5. TWO OFTEN ASKED QUESTIONSOnly a bad Bourbaki scholar may guess that geometrical pictures of numbers must not be a theme of pure mathematics. Essential steps of mathematical progress can be seen as fruits of quarrels between the theory of numbers and the concept of geometry. The form of Euclid's Elements is essentially conditioned by the difficulty that the diagonal of a unit-square can only be measured by √2. Modern real analysis was only possible after Descartes' idea of analytic geometry. The understanding of mathematics as a theory of structures is founded on the discovery of non-Euclidean geometries. So I want to clarify the concept and the position of Natural Geometry in answering two fundamental questions:
1. Does natural geometry of numbers be a non-Euclidean geometry?
2. Does natural geometry of numbers be a Non-Cartesian geometry?
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