What is the aplication of the double bubble conjecture in real life?

Answer 1

It was proven in 2000 that the common double soap bubble is the most efficient structure for containing two separate volumes of air within the least amount of surface area..

The Double Bubble Conjecture is an example of what mathematicians call a problem in "calculus of variations": finding the best configuration that maximizes or minimizes some quantity given geometrical constraints. The range of applications of such methods is enormous.

Mathematicians believe that the insights provided by the proof of the Double Bubble Conjecture and their further investigations of optimal geometry have much to contribute toward helping us solve other essential questions -- such as how can we best design new materials, what are the optimal mechanisms of cellular transport, what efficiency secrets can we learn from the growth patterns of crystals, what is the optimal configuration of an information network, how are black holes structured and how do optimization principles affect the shape of the universe?

"Whether it's soap bubbles or materials or black holes or human cells -- these structures meet in certain ways. So we ask -- how do they fit, how do they pack, on the very small scale and on the very largest of scales. To solve the minimization problems of humanity, we start with a simple example"

An early example of the ingenious application of calculus of variations is found in Queen Dido's problem, recounted by the Roman poet, Virgil (70-19 BC), in his epic Aeneid. After her brother had her husband killed, Dido fled her native city of Tyre (an area of present-day Lebanon) with a number of followers and reached Carthage in North Africa. There, she sought to buy land from the local inhabitants. They struck a bargain allowing Dido to purchase for a fixed price all the land that she could enclose within a bull's hide. To maximize her land acquisition, Dido had the bull's hide cut into thin strips and the strips then sewn into a long ribbon. She placed this ribbon on the ground in the shape of a semi-circle that started and ended with a straight segment of the seacoast. Since the coast length was added to the ribbon length, Dido was able to enclose more land than if she had used the available ribbon length to enclose a circle or square.

Dido had solved a question known to mathematicians as the "isoperimetric theorem": what figure bounded by a line contains the most area within a given perimeter. As Dido showed, the answer is a semi-circle. Though known to the ancient Greeks by 900 B.C., the theorem went without a rigorous mathematical proof until the mid-1800s.

Answer 2

Development of thin films, aerodynamics etc.