Cundy and Rollett's egg is a planar egg cut into pieces that can be rearranged to make pictures, as in a tangram.
The left panel shows an outline made from four circular arcs. In units in which the broad end is a semicircle
of radius 2, its center is . The upper and lower arcs have radius
3 and centers
and
, respectively. The pointed end has radius
1 and center
. The dashed guides show that the two centers
and the joining point are collinear at each join, so
adjacent arcs have a common tangent
line there.
Moss's egg uses the same four-arc construction with a different placement of the side-arc centers. In Moss's egg they lie at the endpoints of the broad semicircle's diameter. In Cundy and Rollett's egg they lie halfway from the midpoint to those endpoints.
Joining the four points where the outline arcs meet gives a trapezoid of area . The semicircle
contributes
, and the other three circular
segments each subtend an angle of
at their centers. Adding these contributions gives the
area
|
(1)
| |||
|
(2)
|
(OEIS A399947).
The straight cuts and the interior circular arc in the right panel divide the egg into twelve pieces.