#Math's working project on visualization of pi using chaos theory
calm oasisBOT
subtle elbow
Hello! This is a very interesting visualization. Let me explain what I think this could be.
I believe this is a double pendulum. However, it doesn't have to do with the laws of physics, nor gravity. Rather, the second arm rotates at pi radians per second, and the first arm at the center rotates at 1 radian per second (I believe). I believe the purpose of this demonstration is to show that the pattern never repeats because pi is irrational.
Both the angles mod (2pi) must equal the starting conditions. Let t1(t) = the angle made by the first arm. Let t2(t) = the angle made by the second arm. note that d/dt(t1(t)) = 1 (rotates at 1 radian per second). d/dt(t2(t)) = pi.
t1(0) = 0, t2(0) = 0, wlog
We need to prove that no there exists no real number t s.t. t1(t) = t1(0) mod 2pi and that t2(t) = t2(0) mod 2pi
Solving these differential equations is trivial, t1(t) = t and t2(t) = pi * t
If there is such a time t, it implies that
t congruent to 0 mod 2pi and pi*t is congruent to 0 mod 2pi
this means that t = 2npi where n is an integer
this also means that pi*t = 2mpi where m is an integer
Or, t = 2m where m is an integer
This means that 2npi = 2m where n,m are integers
This means npi = m where n,m, are integers
This means pi = m/n where n,m are integers
We have reached a contradiction as pi cannot be in the form m/n if both are integers as pi is irrational
raven idol
Okay
So using this we prove that no line will be override and the pattern would never repeat because it is not a perfect fraction, so there would no repetition of numbers.
But like how will I make the model of this because it is very hard to make double pendulum models that I have heard as a small mistake can ruin the unpredictable pattern.
I was thinking of using a motor system to do it
raven idol
you were typing I just saw you
Yeah lol
subtle elbow
Okay
So using this we prove that no line will be override and the pattern would ...
do you want to make one in real life? Just code one. In fact, you don't even need that
You can use desmos
raven idol
do you want to make one in real life? Just code one. In fact, you don't even nee...
Yeah we have a physical math's exhibition
subtle elbow
Yeah we have a physical math's exhibition
this wouldn't be something to present physically
a traditional double pendulum would work
I watched a video on it earlier, one second
raven idol
ah ok
raven idol
Ok I ma watch it and research a bit more