High School Exploring Holonomic Basis in Cartesian Coordinates

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The discussion centers on whether Cartesian coordinates are the sole system with a holonomic basis that is orthonormal everywhere. Participants explore the definition of Cartesian coordinates, emphasizing their rectangular nature and the basis vectors represented as ##e_i = \delta_i^j##. The conversation raises questions about the uniqueness of this property in other coordinate systems. Clarifications on the mathematical implications of holonomic bases are also provided. Ultimately, the focus remains on the characteristics and definitions of Cartesian coordinates in relation to holonomic bases.
mairzydoats
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Are cartesian coordinates the only coordinates with a holonomic basis that's orthonormal everywhere?
 
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How do you define cartesian coordinates?
 
martinbn said:
How do you define cartesian coordinates?
I would assume rectangular coordinates with basis ##e_i = \delta _i^j##
 

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