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Symmetry 2019, 11(2), 184; https://doi.org/10.3390/sym11020184

A New Ellipse or Math Porcelain Service

1
National Research University, Moscow Power Engineering Institute, 111250 Moscow, Russia
2
Joint Institute for High Temperatures of the Russian Academy of Science, 125412 Moscow, Russia
3
Department, Universtity or Institution, Viale delle Mimose 18, 64025 Pineto (TE), Italy
4
Technische Universität Dresden, 01062 Dresden, Germany
5
Saint-Petersburg State Institute of Technology (Technical University), 190013 St. Petersburg, Russia
*
Author to whom correspondence should be addressed.
Received: 9 December 2018 / Revised: 25 January 2019 / Accepted: 29 January 2019 / Published: 4 February 2019

Abstract

Egglipse was first explored by Maxwell, but Descartes discovered a way to modify the pins-and-string construction for ellipses to produce more egg-shaped curves. There are no examples of serious scientific and practical applications of Three-foci ellipses until now. This situation can be changed if porcelain and ellipses are combined. In the introduced concept of the egg-ellipse, unexplored points are observed. The new Three-foci ellipse with an equilateral triangle, a square, and a circle as “foci” are presented for this application and can be transformed by animation. The new elliptic-hyperbolic oval is presented. The other two similar curves, hyperbola and parabola, can be also used to create new porcelain designs. Curves of the order of 3, 4, 5, etc. are interesting for porcelain decoration. An idea of combining of 3D printer and 2D colour printer in the form of 2.5D Printer for porcelain production and painting is introduced and listings functions in Mathcad are provided. View Full-Text
Keywords: ellipse; parabola; hyperbola; elliptic-hyperbolic oval; 2.5D Printer; augmented reality; programming; graphics; animation ellipse; parabola; hyperbola; elliptic-hyperbolic oval; 2.5D Printer; augmented reality; programming; graphics; animation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Ochkov, V.; Nori, M.; Borovinskaya, E.; Reschetilowski, W. A New Ellipse or Math Porcelain Service. Symmetry 2019, 11, 184.

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