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Chasles’ Theorem as a 3D Analogue of Pascal’s TheoremMoscow, Russia
14-17 April, 2020
Authors:
Alexander L. Kheifetc (Kheyfets)
Department of Engineering and Computer Graphics
South Ural State University
Chelyabinsk, Russia
e-mail: [email protected]’s
Alexander L. Kheifetc(Kheyfets)
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The geometrical peculiarity of the line of mutual intersection of second-order surfacesand tetrahedron is considered, which is the essence of Chasles’ theorem. 3D modelshave been developed, which vividly illustrate different variants of the theorem.
The method of building 3D models is given, which allows to use those in aneducational course on the theoretical basics of geometrical modeling.
A proof for one of the theorem variants is given. A conclusion has been made on thenecessity to develop illustrative examples for all the variants of the theorem and itsuniversal proof. The work has been performed using 3D computer modeling inAutoCAD package and SolidWorks.
Work’s objective: building of illustrative 3D models describing the essence of Chasles’theorem.
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CONCLUSION
In our work we have managed to build models only for the first four variants of thetheorem given above. There emerges a task to visualize the remaining variants.
We have found proof for Chasles’ theorem only for the first theorem variant. Theproblem arises of finding these proofs for the remaining options or finding a universalproof for this theorem.
Earlier we have mentioned the similarity between Chasles’ theorem and Pascal’stheorem. This allows to assume that Chasles’ theorem can have the same significancefor geometrical modeling as Pascal’s theorem. The proof and visualization of Chasles’theorem is a relevant educational task.
We plan on including the given models, as relevant and at the same time historicaltasks, into a new educational course on the theoretical basics of 3D geometricalcomputer modeling. The course is intended for students of engineering specialtiesand is an alternative to the course of descriptive geometry [18].
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Chasles’ Theorem as a 3D Analogue of Pascal’s Theorem
Thank you for attention!
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Speacker’s contacts:
Alexander L. Kheifetc (Kheyfets)
Moscow, Russia14-17 April, 2020