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In the plane, the analog of the double bubble consists of three circular arcs meeting in two points. It has been proved that the configuration of arcs meeting at equal angles has the minimum perimeter for enclosing two equal areas Alfaro et al.

It had been conjectured that two equal partial spheres sharing a boundary of a flat disk separate two volumes of air using a total surface area that is less than any other boundary. This equal-volume case was proved by Hass et al. In this case of two unequal partial spheres, Morgan et al.

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  5. Furthermore, the curvature of the partition is simply the difference of the curvatures of the two bubbles,. Furthermore, for three bubbles with radii , , and , and interface radii , and ,. Amazingly, a group of undergraduates has extended the theorem to four-dimensional double bubbles, as well as certain cases in five-space and higher dimensions.

    Dubble Bubbles

    The corresponding triple bubble conjecture remains open Cipra The Newsletter of the Math. News , , Aug.

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    Mathematics and computer science Double bubble conjecture , the mathematical statement that the minimum surface surrounding two given volumes is formed by three spherical patches meeting at a common circle, and the "standard double bubble", the name for this surface Double bubble map , a graphical information visualization technique Double bubble sort , a variation of the bubble sort algorithm Biology and medicine Double bubble radiology , a symptom of a bowel obstruction formed by two air-filled bubbles in the abdomen Double bubble mint, a common name for the agastache cana plant Music and entertainment "Double Bubble", a track on jazz-fusion music album Southern Comfort The Crusaders album "Double Bubble", an episode of British medical television drama Holby City series Disambiguation page providing links to articles with similar titles.

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