The TH ∃ OREM ∀ project: a progress report
Symbolic computation and automated reasoning
Computational construction of a maximum equilateral triangle inscribed in an origami
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Computational Origami Construction as Constraint Solving and Rewriting
Electronic Notes in Theoretical Computer Science (ENTCS)
Modeling origami for computational construction and beyond
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
Morley's theorem revisited: Origami construction and automated proof
Journal of Symbolic Computation
Origami axioms and circle extension
Proceedings of the 2011 ACM Symposium on Applied Computing
A virtual computational paper folding environment based on computer algebraic system
Edutainment'11 Proceedings of the 6th international conference on E-learning and games, edutainment technologies
Proof documents for automated origami theorem proving
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
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We describe Huzita's origami axioms from the logical and algebraic points of view. Observing that Huzita's axioms are statements about the existence of certain origami constructions, we can generate basic origami constructions from those axioms. Origami construction is performed by repeated application of Huzita's axioms. We give the logical specification of Huzita's axioms as constraints among geometric objects of origami in the language of the first-order predicate logic. The logical specification is then translated into logical combinations of algebraic forms, i.e. polynomial equalities, disequalities and inequalities, and further into polynomial ideals (if inequalities are not involved). By constraint solving, we obtain solutions that satisfy the logical specification of the origami construction problem. The solutions include fold lines along which origami paper has to be folded. The obtained solutions both in numeric and symbolic forms make origami computationally tractable for further treatments, such as visualization and automated theorem proving of the correctness of the origami construction.