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- https://phys.libretexts.org/Bookshelves/Relativity/Special_Relativity_(Crowell)/02%3A_Foundations/2.02%3A_FlatnessEuclidean geometry is only an approximate description of the earth’s surface, for example, and this is why flat maps always entail distortions of the actual shapes. The distortions might be negligible...Euclidean geometry is only an approximate description of the earth’s surface, for example, and this is why flat maps always entail distortions of the actual shapes. The distortions might be negligible on a map of Connecticut, but severe for a map of the whole world. That is, the globe is only locally Euclidean. On a spherical surface, the appropriate object to play the role of a “line” is a great circle. The lines of longitude are examples of great circles.
- https://phys.libretexts.org/Bookshelves/Astronomy__Cosmology/Big_Ideas_in_Cosmology_(Coble_et_al.)/15%3A_The_Cosmic_Microwave_Background/15.05%3A_Comparing_Models_and_Data_-_The_CMB_and_the_Curvature_of_SpaceYou will be able to compare models for the effect of the curvature of the Universe on CMB maps and power spectra and choose which one best fits the data
- https://phys.libretexts.org/Courses/Chicago_State_University/PH_S_1150%3A_Basic_Astronomy/15%3A_The_Cosmic_Microwave_Background/15.05%3A_Comparing_Models_and_Data_-_The_CMB_and_the_Curvature_of_SpaceYou will be able to compare models for the effect of the curvature of the Universe on CMB maps and power spectra and choose which one best fits the data
- https://phys.libretexts.org/Bookshelves/Classical_Mechanics/Variational_Principles_in_Classical_Mechanics_(Cline)/05%3A_Calculus_of_Variations/5.10%3A_GeodesicThe geodesic is defined as the shortest path between two fixed points for motion that is constrained to lie on a surface. Variational calculus provides a powerful approach for determining the equation...The geodesic is defined as the shortest path between two fixed points for motion that is constrained to lie on a surface. Variational calculus provides a powerful approach for determining the equations of motion constrained to follow a geodesic.
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/01%3A_Geometric_Theory_of_Spacetime/1.05%3A_The_Equivalence_Principle_(Part_1)A central principle of relativity known is the equivalence principle: - that is, accelerations and gravitational fields are equivalent. There is no experiment that can distinguish one from the other.
- https://phys.libretexts.org/Bookshelves/Relativity/General_Relativity_(Crowell)/05%3A_Curvature/5.08%3A_The_Geodesic_EquationIn this section, which can be skipped at a first reading, we show how the Christoffel symbols can be used to find differential equations that describe geodesics. A geodesic can be defined as a world-l...In this section, which can be skipped at a first reading, we show how the Christoffel symbols can be used to find differential equations that describe geodesics. A geodesic can be defined as a world-line that preserves tangency under parallel transport.
