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Maybe this is a silly question, but I want to ask it anyway.

In high-school level and even in the university courses, the geometric idea of the cartesian plane is the intersection of two lines (two reals lines if you want), the x-axis and the y-axis, cutting in a point called the origin and with an angle of $90º$.

So far so good...

Why must be $90º$ and not other angle?

Ben Grossmann
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    Because it is the Cartesian system. It is perfectly fine to choose any other non-multiple of $\pi$ angle to get another coordinate system. –  Jul 30 '16 at 14:21
  • @AhmedHussein I see... So the cartesian system is only one of the infinite coordinate systems. I guess is not the most relevant of them, but if we move into another system, the concept of orthogonality will change. Hence, depending of our coordinate system, we will say that two vectors are orthogonal if their angle is $\measuredangle$ and not necessarily $90º$. In which contexts is important to choose others systems? –  Jul 30 '16 at 14:35
  • The concept of orthogonality does not have to do with the coordinate system under consideration. I can't imagine adequately answering your questions before putting a huge list of definitions, so I'll leave this task to someone who is better at explaining things than I am. –  Jul 30 '16 at 15:53
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    A useful convention; in the original Cartesian treatise: La Géométrie (1673) the "coordinate axis" $x$ and $y$ are not orthogonal at all. – Mauro ALLEGRANZA Jul 30 '16 at 16:15

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