tag:blogger.com,1999:blog-2433841880619171855.post3399038108283058140..comments2014-04-19T12:13:28.413+01:00Comments on Pat'sBlog: Don't Write the Law of Sines Upside Down, Please!Pat Ballewhttps://plus.google.com/102211537828528656806noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2433841880619171855.post-19905623295514591192011-09-22T12:46:40.250+01:002011-09-22T12:46:40.250+01:00its not necessary to inscribe the triangle in a ci...its not necessary to inscribe the triangle in a circle to prove it<br />u culd create a perpendicular line then there will be no need of the 2R<br /><br />u will be required to use trigonometric ratioNuzhahhttps://www.blogger.com/profile/05693925555933742441noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-51131407863396239042009-02-13T09:31:00.000+00:002009-02-13T09:31:00.000+00:00AHA! Now I get it... and of course, you are right...AHA! Now I get it... and of course, you are right.. thank youPat Bhttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-44654996082905424392009-02-12T22:29:00.000+00:002009-02-12T22:29:00.000+00:00Sorry I wasn't clear enough!What I'm saying is tha...Sorry I wasn't clear enough!<BR/><BR/>What I'm saying is that we can write, for planar triangles,<BR/>a/sin A = etc. = 2R = abc/(2 Area),<BR/><BR/>and for spherical triangles, I think it turns out that<BR/>sin a / sin A = etc. = sin a sin b sin c / (6 V)<BR/><BR/>In other words, to keep the "a b c" term on top, you should flip your spherical law of sines and have the sin a on top, to make it a more parallel construction to the formula in the planar case.Joshua Zuckerhttps://www.blogger.com/profile/04689961247338617418noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-3546983536274824662009-02-12T20:42:00.000+00:002009-02-12T20:42:00.000+00:00I am always reluctant to disagree with anything th...I am always reluctant to disagree with anything that Joshua writes because he has taught me more math than people who were paid to do so... but I think the Area = (abc)/(4R) that he writes is a property of planer triangles and not spherical (I wrote to him to check, and he may yet correct me). <BR/>I have corrected an editing mistake in the blog in which I substituted abc for sin(a)sin(b)sin(c) ... quite a difference. <BR/>Thanks again Josh for reminding me about appropriate notation for the incircle and circumcircle.Pat Bhttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-27728204732531167542009-02-11T21:53:00.000+00:002009-02-11T21:53:00.000+00:00I agree! I'm always sad when I see books discussi...I agree! I'm always sad when I see books discussing the law of sines without the circumcircle in there.<BR/><BR/>A couple minor notes: I would say 2R (for circumcircle), not 2r (which to me would be incircle).<BR/><BR/>Also, your spherical law of sines you tell me is 6V/(abc) or something? I didn't know that one. But if you're going to say it that way, then you should also point out that because Area = (abc)/(4R), then 2R is the same as (abc)/(2*Area) - hm, that looks upside down! Maybe your spherical law of sines should be flipped so that the abc can be on top both times? Or maybe I just made an algebra mistake.Joshua Zuckerhttps://www.blogger.com/profile/04689961247338617418noreply@blogger.com