Geometric thinking in a n-space
Résumé
What does “thinking geometrically” mean in a n-dimensional vector space, with n>3?According to several authors, like Fischbein, or Harel, a productive reasoning in mathematics always relies upon an intuitively accepted model. A first possibility of model in dimension n is provided by the use of coordinates; the use of that model can be called “analytic thinking”. But other possibilities exist, related with synthetic geometry; in that case the expression “geometric thinking” applies. I will display some of these possibilities here, and show on a particular example how they can intervene in students problem solving processes in linear algebra.
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