GENERAL SOLUTION TO THE GASCA-MAEZTU HYPOTHESIS
DOI:
https://doi.org/10.53555/nnas.v8i2.1362Keywords:
hypothesis, point, line, binary combinations, line coincidence, missing pointAbstract
The article provides proof of hypothesis for any n points and uses a fundamentally new approach to proof. The proof is based on the following two propositions: first, that any line passing through two points coincides, and second, that at least two lines pass through any point in the given situation. And the new approach is that the number of binary combinations of the mentioned n points is limited.
That is, after removing a point, when the remaining points are covered with straight lines, matching lines appear because the binary combinations of points are already repeated. Consequently, there will already be (n + 1) points on some straight lines.
References
J. M. Carnicer and M. Gasca, Classification of bivariate configurations with simple Lagrange interpolation formulae, - Advances in Computational Mathematics, 20 (2004), p. 5-16.
J. M. Carnicer and M. Gasca, On Chung and Yao’s geometric characterization for bivariate polynomial interpolation, - Curve and Surface Design: Saint-Malo 2002 (Tom Lyche, Marie- Laurence Mazure, and Larry L. Schumaker Eds.) (2003), p. 11-30.
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