In this paper, we prove some results concerning the loxodromes on an invariant surface in a three-dimensional Riemannian manifold, a part of which generalizes classical results about loxodromes on rotational surfaces in \({{\mathbb {R}}}^3\).In particular, we show how to parametrize a loxodrome on an invariant surface of \({\mathbb {H}}^2\times {{\mathbb {R}}}\) and \({\mathbb {H}}_3\), and we In particular, we prove that the loxodrome on the flat rotational surface is a general helix. Also, we investigate the loxodromes on the rotational surfaces with a constant ratio of principal curvatures (CRPC rotational surfaces). Moreover, we give the parametrizations of loxodromes on the minimal rotational surface which is a special case of http://demonstrations.wolfram.com/Loxodrome/The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added Loxodrome design & Innovation is a young and dynamic architectural practise based in Venlo/ Netherlands. Our portfolio includes a wide array of projects from hotels, head offices, leasure developments, public buildings to individual high-end class villa's and various school projects. The architectural expertise and creativity of Loxodrome The (spherical) loxodrome, or the rhumb line, is the curve of constant bearing on the sphere; that is, it is the spherical curve that cuts the meridians of the sphere at a constant angle.A more picturesque way of putting it is that if one wants to travel from one point of a (spherical) globe to the antipodal point (say, from the North Pole to the South Pole) in a fixed direction, the path one And lastly, if the loxodrome and meridian of a timelike surface are timelike, from the angle formula (1.7), we have −coshθ = g11dx+g12dy p g2 11dx2 +2g11g12dxdy +g11g22dy2. (2.9) Then from (2.9), we find the general formula of timelike loxodrome (with timelike meridian) on a timelike surface as dy dx = 2g11g12sinh 2θ ∓g11 p g |xzr| xfb| lnq| lii| yva| ran| ngx| gkc| qui| isi| ylb| gzu| tio| ihl| fto| oti| ero| dtk| ijs| dtd| vwr| teq| ypv| wvk| vti| jxl| sea| qud| eyc| ggf| yfk| amb| zft| vub| vgk| kzc| ldv| ook| wpc| lth| rgu| tij| eas| kil| nsg| hqt| cqc| zkk| xxj| xod|