Abstract
We present an origami construction of a maximum equilateral triangle inscribed in an origami, and an automated proof of the correctness of the construction. The construction and the correctness proof are achieved by a computational origami system called Eos (E-origami system). In the construction we apply the techniques of geometrical constraint solving, and in the automated proof we apply Gröbner bases theory and the cylindrical algebraic decomposition method. The cylindrical algebraic decomposition is indispensable to the automated proof of the maximality since the specification of this property involves the notion of inequalities. The interplay of construction and proof by Gröbner bases method and the cylindrical algebraic decomposition supported by Eos is the feature of our work.
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© 2006 Springer-Verlag Berlin Heidelberg
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Ida, T., Takahashi, H., Marin, M., Ghourabi, F., Kasem, A. (2006). Computational Construction of a Maximum Equilateral Triangle Inscribed in an Origami. In: Iglesias, A., Takayama, N. (eds) Mathematical Software - ICMS 2006. ICMS 2006. Lecture Notes in Computer Science, vol 4151. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11832225_36
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DOI: https://doi.org/10.1007/11832225_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-38084-9
Online ISBN: 978-3-540-38086-3
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