THE CONCEPT OF FORM IN GEOMETRY: SOME CONSIDERATIONS CONCERNING SCIENCE AND MATHEMATICS EDUCATION
THE CONCEPT OF FORM IN GEOMETRY: SOME CONSIDERATIONS CONCERNING SCIENCE AND MATHEMATICS EDUCATION

Summary/Abstract: The concept of form is one of the most intuitive within our experience. When we say that two objects of different dimensions have or do not have the same form there is not properly a reflexion behind this claim. Rather, it is, at all appearances, based on our visual faculties, which is perfectly in order in the context of our daily life. This intuitive and visual notion of form is suitable to the necessities of our practical, or also esthetical, experience. However, on second thought, things are not so easy: suppose that I look at an object and I find that it is circular. I claim, hence, that it is a circle and my statement is correct. Another person looks at this object from another point of view and sees that this object is an ellipsis or a hyperbola or a parabola. He is not wrong. This person is not the prey of a dream or of a hallucination. He is observing the world from another point of view, or as usually told in mathematics and physics, from another reference frame. A further example is even more indicative: it is well known that, if one treats the problem of the planetary orbits around the Sun as a two bodies problem, the orbit is an ellipsis: but, in respect to what reference frame is it an ellipsis?

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