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We generally use the Pythagoras formula for distance between two points in 2D, when the Cartesian co-ordinates are given....

One directly extends it to 3D..having the distance going as [tex]\sqrt{x^{2}+y^{2}+z^{2}}[/tex]....

For a curved co-ordinate system, we have distances measured by something like

[tex]ds^{2}=g^{\mu\nu}dx_{\mu}dx_{\nu}[/tex]...

I was wondering why it is all about squares and square roots..and not, say cubes and cube roots or fourth roots or something.....

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# Measuring distances: why the Pythagoras formula

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