Special Function Sets & HPs

[Jeff_Kearns]

(01-31-2016 08:29 AM)Paul Dale Wrote:  

Quote:Hyperbolics

Seriously, does anyone actually use these? I have never required them for anything beyond minimal step challenges. Honestly, I'd prefer to include the Jacobi elliptic functions which are a superset of both hyperbolic and trigonometric functions (these didn't make the cut in the 34S).

- Pauli

This comment made me think of one of Valentin's replies back in 2003:
Hyperbolics everywhere ! (almost)
Message #4 Posted by Valentin Albillo on 30 June 2003, 6:38 a.m.,
in response to message #3 by Ernie Malaga
Ernesto wrote:

"How about hyperbolics? So far I haven't learned of a _single_ use for hyperbolic functions in any field."

They're used all the time in some very important Civil Engineering fields, a few assorted examples:

electrical transportation (trains and such, which draw power from a suspended conducting wire). The wire's shape is a curve called catenary, which is a hyperbolic cosine, and thus you need hyperbolics to compute lengths, weights, stress, costs, etc. This also applies to high-voltage power lines and, in general, to any kind of chain, rope or wire suspended from two points that hangs freely under its own weight.
superstructure engineering (suspension bridges and such), where you need to compute the elastic curve and the deflection, also require hyperbolic cosines in spades.
architecture, specially traditional japanese architecture and civil engineering, where curves have various important social and philosophical meanings (temples and other relevant buildings). Japanese and oriental architects frequently use the catenary shape (hyperbolic cosine) for the upward-pointing curves in their constructions instead of the less-quickly-raising parabolas.
aerospatial engineering: engineers (from Boeing, for example) face a problem in applying a surface coating to fighter aircraft. The critical feature is the electrical conductivity at the surface. This physical property determines how an electromagnetic wave will scatter when it hits the aircraft. For some fighter parts, the ideal coating varies along the surface according to the hyperbolic cosine function.
etc, etc. Matter of fact, students of the Civil & Environmental Engineering divisions of most universities are required to be confident with the manipulation of hyperbolic functions and the solution of hyperbolic equations. I guess such an student would find himself as much at a loss using a calculator without hyperbolics as you and me would be using one without division, say.

"There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy."

--From Hamlet, Prince of Denmark - 1601 - Act I. - Scene 5. - Rows: 166-167

:-)

Best regards.

Edited: 30 June 2003, 6:44 a.m.

Jeff Kearns