There is something our text books miss. In this thread I tried to show how science and maths books don't cover the personality and stories of the inventors and discoveries. Then there are history books that don't cover the logic a person used to find something but only the dates and stories of how he did. Aryabhatta was one of the greatest minds India has house. He lived in 4th century AD under the Gupta rule. He is claimed to have done following inventions. He is believed to have found an approximate value of Pi. He hypothesised elliptical orbit of planets. He devised approximate days for eclipses that are true with a small margin of error. He also used primitive algebra, by using Sanskrit letters to denote. He used concepts of trigonometry and spherical trigonometry. He calculated rotation of Earth, true to seconds. But Aryabhatta quite definitely does not "invent" zero because Hindus had a concept of zero since the time of Vedas. Aryabhatta uses Place Value system, that has zeros, ones, tens, hundreds and so on places. That gives an idea that Aryabhatta knows and used zero. Aryabhatta would use decimals too, further concreting this idea. These all inventions we do know. We have read about them in our books. But how many of us try to actively know how did Aryabhatta land on these inventions? What was the logic he used? Great minds think alike people say. Observing the methods used by such a great thinker, we too might solve problems in our life or come up with unique solutions. Seeing facts as just facts is what kills the education in its birth. Education comes from thinking about what we were taught. This is the kind of education that is vouched by ancient Indian schools of philosophy and thinking. Thinking about about education is what leads us to enlightenment.

This is a very nice thread inviting us to ponder over the intelligence and knowledge of some of our ancients who used certain methods to find out the Mathematical identities and formulas. Aryabhatt and Ramanujam are the two names which are generally referenced in this matter. I have gone through a book known as Vedic Mathematics where many Mathematical theorems and axioms are explained in a different way than they are taught today so it is definite that those people knew some different ways to arrive at those Mathematical things. Many of these things are explained but for some there is no explanation as how they arrived at them. For example if I do not know how to find out the value of Pi then I would use my knowledge of the relation between the radius and circumference of a circle and by drawing different sized circles and measuring their circumference and radius can try to find the value of Pi approximately. My deduction is based on the fact that Pi = circumference/2*radius. Now what was the fact based on which Aryabhatt deduced the value of Pi is not known. Was it a Mathematical series or some other manual method, there is no clue about it. There are many ancient observations for which the methodology is not available today but there must have been one and that shows the in depth studies of things by these people of eminence. Our ancients had a good knowledge of Astronomy and they calculated many things to a good precision at that time but those methods are not available today to us. We are using the recently developed methods available to us by progress of science and technology.Knowledge is power.

Even in good olden era India was full of science and maths and the activities were done with calculations and precisions. Only thing is that our forefathers were not able to convince us in the right way and thus we think the science and maths are the invention of modern days and that is wrong. Remember those people are not educated and yet they were doing business and transactions were perfect and they were even paying Kishthi that means tax to the kings. Therefore in many forms are there in the past era and when we dig the same in present day circumstances we can find some enlightening truths.K Mohan @ Moga 'Idhuvum Kadandhu Pogum " Even this challenging situation would ease

If you take pieces of thread which are in equal length and arrange them as a circle, you require a little more three thread pieces of the thread. Irrespective of the length of the thread if we want to form a circle you require a little more than three pieces. Then if we measure the radius of that circle it will be equivalent to the length of one piece of the thread. This is how we can understand pi. If you take I Cm length threads and arrange them as a circle the required length to complete is around 3.14 pieces. Then if we measure the diameter of the circle it will be 1 Cm only. I don't know whether Aryabhatt might have performed this activity when this fact was not known. He might have taken different lengths of pieces and tried the same and he might have found that the circumference divided by the diameter is a constant and he might have named it as Pi. Generally, the researchers will try to make the observations first and from that, they will try to make out a theory. Modelling trials might have been tried to find out the relation between circumference and diameter and he might have come out with this theory.drrao always confident

I have seen one old hindi book published long back and does not appear to be in print now in which there are Hindi names of all the prominent stars in the night sky and it is strange to note that the different patterns of stars in the night are also named in an orderly way. It means long back before the modern Astronomy or Astrophysics took shape our ancestors were already knowing about these things in great details. How they did it is really a big query. Long back, when we were living in a small town in the outskirts of the market in Gujarat state then in the summer due to hot season we used to sleep on the open terrace and it was there that I got some idea of the stars which we were gazing regularly for some time and they were shifting in the night sky in a particular fashion which we came to know later that it was due to the Earth's motion around the Sun that we felt as if stars are moving. Anyway that was the time I got hold of that book and was astonished to see the details of these things there. So, our ancestors learned many things but their methods are not known to us.Thoughts exchanged is knowledge gained.

Dr. Srinivas Rao, that's exactly what I'm talking about. You tried to understand Pi in your own way. That's education. Very well coined. It helped me understand about pi too. I always view Pi as a dimension this required other than the diameter to measure the circumference. I honestly don't have the fullest understanding because, I can spin a rod by its center and it will make a circle. Diameter alone is enough to describe the circumference of the circle in that case.The stronger a light shines the darker are the shadows around it.