If we dip two wire rings into a solution of soapy water, then what is the surface formed by the soap film ? This question is known as the minimal surface problem, or the Plateau problem. This post proposes to discuss a simple solution based on variational calculus and elementary computations.
Dido was the legendary founder of Carthage (Tunisia). When she arrived in 814BC on the coast of Tunisia, she asked for a piece of land. Her request was satisfied provided that the land could be encompassed by an ox-hide. With a remarkable mathematical intuition, she cut the ox-hide into a long thin strip and used it to encircle the land. This land became Carthage and Dido became the Queen.
What is the closed curve which has the maximum area for a given perimeter ?