🚀 go-pugleaf

In article <1992Aug9.135659.22013@usenet.ins.cwru.edu> aa751@cleveland.Freenet.Edu (Fran Rosen) writes:
>
>I just finished a philosophy class which was quite enlightening.
>I now have a conception of the difference between Euclidian and
>non-Euclidian geometry.  What I am curious about is what Calculus
>and Trigonometry show or at least what their purpose is.  

 Mathematics (whether geometry or calculus) does not "show" anything 
 since its purpose is to provide a framework for obtaining reliable 
 answers to well-posed questions within some domain of applicability 
 of that framework.  It spends most of its time on proofs concerning 
 when and how various methods can be used, and inventing more of same. 
 A mathematical method that happens to be useful to describe the physical 
 world is rare and valuable to a physicist, embarrasing to a mathematician. 

 ;-)

 That said: so you know that Euclidean geometry applies when parallel lines 
 do not meet, and non-Euclidean geometries otherwise (such as when doing 
 land surveying on the surface of the earth, or doing general relativity). 
 Trigonometry is a tool for doing *calculations* with geometric figures, 
 as opposed to proving theorems about them.  It is used to compute the 
 relationship between angles and lengths of sides or arcs.  Calculus is 
 a tool for computing the area of a shape, and applies to shapes enclosed 
 by (almost) arbitrary curves -- not just straight lines or arcs.  It is 
 also used to compute the length of a curved line and many other things. 

 This is, of course, radically oversimplified based on your signature 
 comment below (and the fact that someone who knows about non-Euclidean 
 geometry and not about trigonometry is likely to be uninterested in, 
 say, the Heine-Borel theorem).  Hope this helps. 

>An arts and science major,
>Fran

 Now that is interesting.  One often sees a College of Arts and Science, 
 but seldom a student majoring in both!  Even at Lyman Briggs School 
 at Michigan State, which was designed around such a concept, one seldom 
 ran into someone who met that description. 

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)