Definition of Oval

Date: 06/09/2002 at 20:15:44
From: Jeff McAffer
Subject: definition of an "oval"

We were recently given a book of geometrical shapes for our 7 month 
old daughter (never too early for math!).  In the book there is a 
drawing of an ellipse with the label "oval".  The next page has a 
real world example of a chicken's egg.  We both agree that the egg is 
oval (I believe this is the origin of the word) but what of the 
ellipse?  So I started searching your site (very nice!) and found

 http://mathforum.org/library/drmath/view/55368.html 

which clearly positions ellipses as ovals.   Great.  But the 
discussion raised questions as to the exact definition of "oval". 
 
The Exeter description says: 

    "... This is distinct from an oval where the 
     perimeter has only to be a concave curve, and
     there are many possibilities"

By this wording, a circle is an oval.  Something resembling a right 
angle triangle with rounded corners is an oval, ...  Seems overly 
broad and quite contrary to popular conception.  Is there a more 
exact/narrow definition of "oval"?

Many thanks and keep up the good work.

Jeff

Date: 06/09/2002 at 23:10:26
From: Doctor Peterson
Subject: Re: definition of an "oval"

Hi, Jeff.

The word "oval" merely means "egg-shaped"; you are right that it 
comes from the Latin word for "egg". It is not a precisely defined 
mathematical term. If we wanted to make it more precise, we might 
require these features:

    continuous, smooth closed curve
    convex ("concave" is a misprint on that site!)
    not an exact circle
    one axis of symmetry
    longer along the axis than across it

An ellipse fits all but the single axis of symmetry; it is more 
symmetrical than many eggs. That requirement is not always included 
in defining "oval".

But because there is no mathematical gain in defining this term, 
which covers a variety of figures anyway, there is no need to define 
it more precisely from our perspective. We just know an "egg" when we 
see it (and don't argue if someone else disagrees!).

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/