An oval is a curve resembling a squashed circle but, unlike the ellipse, without a precise mathematical definition. The word oval derived from the Latin word "ovus" for egg. Unlike ellipses, ovals sometimes have only a single axis of symmetry (instead of two).
The particular variant illustrated above can be constructed with a compass by joining together arcs of different radii
such that the centers of the arcs
lie on a line passing through the join point (Dixon 1991).
Albrecht Dürer used this method to design a Roman letter font. If the separation
between left and right caps is 
and the radii are 
and 
,
respectively, with 
and 
, then the center 
and radius 
of the joining circle
are
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is a signed Cartesian
coordinate, rather than a positive distance. The
cap centers are 
and 
,
and 
.
Call the three circles 
, 
,
and 
. Let the upper point of intersection
of 
and 
be 
,
let the angle between the vertical dashed line
and the line through 
be 
, and let the angle between the
horizontal radius of 
and dashed line through 
be 
. Then
 |  |  |
(3)
|
 |  |  |
(4)
|
 |  |  |
(5)
|
 |  |  |
(6)
|
and half the area enclosed by the oval is the sum of the areas of the leftmost quarter-disk,
the circular sector of 
, and the circular sector
of 
minus the area
of the triangular portion of the circular sector
of 
lying below the 
-axis, so
 |  |  |
(7)
|
 |  |  |
(8)
|
 |  | )/(2(R-r)^2)tan^(-1)((2a(R-r))/(a^2-(R-r)^2))].](/images/equations/Oval/Inline53.svg) |
(9)
|
As expected, this formula reduces to the area of a circle
 |
(10)
|
for 
, and to the area
of a stadium
 |
(11)
|
for 
.
