Parallel Projected Sphere on a Plane: A New Plane–Geometric Investigation

Yıl 2017, Cilt: 10 Sayı: 1, 58 - 80, 30.04.2017

Thomas L. Toulias George E. Lefkaditis

https://doi.org/10.36890/iejg.584443

Öz

Anahtar Kelimeler

Pohlke’s Theorem, conjugate semi–diameters of an ellipse, affine transformations, orthogonal decomposition of a symmetric matrix

Kaynakça

• [1] Emch, A., Proof of Pohlke’s theorem and its generalizations by affinity. American Journal of Mathematics 40(2) (1918), 366-374.
• [2] Fishburn, P.C. and Trotter, W.T., Containment orders for similar ellipses with a common center. Discrete Mathematics 256 (2002), 129–136.
• [3] Lefkaditis, G.E., Thomas, T.L. and Markatis, S., The four ellipses problem. International Journal of Geometry 5(2) (2016), 77–92.
• [4] Müller, E. and Kruppa, E., Lehrbuch der Darstellenden Geometrie. Springer–Verlag, Wien, 1961.
• [5] Peschka, G. A., Elementarer beweis des Pohlke’schen fundamentalsatzes der Axonometrie. Stzgsb. Math. Nat., Akad. Wien LXXVIII II Abth. (1879), 1043-1054.
• [6] Sklenáriková, Z. and Pémová, M., The Pohlke-Schwarz theorem and its relevancy in the didactics of mathematics. Quaderni di Ricerca in Didattica. http://math.unipa.it/~grim/quad17_sklenarikova-pemova_07.pdf 7).