All these facts came in my mind while the study of fluid mechanics where I got to know that fluids always have a tendency to decrease their surface area.
Assume that a closed irregular shaped loop of thread is put on the surface of a ring having a film of soap solution on it,now prick a hole in the middle by my observation I came to know that after pricking the hole the force of surface tension pulls the thread which leads to the formation of a circle.If fluids want to get the minimum area possible then the loop formed must have the maximum surface area possible and by observation loop is a circle.
It's my appeal to mathematicians that please give me the rigid proof regarding this observation that circle had the largest area possible formed by a closed loop.
A small drop of liquid takes nearly a spherical shape.Because of gravitational force between the particles there is some deviation from the spherical shape but for small drops it can be neglected.
The formation of spherical shape must be due to the property of fluid to decrease its surface area.Please give here a proof regarding the fact that for a given volume sphere assumes the smallest surface area possible.
Edit:- Give a rigid proof to the concerned problems do not apply induction or arguments.If a proof by geometry or high order calculus exists then only give the answer.Well I know the whole physics of this problem and basically the mathematics is complex that's why I am concerned to it.