Booth Id:
MATH030
Category:
Mathematics
Year:
2021
Finalist Names:
Klippgen, Victor (School: Blindern VGS)
Abstract:
This paper provides an alternative derivation of the graph which represents the shape of the catenary curve. A catenary is the shape that takes place when a chain hangs freely between two fixed points. The traditional approach to derive the catenary is to solve a differential equation which is obtained from studying the forces acting on an arbitrary point on the curve. In this paper, however, a mechanical analysis of a simplified version of the catenary followed by function composition and integration. Contrary to the classical solution, this avoids the use of differential equations.
The math required by this derivation is arguably less abstract than that of the conventional derivation. This derivation also provides a new interpretation of the required parameter of the equation of the catenary.