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An Algebraic Surface Projecting onto Squares

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References

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  3. J. Bochnak, M. Coste, and M. F. Roy. Real Algebraic Geometry, Ergeb. Math. 36. Springer, 1998.

  4. J. F. Fernando, J. M. Gamboa, and C. Ueno. Unbounded convex polyhedra as polynomial images of Euclidean spaces. Ann. Sc. Norm. Super. Pisa Cl. Sci., XIX (2019), 509–565.

  5. T. S. Motzkin. The real solution set of a system of algebraic inequalities is the projection of a hypersurface in one more dimension. In Inequalities II: Proceedings of the Second Symposium on Inequalities Held at the United States Air Force Academy, Colorado, August 14–22, 1967, pp. 251–254. Academic Press, 1970.

  6. D. Pecker. Sur l’équation d’un ensemble algébrique de \(\mathbb{R}^{n+1}\) dont la projection dans \(\mathbb{R}^n\) est un ensemble semi-algébrique fermé donné. C. R. Acad. Sci. Paris 306 (1988), 265–268.

  7. D. Pecker. On the elimination of algebraic inequalities. Pacific J. Math., 146 (1990), 305–314.

  8. D. Pecker. Sur la projection de variétés algébriques réelles. Pac. J. Math. 152 (1992), 165–172.

  9. Plato: The Republic. Penguin Classics, 2007.

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Acknowledgments

The author thanks J. F. Fernando for a careful reading of this article and his valuable suggestions on improving it. Some of the images were obtained using the software Surfer (https://imaginary.org/program/surfer), which was brought to the author’s attention by Gaël Cousin.

This work was developed during a one-year research stay at the Department of Mathematics of the Università di Pisa (D.R. no 27519 of 29/07/2013, MAT/03).

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  1. Matematika Munkaközösség, Pécsi Kodály Zoltán Gimnázium, Dobó István utca 35-37, Pécs, 7629, Hungary

    Carlos Ueno

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Correspondence to Carlos Ueno.

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Ueno, C. An Algebraic Surface Projecting onto Squares. Math Intelligencer 42, 66–69 (2020). https://doi.org/10.1007/s00283-019-09930-7

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