Abstract
The concluding chapter of this book is the topic of origami modeling. So far, we mainly consider discrete origami problems, which suit computers. However, when we consider continuous problem on origami, we have to face a gap between discrete and continuous models. Using this gap, we can consider undecidability on origami.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
According to the Guinness World Records (https://www.guinnessworldrecords.com/world-records/494571-most-times-to-fold-a-piece-of-paper), a high school student, Britney Gallivan, folded a single piece of paper in half 12 times on January 27, 2002. However, she used the tissue paper of 4,000 ft long. So I bet nobody can fold a newspaper in half 10 times.
- 2.
This is an example that often appears as an introduction to the contradiction method, but let us introduce it briefly. Assuming that there is only a finite number of prime numbers. Then “the number multiplied by all prime numbers” \(+1\) is a new prime number. This is a contradiction.
- 3.
Finite sets are also called countable sets. A finite set cannot make a one-to-one correspondence with N, but it can be arranged in order.
- 4.
This symbol “\(\bot \)” is called bottom, and it is customary to use it in the society of theoretical computer science. I do not know the historical origin.
Reference
E.D. Demaine, J. O’Rourke, Geometric Folding Algorithms: Linkages, Origami (Polyhedra, Cambridge, 2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Uehara, R. (2020). Undecidability of Folding. In: Introduction to Computational Origami. Springer, Singapore. https://doi.org/10.1007/978-981-15-4470-5_11
Download citation
DOI: https://doi.org/10.1007/978-981-15-4470-5_11
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-4469-9
Online ISBN: 978-981-15-4470-5
eBook Packages: Computer ScienceComputer Science (R0)