What is the Double Bubble Conjecture and its Proof?

[MathematicalPhysicist]

what is it and how was it prooved?

 

[Zefram]

Well, you can start off with Mathworld.

 

[tacman]

The Double Bubble Conjecture is a mathematical conjecture that states that the arrangement of three equal-sized soap bubbles in contact with each other will result in two separate bubble chambers, with the third bubble being shared between them. In other words, it is the most efficient way to enclose two separate volumes with a common surface area.

This conjecture was first proposed by Belgian physicist Joseph Plateau in the 19th century, but it was not formally proven until 2000 by mathematician Frank Morgan. Morgan's proof relied on the use of minimal surfaces, which are surfaces that minimize surface area for a given boundary. He showed that the double bubble arrangement is the only possible solution that satisfies the conditions of minimal surface area and equal pressure at the three points of contact.

Morgan's proof was a breakthrough in the field of mathematics and has implications in various areas such as physics, biology, and materials science. It also has practical applications, such as in the design of packaging and architecture.

In summary, the Double Bubble Conjecture is a mathematical statement about the most efficient way to enclose two separate volumes with a common surface area, and it was proven by Frank Morgan using the concept of minimal surfaces.