 🙂 

 

Destination Infinity

PS: I am supposed to tag some people. So, consider yourself to be tagged if you wanna add some more salt….

Otto Von Bismarck

1815 – 1898

Germany, unlike England and France was not a united nation, for quite a long time. Bismarck’s most important legacy is the unification of Germany. Germany had existed as a collection of a lot of separate principalities, and free cities, since the formation of the Holy Roman Empire. Bismarck was the first leader to unite a major portion of what is referred to as Germany, today.

Otto Von Bismarck was not the prince of Prussia – which was by far the largest constituent of the divided Germany. In 1848, Prussia faced a revolution, which resulted in the creation of the constitution and legislature (Landtag). Bismarck was even elected to this Landtag but later was made an envoy (Of Prussia) to Frankfurt, Russia and France.

In 1862, the King of Prussia – Wilhem appointed Bismarck as the Minister-President and Foreign Minister of Prussia. Bismarck used both diplomacy and the Prussian military to achieve unification of a multitude of principalities loosely bound together as members of the German Confederation. Prussia became the most powerful and dominant member of this new Germany, and Austria was excluded. The new German empire was a federation. Each of constituent states retained some autonomy. Bismarck was appointed the imperial chancellor of the German empire.

During most of his nearly 30 years long tenure, Bismarck held undisputed control over the Government policy. He was well supported by his friend Albrecht Von Roon, the War Minister and the leader of the Prussian Army – Helmuth Von Moltke. Bismarck mostly devoted himself to keeping peace in Europe so that the strength of the German empire would not be threatened.

Bismarck’s astute, cautious, and pragmatic foreign policies allowed Germany to retain peacefully the powerful position into which he had brought it. He maintained amiable diplomacy with almost all the European nations, except maybe France.

Some of Otto Von Bismarck’s famous quotations:

“Only self interest makes a war worthy cause for a major state. At the end of the conflict we would scarcely know why we had fought”

“Man cannot create the current of events. He can only float with them and steer”

“What we learn from History is that no one learns from History”

“The most significant event of the 20^th Century will be that the North Americans speak English”

“Never believe anything in politics until it has been officially denied”

“When a man says he approves of something in principle, it means he hasn’t the slightest intention of putting it into practice”

“When you want to fool the world, tell the truth”

 

Destination Infinity

 You could visit the People Places and Culture section of this blog for similar articles.

Where do we play?

Sundar was in his early sixties. He had been working in a good position in a leading Government firm and had retired recently. He was always active during his working days and hence even after retirement he chose to be active by becoming the General Secretary of the apartment where he and his son’s family lived – in separate apartments. One of the proposal that he was instrumental in taking forward was the expansion of the apartments. The Government had left some good space in front of the four blocks as a part of its planned apartment construction (When the apartments were originally constructed before some years) as per its procedures. The Government then sold off the apartments to individual tenants. Recently a lot of such Government built apartments were expanding in the open spaces available with them, across the city. Not to be left behind, Sundar too managed to get the permission to expand his apartments. Dharma, was his grand son. He was studying in the eighth standard.

 

“Today is one of the most important dates for this apartment Dharma. We have managed to get the permission to expand the apartments. We will no longer be a 2BHK apartment owners. We will be the proud owners of Three Bedroom, Two Hall and Kitchen apartments. You should be very happy as we are doing all this for you. Aren’t you exited to have a bigger house?”

 

“But Grandpa, all the owners have to pay for the expansion, right?”

 

“Yes. But we managed to get almost everybody’s approval except a couple of the owners. The turning point was the deal that we struck with this construction company. They have offered to do the construction, free of cost for us. We need to pay only for the materials. All they wanted in exchange was to construct one more floor – The Third floor and sell it at the prevailing market rates today. So, the owners were very happy. And so was the construction company as the existing real estate prices in this area has sky-rocketed recently”

 

“But what is the advantage to us?”

 

“We would be the proud owners of such a big apartment house, that too in a prime location in the city. That’s why I insisted that your father buy an apartment here itself”

 

“But Grandpa, you and Grandma live in a separate apartment. My parents and myself too live in our own apartment. Why do we need four halls and six rooms for the five of us?”

 

“You are too young to understand the real estate market. It is something like this – If we ever decide to sell an apartment after expansion, the returns would be very high”

 

“But would we ever sell, Grandpa?”

 

“That, I am not sure. Maybe not in the near future. But we can feel secure as we have such a high value property with us. Investing in property is always the best investment, dear”

 

“But we have already taken a loan to buy the house. Now we need to take another one for the expansion”

 

“Yes, that is there. But think about this – If we stayed in rental houses, we would be paying a considerable amount as rental every month and after a long time we would have paid a lot of money but we would not own any property. This is better than that, isn’t it?”

 

“But the rental amount would be considerably lesser, Grandpa. We would also be able to use the differential amount for having a better standard of living. Imagine if there is a misfortune and we are not able to pay the Bank installments”

 

“That is exactly what I was talking about. If ever such a misfortune arises, we could sell one of the apartments, settle the bank loan and still have a handsome amount to spend in our hands. All of us could always live in a single apartment after that”

 

“You are talking about the advantage that we could get, in the event of a misfortune, Grandpa. I was talking about the advantages we could have, without that misfortune. And on the top of that we require a misfortune to stay together!”

 

“Nothing like that. This is also like living together. You could always come here anytime you want, right?”

 

“Yes. But everything is separate, right? We have two kitchens, two separate furniture sets, double maintenance charges, when we could have easily avoided all that”

 

“But this was the best option available to me when your parents wanted to live separately. You are young. You cannot understand certain things in life. It will take some time before you grasp all these things”

 

“I too guess so. But Grandpa, where do we play Cricket after the expansion?”

 

Destination Infinity

PS: This post was inspired by This Blogpost by An Alien Earthling. Wondering if there is any connection between that post and this one? There is.