Research ArticleMATHEMATICS

The Euler spiral of rat whiskers

See allHide authors and affiliations

Science Advances  15 Jan 2020:
Vol. 6, no. 3, eaax5145
DOI: 10.1126/sciadv.aax5145


This paper reports on an analytical study of the intrinsic shapes of 523 whiskers from 15 rats. We show that the variety of whiskers on a rat’s cheek, each of which has different lengths and shapes, can be described by a simple mathematical equation such that each whisker is represented as an interval on the Euler spiral. When all the representative curves of mystacial vibrissae for a single rat are assembled together, they span an interval extending from one coiled domain of the Euler spiral to the other. We additionally find that each whisker makes nearly the same angle of 47 with the normal to the spherical virtual surface formed by the tips of whiskers, which constitutes the rat’s tactile sensory shroud or “search space.” The implications of the linear curvature model for gaining insight into relationships between growth, form, and function are discussed.

This is an open-access article distributed under the terms of the Creative Commons Attribution license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

View Full Text

Stay Connected to Science Advances