The hyperbolic sine cardinal and the Catenary
2012 - J. Sánchez-Reyes
The College Mathematics Journal 43, 285-290 (2012)
The hyperbolic function sinh(x)/x receives scant attention in the literature. We show that it admits a clear geometric interpretation as the ratio between length and chord of a symmetric catenary segment. The inverse, together with the use of dimensionless parameters, furnishes a compact, explicit construction of a general catenary segment of given length hanging from supports of different heights.