Buffon's Needle Animated in 3D

This video shows a simulation of Buffon's Needle: a way of calculating Pi by dropping a series of needles on a surface with parallel lines. This simulation makes it easy to see how this calculation is done.
It also makes it clear that you need a lot of needles! Check out the original Java applet:
www.ventrella.c...

[@mhillh]

Yes, he posed and solved this probability in 1777. Even though pi was defined originally in geometry, it appears very frequentry and unexpectedly in the calculation of probabilities.

[@ColoredScreens]

+mhillh the probability of the needle crossing depends upon trigonometric functions, so it makes sense for pi to pop up here

[@MrSaad1932]

okok.... the reason it was so off is because they were droping in the middle MOST of the time... ok seriosly , if it was actually random you could have gotten pi to 4 or 5 decimal place with only 1000 needles

[@JeffreyVentrella]

Good point!
So, if I distributed the needles across a larger area, it might result in a more accurate approximation of Pi. That makes sense. Thanks for the observation. The question then is....how big an area (i.e., how many parallel lines) are needed for accuracy? My intuition is that increasing the size to cover a few more lines would help more, but increasing beyond that would help only a little bit, with a drop off in added benefit for each increase in area.
Thanks!
-j

[@JeffreyVentrella]

@videowala007 Yea, totally. btw - somehow I feel like Buffon's needle gets to the heart of Pi in a significant way. I've always felt a little unsatisfied with the "diameter...circumference" thing. Perpendicularity is a key notion here - as you point out :)

[@JeffreyVentrella]

@videowala007
Depends on how you want to do the experiment. I prefer to use needles whose lengths are 1/2 the width between the lines.

[@JeffreyVentrella]

Yea. I think the important thing is that the needle can be any length as long as it is no longer than the width between the parallel lines. The calculation of Pi needs to take this ratio into account, unless the needles are 1/2 the width between the lines, in which case the calculation is simpler.

[@JeffreyVentrella]

@RandomRhinos
Could you be more specific? What generates the relevant information is the relationship of the dropped needles to the spaces, not the spaces themselves. Also, the number of spaces is not so important, as long as the needles drop in random positions across the span of at least a few spaces.

[@anthonyip]

if you did this with hot dogs you'd get to pi in only 10 iterations

[@CafecitoConLeche]

I wonder, in your simulation do the needles collide with each other?

[@videowala007]

@JeffreyVentrella
Nice one!! I pointed this out because this has not been mentioned anywhere in this video

[@RandomRhinos]

its not so much the amount of needles as it is the amount of spaces you have

[@videowala007]

@JeffreyVentrella
Also I hope you are measuring width perpendicular to the lines :)

[@videowala007]

Distance between parallel lines should be twice of the length of the needle

[@MrSaad1932]

its not the area of distribution , its the spreading of the needles

[@argus456]

You do know that those two things are exactly the same right?

[@petroleumalley]

Nice ;-)