ADG 2012: Automated Deduction in Geometry pp 143-160

# Algebraic Analysis of Huzita’s Origami Operations and Their Extensions

• Asem Kasem
• Cezary Kaliszyk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7993)

## Abstract

We investigate the basic fold operations, often referred to as Huzita’s axioms, which represent the standard seven operations used commonly in computational origami. We reformulate the operations by giving them precise conditions that eliminate the degenerate and incident cases. We prove that the reformulated ones yield a finite number of fold lines. Furthermore, we show how the incident cases reduce certain operations to simpler ones. We present an alternative single operation based on one of the operations without side conditions. We show how each of the reformulated operations can be realized by the alternative one. It is known that cubic equations can be solved using origami folding. We study the extension of origami by introducing fold operations that involve conic sections. We show that the new extended set of fold operations generates polynomial equations of degree up to six.

## Keywords

fold operations computational origami conic section

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