Message-Id: <l03102800b0b6075ac0d6@[153.90.236.25]>
In-Reply-To: <3.0.3.32.19971211103620.006a463c@mail.walltech.com>
Date: Thu, 11 Dec 1997 14:22:06 -0700
To: pinhole@exploratorium.edu
From: Steven Eiger <eiger@montana.edu>
Subject: Re: Vectors
>>>As we know that all vectors have both magnitudes and directions. Is it
>>>also true that if a quantity which has magnitude and direction, is a
>>>vector quantity? A. Rahbar {rahbar@alpha.nsula.edu}
>>
>>I once heard, I think from a mathematician, that anything that requires two
>>numbers to describe it is called a vector. This is a much more general
>>meaning than most physics folks are used to. Eiger
>>
>>
>
>I can come up with a counterexample. Say that you want to describe the area
>of something. Area = length x width, which are two numbers. Yet both length
>and
>width are scalars, since they involve only magnitude and not direction. So
>therefore
>area wouldn't be a vector. It wouldn't make sense to speak of the magnitude
>and
>direction of area.
>
>Is this logic correct?
>Geoff Ruth
I do not think so because area can be described very well by a single
number, eg. 20 cm2. One should try to envision a scalar quantity coupled
with another quality. Speed and direction work well to make velocity,
Perhaps position on a two-dimensional surface is a vector quantity; that
requires two numbers. I am definitely out of my league here, but I bet the
math people would be aware of examples of descriptions which do require two
numbers. The mass and spin of elementary partcicles comes to mind. I do
not think it matters how many scalar quantities one begins with, but rather
the need for using two numbers to describe the final result. That is why
area is a scalar. Eiger