Manfrin, Renato A proof of Pohlke’s theorem with an analytic determination of the reference trihedron. (English) Zbl 1415.51032 J. Geom. Graph. 22, No. 2, 195-205 (2018). The author offers a linear algebra proof of Pohlke’s theorem (Given three arbitrary segments \(OP_1\), \(OP_2\), \(OP_3\) in a plane, not contained in a line, there is a cube, such that the parallel projection of three of its edges \(OQ_1\), \(OQ_2\), \(QQ_3\) is \(OP_1\), \(OP_2\), \(OP_3\)) and provides “explicit formulae for the reference trihedrons (Pohlke matrices) and the corresponding directions of projection.” Reviewer: Victor V. Pambuccian (Glendale) Cited in 1 ReviewCited in 1 Document MSC: 51N10 Affine analytic geometry 51N05 Descriptive geometry Keywords:Pohlke’s theorem; oblique axonometry PDFBibTeX XMLCite \textit{R. Manfrin}, J. Geom. Graph. 22, No. 2, 195--205 (2018; Zbl 1415.51032) Full Text: Link References: [1] N. Beskin: An Analogue of Pohlke-Schwarz’s theorem in central axonometry. Recueil Mathématique [Math. Sbornik] N.S., 19 (61), 5772 (1946). · Zbl 0061.38502 [2] H. Brauner: Lineare Abbildungen aus Euklidischen Räumen. Beitr. Algebra Geom. 21, 526 (1986). · Zbl 0589.51004 [3] L. Campedelli: Lezioni di Geometria. Vol. II, Parte I, Cedam, Padova 1972. · Zbl 0046.38102 [4] A. Cayley: On a Problem of Projection. Quartely Journal of Pure and Applied Mathematics XIII, 1929 (1875). [5] A. Emch: Proof of Pohlke’s Theorem and Its Generalizations by Anity. Amer. J. Math. 40, 366374 (1918). · JFM 46.0871.04 [6] H. Eves: Elementary Matrix Theory. Dover Publications, New York 1966. · Zbl 0136.24706 [7] F. Klein: Elementary Mathematics From An Advanced Standpoint. Geometry. Dover Publications, New York 1939. · JFM 65.0640.01 [8] G. Loria: Storia della Geometria Descrittiva. Hoepli, Milano 1921. · JFM 48.0030.01 [9] C.F. Manara: L’aspetto Algebrico di un Fondamentale Teorema di Geometria Descrittiva. Periodico di Matematiche Serie IV, XXXII, 142149 (1954). · Zbl 0056.42104 [10] E. Müller, E. Kruppa: Vorlesungen über Darstellende Geometrie, I. Band: Die Linearen Abbildungen. Franz Deuticke, Leipzig und Wien 1923, pp. 172181. [11] K.W. Pohlke: Lehrbuch der Darstellenden Geometrie. Part I, Berlin 1860. [12] H.A. Schwarz: Elementarer Beweis des Pohlkeschen Fundamentalsatzes der Axonometrie. Crelle’s Journal LXIII, 309314 (1864). · ERAM 063.1654cj [13] H. Stachel: Mehrdimensionale Axonometrie. In N.K. Stephanidis (ed.): Proceedings of the Congress of Geometry, Thessaloniki 1987, pp. 159168. [14] H. Steinhaus: Mathematical Snapshots. Oxford University Press, Oxford 1950. · Zbl 0041.27502 [15] E. Stiefel: Zum Satz von Pohlke. Comment. Math. Helv. 10, 208225 (1938). · JFM 64.0649.02 [16] D.J. Struik: Lectures on Analytic and Projective Geometry. Addison-Wesley, 1953. Received March 29, 2018; nal form November 17, 2018 · Zbl 0053.28701 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.