What is the meaning of homogenous and isotropic in Gallilean transformation?

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The discussion clarifies the concepts of homogeneity and isotropy within the context of Galilean transformations. Homogeneous space indicates that spatial properties remain consistent across all locations, implying invariance under translation. Isotropic space signifies that spatial properties are uniform in all directions, indicating invariance under rotation. These definitions are essential for understanding the fundamental principles of classical mechanics and the behavior of physical systems.

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in this kind of transformation , what is the meaning of homogenous and isotropic??
 
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In this case, we are referring to the statement that space is homogeneous and isotropic. Homogeneous means the properties of space are the same everywhere, that is, space is invariant under any translation. Isotropy means the properties of space are the same in all directions, that is, space is invariant under all rotations
 
okay now i got it because our profeesor said that homogenous means that the center of coordinates is chosen anywhere while isotropic means the direction for any axis is invarient . thank you
 

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