Access

Published online 18 June 2008 | Nature 453, 966 (2008) | doi:10.1038/453966b

News

Universal law of coiling

Physicists reveal why paper curls the way it does.

Philip Ball

Ever noticed that when a piece of paper is rolled into a tube, the innermost part straightens away from the coil before touching down? Try it and see. A team of researchers has investigated this phenomenon and discovered that the precise shape of this rolled-up material is not only surprisingly subtle but also universal.

Comments

Reader comments are usually moderated after posting. If you find something offensive or inappropriate, you can speed this process by clicking 'Report this comment' (or, if that doesn't work for you, email redesign@nature.com). For more controversial topics, we reserve the right to moderate before comments are published.

  • The geometry is simply based on the tetrahedron. Thus the number 3 is key. Arcsin(1/3)= 19.471 deg. 90 + 19.471 = 109.471 deg. This gives - Beta = 180- (109.471/2)= 125.274 deg. Alpha = (109.471/2)-30 = 24.736 deg. One finds the basic tetrahedral angle everywhere in physics and chemistry, from the Kelvin wedge to the structure of methane and the angular distribution of volcanoes, e, Easter Island.

    • 20 Jun, 2008
    • Posted by: James Lyons

  • Formation of coiled structures that show similar behaviour as described in the article has been observed also at the microscale. When a few hundreds nanometers thick metal alkoxide polymer sheets self-roll in a solvent a few microns diameter tubular structures are formed, which electron microscopy images (http://www.imagebam.com/image/af87ff10961353 ) resemble macroscopic analogs. More details about the structures can be found (http://www3.interscience.wiley.com/journal/119163289/abstract)

    • 11 Aug, 2008
    • Posted by: Valter Reedo