Being a weblog devoted to a variety of topics. Including Mathematics. And Mathematical Finance. Sometimes with homework.

Thursday, August 27, 2009

The Father of Sinh

A student asked me about the origin of the hyperbolic functions in one of my recitations today. The Wikipedia article credits the Alsatian mathematician-physicist-philosopher-spelunker Johann Heinrich Lambert (who was apparently obsessed with equal-area map projections) with the invention of these functions, but his own article doesn't mention them at all. Maybe a disgruntled calculus student edited them out.

Google Timeline lists a reference back in 1631, by an English mathematician Richard Norwood, but that link is actually referring to trigonometric functions. The second reference in Timeline (A History of Mathematical Notations: Notations Mainly in Higher Mathematics by Florian Cajori) says that the hyperbolic functions were first used by Vincenzo Riccati in 1757, but he used the notation "Sh." for hyperbolic sine and "Ch." for hyperbolic cosine. Lambert is said to have invented the notation that we now use for these functions (sinh,cosh,tanh) in 1768. However, several other notations were used for these functions well into the 1900s.

So, we can take away from this that

(a) Wikipedia is not to be trusted, even in math;
(b) mathematical notation is all over the place; and
(c) inventing good notation for a concept will make you as famous as the people who invented the actual concept.

1 comment:

Dr. Handron said...

Incidentally, the reason they are "Hyperbolic" is because of you plot (cosh(t),sinh(t)) for real values of t, the graph is a hyperbola.