Euclidean geometry problems rephrased in terms of midpoints and point-reflections | Zendy

Victor Pambuccian | Zendy

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Euclidean geometry problems rephrased in terms of midpoints and point-reflections

Author(s) -

Victor Pambuccian

Publication year - 2005

Publication title -

elemente der mathematik

Language(s) - English

Resource type - Journals

eISSN - 1420-8962

pISSN - 0013-6018

DOI - 10.4171/em/3

Subject(s) - foundations of geometry , euclidean geometry , non euclidean geometry , conjecture , point (geometry) , midpoint , mathematics , analytic geometry , geometry , synthetic geometry , hilbert space , pure mathematics , algebra over a field , differential geometry , projective geometry

When we conjecture a theorem in geometry, we first try to prove it using whatever means we find at our disposal. After establishing its truth, we may follow it up by a reverse analysis, first described by Pappus of Alexandria as analysis, asking not whether the theorem in question holds, but what does one need to assume for it to hold (see [10] for the history of the regressive undertaking). Hilbert [4] expressed this enterprise with his characteristic eloquence:

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