tag:blogger.com,1999:blog-9004452969563620551.post6478591251895058895..comments2018-07-27T19:39:01.133+05:30Comments on Paramanand's Math Notes: Theories of Circular Functions: Part 1testernoreply@blogger.comBlogger1125tag:blogger.com,1999:blog-9004452969563620551.post-40115552333713199092016-05-05T12:08:23.101+05:302016-05-05T12:08:23.101+05:30Circular functions actually live naturally on S^1 ...Circular functions actually live naturally on S^1 and not on the reals but in school we only introduce the reals hence the trouble. But I don't know why we teach it like that in school since we are intuitively aware of at least (and this is enough) two one-dimensional 'spaces': one that extends indefinitely in either 'direction' (actually, orientation) and one that returns to the start. In fact, in certain Brahmin cosmologies time was modelled using what we would now think of S^1.<br /><br />But we are lucky that S^1 does have the reals as its <a href="https://en.wikipedia.org/wiki/Covering_space#Universal_covers" rel="nofollow">universal cover.</a><br /><br />Btw, let me say that its great that you have kept your interest in math alive despite working in the industry. Anonymousnoreply@blogger.com