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How to Fold It
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  • Cited by 16
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Greenberg, H. C. Gong, M. L. Magleby, S. P. and Howell, L. L. 2011. Identifying links between origami and compliant mechanisms. Mechanical Sciences, Vol. 2, Issue. 2, p. 217.

    Ghomi, Mohammad 2014. Affine unfoldings of convex polyhedra. Geometry & Topology, Vol. 18, Issue. 5, p. 3055.

    Le, Sang N. Su-Jun Leow Tuong-Vu Le-Nguyen Ruiz, Conrado and Kok-Lim Low 2014. Surface and contour-preserving origamic architecture paper pop-ups. IEEE Transactions on Visualization and Computer Graphics, Vol. 20, Issue. 2, p. 276.

    Ruiz, Conrado R. Le, Sang N. Yu, Jinze and Low, Kok-Lim 2014. Multi-style paper pop-up designs from 3D models. Computer Graphics Forum, Vol. 33, Issue. 2, p. 487.

    Florijn, Bastiaan Coulais, Corentin and van Hecke, Martin 2014. Programmable Mechanical Metamaterials. Physical Review Letters, Vol. 113, Issue. 17,

    Zhou, Yahan Sueda, Shinjiro Matusik, Wojciech and Shamir, Ariel 2014. Boxelization. ACM Transactions on Graphics, Vol. 33, Issue. 4, p. 1.

    Sareh, Pooya and Guest, Simon D. 2015. A Framework for the Symmetric Generalisation of the Miura-ori. International Journal of Space Structures, Vol. 30, Issue. 2, p. 141.

    Tabachnikov, Serge 2015. A Baker’s Dozen of Problems. Arnold Mathematical Journal, Vol. 1, Issue. 1, p. 59.

    Nido, Gonzalo S. Bachschmid-Romano, Ludovica Bastolla, Ugo and Pascual-García, Alberto 2016. Learning structural bioinformatics and evolution with a snake puzzle. PeerJ Computer Science, Vol. 2, Issue. , p. e100.

    Shen, Tao and Nagai, Yukari 2017. An Overview of Folding Techniques in Architecture Design. World Journal of Engineering and Technology, Vol. 05, Issue. 03, p. 12.

    Chen, Po-Yen Liu, Muchun Wang, Zhongying Hurt, Robert H. and Wong, Ian Y. 2017. From Flatland to Spaceland: Higher Dimensional Patterning with Two-Dimensional Materials. Advanced Materials, Vol. 29, Issue. 23, p. 1605096.

    Rus, Daniela and Tolley, Michael T. 2018. Design, fabrication and control of origami robots. Nature Reviews Materials, Vol. 3, Issue. 6, p. 101.

    Feng, Huijuan Peng, Rui Ma, Jiayao and Chen, Yan 2018. Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages. Journal of Mechanisms and Robotics, Vol. 10, Issue. 5, p. 051003.

    Teoh, Zhi Ern Phillips, Brennan T. Becker, Kaitlyn P. Whittredge, Griffin Weaver, James C. Hoberman, Chuck Gruber, David F. and Wood, Robert J. 2018. Rotary-actuated folding polyhedrons for midwater investigation of delicate marine organisms. Science Robotics, Vol. 3, Issue. 20, p. eaat5276.

    Vorkov, Vitalii Dewil, Reginald Cattrysse, Dirk Vandepitte, Dirk and Duflou, Joost R. 2018. Generating flat patterns for folded structures: Search space reduction. Packaging Technology and Science, Vol. 31, Issue. 2, p. 97.

    McAdams, Daniel A. 2018. Discussion of “A Review of Thickness-Accommodation Techniques in Origami-Inspired Engineering” (Lang, R. J., Tolman, K. A., Crampton, E. B., Magleby, S. P., and Howell, L. L., 2018, ASME Appl. Mech. Rev., 70(1), p. 010805. Applied Mechanics Reviews, Vol. 70, Issue. 1, p. 015504.

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    How to Fold It
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Book description

What do proteins and pop-up cards have in common? How is opening a grocery bag different from opening a gift box? How can you cut out the letters for a whole word all at once with one straight scissors cut? How many ways are there to flatten a cube? With the help of 200 colour figures, author Joseph O'Rourke explains these fascinating folding problems starting from high school algebra and geometry and introducing more advanced concepts in tangible contexts as they arise. He shows how variations on these basic problems lead directly to the frontiers of current mathematical research and offers ten accessible unsolved problems for the enterprising reader. Before tackling these, you can test your skills on fifty exercises with complete solutions. The book's website,, has dynamic animations of many of the foldings and downloadable templates for readers to fold or cut out.


'The major theorems presented are remarkable - results that may surprise the reader include the fact that, with the right folds, any shape or collection of shapes (even ones with holes in) … composed of straight lines may be cut out from a sheet of paper with just a single cut.'

Source: London Mathematical Society Newsletter

‘In this beautiful and inspiring book with many colour figures the reader can find a fascinating mathematical approach to linkages, foldings and unfoldings. Many exercises with detailed solutions give the reader the chance to control the acquired skills.’

Hansueli Hosli Source: Zentralblatt MATH

'… a great book for someone who wants to learn about the mathematics behind origami without being overwhelmed by the mathematics itself. This is a great book for a high school or undergraduate student to get introduced to the open problems in computational origami.'

Brittany Terese Fasy and David L. Millman Source: SIGACT News

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