Computational Construction of a Maximum Equilateral Triangle Inscribed in an Origami

• Published in: Lecture notes in computer science pp. 361 - 372
• Main Authors: Ida, Tetsuo, Takahashi, Hidekazu, Marin, Mircea, Ghourabi, Fadoua, Kasem, Asem
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Algebraic Constraint; Algorithmics. Computability. Computer arithmetics; Applied sciences; Computer science; control theory; systems; Correctness Proof; Equilateral Triangle; Exact sciences and technology; Geometric Constraint; Geometrical Property; Theoretical computing; Mathematical function; Gröbner basis; Program library; Algebraic method; Constraint satisfaction; Automatic proving; Proof theory; Construction system; Program verification
• ISBN: 9783540380849; 3540380841
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11832225_36

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.