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• The soap wants minimize tension, the minimized tension yields the minimized area of the soap 'walls' between the squares.

What is the logic behind this in two dimensions?

As﻿ in, considering there are infinite configurations - how would you prove this correct without the use of the soap that wants to minimize tension?

• Do you mean what is the theory and the﻿ maths? It's called Calculus of Variations.

• You're awesome ! Period. Exclamation mark ! ﻿

#### Video Responses

This video is a response to Maths Problem: Connect the towns

• It's called Calculus of Variation.﻿

• With the 8 towns, you could leave one road out and it would be even smaller. By the way, in 3-dimensional environment, would the vertices there be the same as when﻿ you connect the center of mass of a tetrahedron to its vertices?

• the blow part at the end﻿ was "mind-blowing".

• Does anyone know of a reference in which the math of this problem's solution is shown?

How about for higher dimensions? For instance, if you take the eight vertices﻿ of a cube as the points to be connected, what will the minimum solution look like? Maybe the projection onto one (or more or all) of the planes will correspond to the four-point plane solution.

• could you do like a video on how to - mathematically - prove/come﻿ to the solution? :D

• sweet,﻿ computers made of soap :D

• Damn, I was close. I thought about a shape like )-(

A sort of bent﻿ H-shape.

I had trouble figuring out how to calculate the total length.

• Mind. Blown.﻿

• simply amazing!!!!!﻿