Finally, some convincing ammunition against all those postmodernists who would have us believe that there are no universals. Au contraire. Enter the universal coiling angle! Ever notice when you roll up a poster that there’s a bit of the paper on the very inside that sticks out almost straight and doesn’t fall in line with the curve of all the other layers? Well, according to research published in the Proceedings of the Royal Society (brought to you here via Nature magazine, and my recent addiction to it), the angle that that stuck-out bit makes with the rest of the coil is the same, regardless of what material you roll up! Doesn’t matter if it’s a rug, a fruit roll-up or a Radiohead poster — 24.1° is the universal angle! Stay tuned for my next post, where I will argue that this research proves the existence of God and/or extraterrestrial life.

Here’s a diagram from the actual news article in Nature:

The angle that the innermost sheet makes with the coiled roll (α in the diagram) is always the same, say Enrique Cerda of the University of Santiago in Chile and his co-workers, about 24.1° — regardless of the thickness of the sheet or the width of the coil.

What’s more, the angle subtended between this contact point and the place where the sheet first detaches from the coil’s inner face (β) is always 125.2°. This universal shape confounds the intuition that stiffer sheets would have a different cross-sectional profile from flimsy ones. Rolled-up carpet, paper or metal will all adopt the same shape.

To prove it, Cerda’s team measured the ‘touchdown’ angle for a thin slab of mica (a sheet-like mineral) and a strip of metal coiled within tubes of various widths. They found that the angles deviated from the predicted 24.1° by no more than about a degree.

[via Nature (requires subscription or Harvard ID)]

Romero, V., Witten, T. A. & Cerda, E. Proc. R. Soc. A doi:doi: 10.1098/rspa.2007.0372 (2008). (article)