In the 1300s an Indian mathematician derived what is now called the Taylor series for sine. But Taylor was hundreds of years later. See how Madhava anticipated ideas from Calculus to derive this formula.
I hear this refrain a lot and I don't get it. I studied in Indian school system and I knew about this - and I did my schooling when there was no internet. It is less visible in middle and high school texts or associated lectures in class than say Aryabhatta simply because its more advanced. You will miss it if you are not curious about it. I think you learn depends on what you value rather than what you are taught. There is another associated refrain is that Indian mathematics was destroyed ~1100 AD due to Islamic invasion. These works show that not to be true.
@@prateemmandal743 Indian civilizational produces were plain copied by the arabs and thence to europe. That is true. I am forgetting the name of one book written by arab scholar but on the first page of that book itself he wrote that his was a work of translation. In my school too, never did I ever mention the name of Madhava. If you are hearing this refrain a lot, it is probably true. Leftists have hijacked our civilization since independence. Not any more though.
@@shethtejas104 You are probably referring to Al-Khwarizmi who wrote two books on mathematical techniques used by Indian mathematicians. This was many centuries before Madhava. It is generally true that many techniques of ancient Indian mathematicians were generally adopted but that is true for mathematical techniques of mathematicians from other parts of the world too. Also Al-Khwarizmi wasn't a mere copier of texts. Madhava's works AFAIK had no influence on mathematical developments in West as by the time they found their way to West, it has already progressed beyond that point. There is nothing special about land of India, math and science are no one's preserve. Even if all mathematics emanated from India (which is evidently untrue) it proves what according to you? Please try to be less tribal.
@@prateemmandal743 Tribal are your western so-called civilized masters(in particular white brits of the past) who do not forget to lay claim on what is not even theirs. But you are probably well trained in scorning your own brethren, after all thats how a trading company ruled us for over a century. You did not surprise me at all there, and more so because it is said that many Bengalis were quite happy under the British rule. But thats a different point. I am calling you out not for your harsh criticism of me but for your glossing over the acts of plagiarism by the west through the arabs and failing to call THAT act tribal. Instead, you took the easy step of disparaging a fellow Indian (in case that term even means anything to you). The whole point is about plagiarism but you deflected it to the continuation or continuum of the scientific/mathematical advancement. My rant is against the plain lifting of credit, and not just the riches, off our lands. By the way, for some families and their future progenies, even the feeling of self-worth and self-esteem got lifted which is why to this day, long after the sleazy traders left our shores, their Indian solicitors are fighting fellow Indians to save the grace of their masters. Please read my comment again and be less subservient.
@@shethtejas104 Re-reading your previous comment, I could not still see where you complained about "plagiarism"or "plain lifting of credit". In-fact you wrote that you read the book where arab scholar acknowledged that he is translating (I dont know if that is true but thats pretty much what you wrote). And even if you were making that point (which you weren't) by minimising other contributors to the field (which is what you did), my response was to that minimisation. Tribal is when you make race/relegion/ethnicity based arguments, first against Whites and Arabs then against Bengalis. I hope you enjoyed a white man's exposition of Madhava's results. I derive my feeling of self worth and self esteem from trying (and sometimes succeeding) to understand lectures like these, marvelling about these ancient mathematical achievements and knowing about them through other people who share such curiosity.
It is interesting to note the rstio between arc value and sine value don't follow the same ratio as a slope as up distance/ horizontal distance as a/b decreased against b increases slightly and if you put the slope line and the integral value finding the area will not be proportional as squeezing character is differed at the bottom and lessened at the top.
I wonder the west found our great scientists and mathematicians, but we know about them when they mention it on Twitter..Madhava lived some what 50 km from my home but I didn't know about him in my school education.. That's our system of education.. totally imitated the British colonial system..I don't say we have to ignore the English system but we should put efforts to find works of our forefathers and take further research on it..I see people leaving the country saying our land is back in science and technology, especially from Kerala..
Madhava discovered calculus but the books tell you it was someone else. Madhava discovered series but the books tell you it was someone else. If it wasn't the Arabs, the numeric system the west uses would be called something else and invented by the two above .....
Madhava's Tantrasangraha, JyeshThadeva's Yuktibhasha and AryabhaTiyam are extant books. India has had a continuous tradition of works in Astronomy all the way till 17 th century. After that colonialism took over. :( so much so that even after "Independence" in 1947, we were not taught about the achievements of our own ancestors.
The cosine signs forming compression with decrease in degrees rather expansion over the increase in degrees of sign and any integration correction can be arrived at between differentiated value and integrated value in basic calculus mathematics.
This expansion and compression by a magnetic field penetrating a superconductive conical plane in between aligning and opposing magneticfield follow similar force of compression and expansion as this may follow a similar mode in understanding superconductive electrons forming vortex by analogy.
I love the breadth of your content. Can you please do a video how the Taylor series is derived. The Taylor series can be used to approximate Sine. I have been struggling to understand why this is true. Do you have a patreon account?
It’s amazing how people have come up with series that approximates curves. I am fascinated by people’s thought processes. Do they have a strategy or do they “feel” their way to these magnificent discoveries, or it’s a mysterious mental process. Maybe AI models will help investigate these cognitive processes?
If the first education minister, who kept the office for four consecutive terms, was not a Jihadi, the generations of India that were raised since independence would have known about the glorious past of our very advanced civilization and names like Madhava or the Kerala School of Mathematics would be common knowledge. The sleazy traders from brittania, who use paper instead of water to wipe their crap every morning even today, kept telling the world that they were civilizing us. A civilization that developed calculus much before "Sir" newton stole it all needed no civility coming from the dwellers of dark ages. I have, and will forever have, only h.a.t.e for the union jack.
I should have made a note that these formulas are more accurate the bigger n gets. So the first formula for sums of odds is always true but the others approach those formulas as n goes to infinity.
This is a pale shadow of a shadow of what Mahadeva did. He fully understood the idea of the infinitesimal and of the sum of an infinite series. There are much better videos of lectures on these by Indian scientists that do a better job of explaining the content, e.g. P. P. Divakaran, but they are heavily caught up in the nationalistic aspects, and westerners will have a tough time watching.
Jesuits came to India and took back Indian knowledge to europe which was circulated to the universities of Europe. The thing that irks me most is that whitey European does not give credit to where it’s due ie the Hindus . But the Greeks no problem but cat gets the tongue when it involves the Hindus. For the Europeans it’s ok to appropriate knowledge from hindus and shamelessly call it European.
