tag:blogger.com,1999:blog-2183388327040813760.post5210743780747443073..comments2021-07-28T10:39:10.541+05:30Comments on Ajivaka Wallacian ஆசிவக வாலேசன்: Manjul Bhargava on Sanskrit and Mathematics VarahaMihira Gopuhttp://www.blogger.com/profile/08159184223145034793noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-2183388327040813760.post-58293867908218239082020-04-25T12:12:02.479+05:302020-04-25T12:12:02.479+05:30Very useful. When I wrote my "The number lin...Very useful. When I wrote my "The number line" article, this history of number origin is something that I lacked. This article seems to give me those pointers. Thank you.<br /><br />For your line,<br />"I think between Madhava and Jyeshtadeva they discovered infinitesimals. Whether this can be called calculus, I don't know."<br />I'm reminded of how I tried to connect between limits and calculus years ago while trying to understand the concept. So, if I may take the liberty of using Infinitesimals and Limits interchangeably, here's how I think of the connection between Limits and Calculus:<br />The concept of Limit serves as a tool for two goals :<br />1. Limit of f(x) at x=x1 is an extrapolation procedure to find the value of f(x) at x=x1 when the values of f(x) are known at some discrete values of x around the neighbourhood of x1 (both on the left side and the right side of x1). In this sense, it helps you form a continuum from a set of discrete values of function. i.e. This 'Discrete to Continuous' perspective forms the basis of Integral calculus.<br />2. On the other hand, Limit also helps you discretize a continuous function to be able to calculate the change of f(x) with respect to minute changes in x. This 'Continuous to Discrete' perspective forms the basis of Differential calculus. <br /><br />That said, my mathematical knowledge is bereft of any deep research or book study. I attempt to intuitively figure out. At some point, I did realize I should do a study of the work available already. Hope I get to do that sometime soon. Shantalahttps://www.blogger.com/profile/02251197087245816892noreply@blogger.comtag:blogger.com,1999:blog-2183388327040813760.post-28703874147046500272016-02-06T13:35:24.435+05:302016-02-06T13:35:24.435+05:30Yes I understand that infinitesimals are the germ ...<br />Yes I understand that infinitesimals are the germ of calculus. But calculus is more than that, we understand it as including differentiation and integration and the whole set of mathematics derived from them.<br /><br />I also understand that Newton-Leibnitz calculus did have to depend on Cartesian geometry, but they exploited it, didn't they? I cant imagine an area under the curve without x and y axis...<br /><br />I can understand Brahmagupta's Bija ganita as the foundation of modern algebra, without the five basic arithmetic signs + - * / = though I wouldnt try it with Roman numerals. Calculus without co-ordinate geometry would be a more bizarre creature.. I would love to see it fleshed out, though!VarahaMihira Gopuhttps://www.blogger.com/profile/08159184223145034793noreply@blogger.comtag:blogger.com,1999:blog-2183388327040813760.post-26998476011150306162016-02-06T13:28:19.678+05:302016-02-06T13:28:19.678+05:30Badri: Looking forward to it.
Arkay: Thank you sir...Badri: Looking forward to it.<br />Arkay: Thank you sir.<br /><br />VarahaMihira Gopuhttps://www.blogger.com/profile/08159184223145034793noreply@blogger.comtag:blogger.com,1999:blog-2183388327040813760.post-14067856695226674722016-01-10T13:18:18.212+05:302016-01-10T13:18:18.212+05:30Gopu: Had some interesting conversation with TV Ve...Gopu: Had some interesting conversation with TV Venkateswaran on Indian Astronomy. He says he is doing some work on this and will send me a draft copy of his article. When he is in Chennai next we should arrange for a discussion.Badri Seshadrihttps://www.blogger.com/profile/02563596810587587859noreply@blogger.comtag:blogger.com,1999:blog-2183388327040813760.post-14637525957921034182016-01-05T21:55:35.387+05:302016-01-05T21:55:35.387+05:30Well, I missed the talk..I went to Sanskrit collag...Well, I missed the talk..I went to Sanskrit collage, but it was full and from hwere I sttod, I could not hear him..so I walked out. Nicely summed up by you<br />arkayhttps://www.blogger.com/profile/14845888589814932810noreply@blogger.comtag:blogger.com,1999:blog-2183388327040813760.post-18103881250623759212016-01-03T23:56:56.826+05:302016-01-03T23:56:56.826+05:30Brilllliant, Gopu, Brillliant notes!
1)*Whether I...Brilllliant, Gopu, Brillliant notes!<br /><br />1)*Whether Infinitesimals can be called Calculus. I don't know." I thought you understood it when I told you: Infinitesimals is the germ of Newton-Leibnitz's Calculus.<br /><br />2)Newton-Leibnitz Calculus germination of basic cocepts did not have to depend on the birth of Co-ordinate Geometry. The Concept of continuous time variation perceived by Gallileo [acceleration [due to gravity in the first instance] led to 'infinitesimal' as mathematical thought entity even before the advent of graphs of functions. N.Balasubramanianhttps://www.blogger.com/profile/05037145946437492885noreply@blogger.com