Double Bubble
The planar double bubble (three circular arcs meeting in two points at equal 120° Angles) has theminimum Perimeter for enclosing two equal areas (Foisy 1993, Morgan 1995).
See also Apple, Bubble, Double Bubble Conjecture, Sphere-Sphere Intersection
References
Campbell, P. J. (Ed.). Reviews. Math. Mag. 68, 321, 1995. Foisy, J.; Alfaro, M.; Brock, J.; Hodges, N.; and Zimba, J. ``The Standard Double Soap Bubble in Morgan, F. ``The Double Bubble Conjecture.'' FOCUS 15, 6-7, 1995. Peterson, I. ``Toil and Trouble over Double Bubbles.'' Sci. News 148, 101, Aug. 12, 1995.
Uniquely Minimizes Perimeter.'' Pacific J. Math. 159, 47-59, 1993.
- Parallelism
- Parallelizable
- Parallelogram
- Parallelogram Illusion
- Parallelogram Law
- Parallelohedron
- Parallelotope
- Parallel Postulate
- Parallel (Surface of Revolution)
- Paralogic Triangles
- Parameter
- Parameterization
- Parameter (Quadric)
- Parametric Latitude
- Parametric Test
- Pareto Distribution
- Parity
- Parity Constant
- Parking Constant
- Parodi's Theorem
- Parry Circle
- Parry Point
- Parseval's Integral
- Parseval's Relation
- Parseval's Theorem