Pi and Bouncing Balls - Numberphile
video description
digits = int(input(-How many digits you want: -)
bigMass = 16 - (100 -- digits)
bigVel = 10
smallVel = 0
i = 0
while bigVel > 0:
i += 1
momentum = 2-(bigVel - smallVel)-bigMass/(bigMass+1)
bigVel -= momentum / bigMass
smallVel += momentum
smallVel -= -1
print(str(bigVel) + - - + str(smallVel)
print(i-1)
Date: 2022-04-08
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Comments and reviews: 9
alpha4021
I just calculated the speeds after the first collision given N=0, so x=1/16
Mu0=Mu1+mv1 by conservation of momentum
Mu0-2=Mu1-2+mv1-2 by conservation of energy
so make both equations be a term of u1-2 will get a new equation u0=17/32-v1
substitute it back to the equation will yield u1=15/32-v1
thus u1=15/17-u0 and v1=32/17-u0
now we check the given formula, u1=(1+1/16)-sqrt(1/16)-u0-cos(15/17)
so u1=0. 16876 u0 which contradicts with the result above.
reply
I just calculated the speeds after the first collision given N=0, so x=1/16
Mu0=Mu1+mv1 by conservation of momentum
Mu0-2=Mu1-2+mv1-2 by conservation of energy
so make both equations be a term of u1-2 will get a new equation u0=17/32-v1
substitute it back to the equation will yield u1=15/32-v1
thus u1=15/17-u0 and v1=32/17-u0
now we check the given formula, u1=(1+1/16)-sqrt(1/16)-u0-cos(15/17)
so u1=0. 16876 u0 which contradicts with the result above.
reply
Sumanth
For those interested, it is possible to derive this from first principles of conservation of momentum and energy as well (Had a fun day figuring that out)
m = 1
u = 1
v = 0
n = 4
M = 16-100--n
count = 0
while u > 0. 0001:
v = v + 2-M-m-u/(m-M + m--2)
u = u - 2-m-v/M
count += 1
print(-Number of times collision occurs = -, count)
print(-Therefore pi --, (count+1)/(10--(n)
reply
For those interested, it is possible to derive this from first principles of conservation of momentum and energy as well (Had a fun day figuring that out)
m = 1
u = 1
v = 0
n = 4
M = 16-100--n
count = 0
while u > 0. 0001:
v = v + 2-M-m-u/(m-M + m--2)
u = u - 2-m-v/M
count += 1
print(-Number of times collision occurs = -, count)
print(-Therefore pi --, (count+1)/(10--(n)
reply
Joshua
I was taught that Pi was a two-dimensional phenomena. If in three dimensional space with the required mechanisms for this to work we generate the same irrational number, does this suggest an interdimensional geometric law that with enough logic and creativity we could translate in to the 4th dimensions and beyond? Or are the forces on the objects operating at a lower dimension than the objects themselves?
reply
I was taught that Pi was a two-dimensional phenomena. If in three dimensional space with the required mechanisms for this to work we generate the same irrational number, does this suggest an interdimensional geometric law that with enough logic and creativity we could translate in to the 4th dimensions and beyond? Or are the forces on the objects operating at a lower dimension than the objects themselves?
reply
Peter
two things:
a) you could have a wagon or air hockey puck collide, and that would allow 10, 100 times the weight without a bigger ball
b) my OCD must be kicking in, since I wonder if the marking pens would seep through the brown paper onto the felt of the pool table, leaving a permanent mark. (sigh -- I'm getting old and worried about such things)
reply
two things:
a) you could have a wagon or air hockey puck collide, and that would allow 10, 100 times the weight without a bigger ball
b) my OCD must be kicking in, since I wonder if the marking pens would seep through the brown paper onto the felt of the pool table, leaving a permanent mark. (sigh -- I'm getting old and worried about such things)
reply
Jim
It seems to me that in order to cause the big mass to reverse direction, the momentum of the big ball would not only have to be eliminated, it would have to be -negated. - How can the small ball, with no initial momentum, receive more momentum than the big ball has the instant before the first collision?
reply
It seems to me that in order to cause the big mass to reverse direction, the momentum of the big ball would not only have to be eliminated, it would have to be -negated. - How can the small ball, with no initial momentum, receive more momentum than the big ball has the instant before the first collision?
reply
boumbh
Is this mathematical obfuscation?
4: 35 -And now the more complicated maths part. - should have say -And now we will be throwing equations without explanation in order to confuse you. -
Do you understand what you are talking about or are you just very bad at explaining things?
reply
Is this mathematical obfuscation?
4: 35 -And now the more complicated maths part. - should have say -And now we will be throwing equations without explanation in order to confuse you. -
Do you understand what you are talking about or are you just very bad at explaining things?
reply
Venkat
Pi is the ratio of the spheres of the heavenly bodies which are close by. Sun to Jupiter size ratio. But log. Approximately 3. 14. Meaning ten thousands ratio. That's the ratio needed to hold things together in space. G. To keep them apart at a distance d the opposite spin ratio.
reply
Pi is the ratio of the spheres of the heavenly bodies which are close by. Sun to Jupiter size ratio. But log. Approximately 3. 14. Meaning ten thousands ratio. That's the ratio needed to hold things together in space. G. To keep them apart at a distance d the opposite spin ratio.
reply
Ken
Absolutely amazing! I verified this with a short Python program, running N up to 9, giving a result of 314, 159, 265 collisions. Exactly matching the first 9 digits of pi! The program runs in about 5 minutes. For N=10 the result would be 50 minutes. I didn't run it that long: -)
reply
Absolutely amazing! I verified this with a short Python program, running N up to 9, giving a result of 314, 159, 265 collisions. Exactly matching the first 9 digits of pi! The program runs in about 5 minutes. For N=10 the result would be 50 minutes. I didn't run it that long: -)
reply
numberphile
I think this video is not good, they describe twice the physics and the results and show only some mathematical results with absolutly no link between both.
However Pi_Balls_Ed. pdf is very interesting, i think the video should tell way more about Pi_Balls_Ed. pdf
reply
I think this video is not good, they describe twice the physics and the results and show only some mathematical results with absolutly no link between both.
However Pi_Balls_Ed. pdf is very interesting, i think the video should tell way more about Pi_Balls_Ed. pdf
reply
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