What is condition for equilibrium of particle in 2D and 3D?

Answer 1

What I had in mind was to ask if Particles primarily will form in 2D environment or in 3D?like snow flakes that apparently are having 2D geometrical shape.

By studying loads of mathematical Models and arranging numerical as well as geometrical Functions I came to the point that Existence will start forming in 2 dimensional environment and will continue for geometrical mating one step higher than 2D.

Geometrical mating is done when you divide a rectangle with the Sides m&n(where m is greater than n) by it's hypotenuse into two identical Rightangle Triagles, this can be done in 2D environment,but to make a isosceles triangle by combining these two pieces,one of the pieces has to rotate spacial.

Draw a perpendicular Line from one side of the Base to opposite Side to get two new right angle Triangles and read them according to m and n,one of them is proportional to half rectangle (half of new isosceles) and the other one will read:

2mn/m^2-n^2/m^2+n^2.

Equilibrium occurs in 2D,where dynamism needs higher dimension than 2th.D

this is just an opinion dictated by mathematical facts.