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Cundy and Rollett's Egg


CundyandRollettsEgg

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 O=(0,0). The upper and lower arcs have radius 3 and centers B=(0,-1) and A=(0,1), respectively. The pointed end has radius 1 and center C=(sqrt(3),0). 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 15sqrt(3)/4. The semicircle contributes 2pi, and the other three circular segments each subtend an angle of pi/3 at their centers. Adding these contributions gives the area

A=(31pi)/6-sqrt(3)
(1)
=14.4995112359...
(2)

(OEIS A399947).

The straight cuts and the interior circular arc in the right panel divide the egg into twelve pieces.


See also

Dissection, Egg, Moss's Egg, Oval, Pentagon Egg, Tangram, Thom's Eggs

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References

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., pp. 19-21, 1989.Dixon, R. Mathographics. New York: Dover, p. 11, 1991.Sloane, N. J. A. Sequence A399947 in "The On-Line Encyclopedia of Integer Sequences."

Referenced on Wolfram|Alpha

Cundy and Rollett's Egg

Cite this as:

Weisstein, Eric W. "Cundy and Rollett's Egg." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CundyandRollettsEgg.html

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