Math 1; A coin on its edge.
The statistics of falling objects.
A long time I was asking myself what would be the chance that a coin falls on its edge ?. And in 2015 it was time to systematically find that out.
We know it is not zero, there is a small chance that a coin land on its edge.
For that reason I performed the next series of experiments:
www.youtube.com/watch?v=OycMOmnW_hg
I took a bunch of coins (5 Euro cent coins since the have a nice flat edge) and made so called "coin-rods"by glue-ing 2, 3, 4, 5 etc coins together and I tossed then about a 100 times each.
This data I have put in a table and drew on that data a graph.
Now it turns out to be a cumulative log normal distribution (in which a log normal distribution is simply integrated).
Once you know this you can try to fit it with the parameters of this type of curve and calculate back for any amount of coins or any thickness of the "coinrod"what its chance will be to land on its edge.
It turns out to be that the estimated chance based on these limited amount of numbers of coin-rod-flips the chance of a 5 Eurocent landing on its edge is about 1 in 300-400. For more accuracy it would be better to increase the number of coin-rod-flips. of course, But for now it will do.
You may think that we can stop here right now, but then you are mistaking, There is more. This subject turned out to be far more interesting then expected and therefor I continue.
You see there are questions that rose based on this issue. since we could ask
a) what would be the results if we replace the coin rod for an other rod like objects, Like a tube and does the weight of these objects influence it.
b) can we alter the shape of the rods by cutting off some part in such a way that we obtain a non right angled rod due to which the coin side is increased
c) What would be the results be if the rod would be modified in all kinds of ways. and weight distributions within the rod.
and of course these results would bring about some more questions, So this was an interesting start of an interesting subject: in general Falling objects, How would they behave statistically. Not very high tech I agree but intersting non the less.
This "reseach" is still in progress, but is shifted aside from time to time for even more research.
some more (recent) data to be added:
no coins 1 2 3 4 5 6 7 8 9 10
head 52 52 51 94 87 x 60 50 x 28
coin 48 48 57 98 94 x 64 41 x 24
edge 0 0 2 8 19 x 76 109 x 148
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