| Using this approximation in Maxwell's equations we see that light travels along null geodesics. |
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| Since geodesics aren't always straight, light doesn't always travel in straight lines. |
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| The photons that reached its senses followed paths that varied slightly from the straight-line geodesics of flat spacetime. |
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| This reminded me of an interesting property of geodesics in general relativity. |
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| When this happens, the necessary conditions for the existence and uniqueness of these geodesics are violated. |
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| He then considered the problem of when the geodesics on a surface could be represented as straight lines on the plane. |
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| Those distortions guide the moving masses along straight-line geodesics, which look like the curved trajectories that physicists call orbits. |
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| Hence, we can produce poles, polars, points, geodesics, angles, and so forth readily by converting back to the Poincare model. |
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| Since no strong theoretical reason exists to confine the analysis to geodesics, Stephenson and Zelen's measure might be preferable. |
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| The theory of the geodesics in the large on such surfaces was developed later in the famous memoirs by P Koebe. |
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| It possesses shortest lines, now called geodesics, which resemble ordinary straight lines. |
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| In this latter topic he had to solve various problems of differential geometry and geodesics. |
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| So many blobs are simply the result of stacked geodesics, like Grimshaw's Eden project, a series of bubble-forms that remind me of what geologists call globular clusters. |
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| Second, geodesics are circular arcs orthogonal to the unit circle. |
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| What he suggested was that Bolyai and Lobachevsky had not really introduced new concepts at all but had described the theory of geodesics on surfaces of negative curvature. |
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| His work in studying the trajectories of point masses on a surface led to certain non-linear differential equations whose solution also gave properties of geodesics. |
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| Klingenberg worked during his years at Bonn on closed geodesics. |
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| He showed how strong triangle-based designs are with his geodesics. |
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| In particular, we obtain a complete description of the geodesics starting from the distinguished point called the root. |
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| This explains why moving along the geodesics in spacetime is considered inertial. |
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| The visible areas obtained by the analysis of normal vectors in Gaussian image are connected with geodesics along a certain direction. |
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| If M is a smooth manifold in the traditional sense, then a classical example is how tangent vectors coalesce with osculating curves such as the local geodesics. |
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| Its most important application is in the theory of ellipsoid geodesics. |
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