tag:blogger.com,1999:blog-2433841880619171855.post8217280841772285102..comments2024-03-27T21:09:44.320+00:00Comments on Pat'sBlog: Oops, Not Quite to SpecificationUnknownnoreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2433841880619171855.post-8142636453648920022011-03-24T16:30:18.699+00:002011-03-24T16:30:18.699+00:00Thanks for this interesting geometry problem which...Thanks for this interesting geometry problem which shows how circular lengths can only be compared approximately to rectilinear lengths, except if the angle has a sine which we know precisely (60, 45, 30, ... deg). If we had arc = chord * pi/2 (rad), or 2*pi/(3*sqrt(3)), ... the height can be determined to the precision of which we know pi or square roots. I don't know about the compression of steel, but as it is a thin rail of steel, it is probable that it will bend. Maybe a physically more probable solution would be that the rail bends parabolically. <a href="http://mathworld.wolfram.com/ParabolicSegment.html" rel="nofollow">Parabolic segments</a> and heights can be calculated more precisely than circular segments and heights, so this would yield a more precise height.Arjen Dijksmanhttps://www.blogger.com/profile/09450431291713605237noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-24277585457057595262011-03-23T23:43:11.653+00:002011-03-23T23:43:11.653+00:00I think you need to take the compression of the st...I think you need to take the compression of the steel into account. A mile of steel rail would be pretty heavy and at that small angle (if it could be held perfectly in a line above the ground) it would probably compress itself until almost flat...Lanseyhttps://www.blogger.com/profile/08825175323995592999noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-80316741439012370622011-03-23T19:05:21.462+00:002011-03-23T19:05:21.462+00:00Yes, now that I'm looking at it, your system w...Yes, now that I'm looking at it, your system was equivalent to mine. . .Jeffohttps://www.blogger.com/profile/06989946392105339862noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-32841633609698446902011-03-23T15:05:07.108+00:002011-03-23T15:05:07.108+00:00Jeffo,
I actually only tried them with the syste...Jeffo,<br /> I actually only tried them with the system, never even tried to use the simpler single variable equation.. thanks, will make a note on the blog...Pat's Bloghttps://www.blogger.com/profile/15234744401613958081noreply@blogger.comtag:blogger.com,1999:blog-2433841880619171855.post-25186572222878928172011-03-23T13:51:30.198+00:002011-03-23T13:51:30.198+00:00I got the same answer, but with a different approa...I got the same answer, but with a different approach. I put A at the origin and D on the positive x-axis. Then the equation (sin x)/x = 2640/2640.5 falls out with simple trig. WA can handle that (with FindRoot) quickly to get x = 0.0337.Jeffohttps://www.blogger.com/profile/06989946392105339862noreply@blogger.com