Following to the conjectures (1), (2), (3) and (4) in articles of "The Distances among The Particles in The Space (1)" and "The Distances among The Particles in The Space (2)", you can herewith find new conjectures as follows:
Conjecture (5):
By using this theorem or conjecture,
I am willing to show you that there is below figure among five points in the
space:
Suppose we have point P1 (x, y, z)
and an independent variable “t” where there is below functions between them:
If points Pm
and Pn have below coordination:
Pm (f(x,y,z,t),
f(x,y,z,t), f(x,y,z,t))
Pn (g(x,y,z,t),
g(x,y,z,t), g(x,y,z,t))
Then, in
according to conjecture (3), the distance of points Pm and Pn will be equal
with the points P1, P2 and P3 stated in conjecture (3). (Please see conjecture
(3) on above links).
It means:
d(Pm,P1)= d(Pm,P2)
= d(Pm,P3) = d(Pn,P1) = d(Pn,P2) = d(Pn,P3) =R
Example (1):
Suppose we have below data:
P1 (-11, 3, 31)
t = 129
The results will be as follows:
Example (2):
Suppose we have below data:
P1 (-3.57, 9.4, -1.84)
t = 32.83
The results will be as follows:
The Mapping A System of five Particle for Given Gravity Potential
Energy
Suppose we have five particles Pm, Pn, P1, P2 and P3 with the
distances among them in infinity which have the same masses of “m”. If an
external force brings all these particles in new location just like above figure,
how can we map the location of these particles for a constant gravity potential
energy?
The method of analysis is just like the steps stated in previous
article (The Distances among The Particles in The Space (2))
The only difference is to solve a system of three nonlinear equations instead of a system of two
nonlinear equations in previous articles as follows:
Example:
To simplify above system of
equations, I consider “t” as a constant number.
Assume we have:
r = 0.24 m
t = 3
Thus, we should solve below system
of three equations:
I found 190 models that some of them are as follows:
For testing of these models, I use model (1) in above table and we
can see the results as follows:
