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Monte Carlo Approximation of Pi
Monte Carlo Approximation of Pi
tcmartin


Photograph Information Photographer's Comments
Challenge: Pi II (Basic Editing)
Camera: Canon EOS-350D Rebel XT
Lens: Tamron SP AF 28-75mm f/2.8 XR Di for Canon
Location: Basement studio
Date: Apr 30, 2007
Aperture: f/9
ISO: 100
Shutter: 1/30 sec.
Galleries: Abstract, Science and Technology
Date Uploaded: May 1, 2007

Shot RAW but preferred JPG
Crop, Smart sharpen, Levels, Hue/Saturation by color channel – to reduce the color in the square and help the inscribed circle stand out, PS CS2 noise reduction, border, neat image
(extra noise was introduced during separate color hue/saturation changes)

Two lights: one on the tile and ring and fallen dots and a flash low and in front pointed up at the falling dots.

Folks might not get this, but I really wanted something different that a Pi symbol and/or lots of repeating digits.

Briefly, the math behind this is:
Given a circle inscribed in a square. If we drop lots of these circles, or dots, or throw a dart as in other experiments, and this is done at random, then every point within the square (which includes the circle) has an equal chance of being landed on by one of the little circles - excluding other forces such as dot interaction, friction, etc.

If the radius of the circle is R, then the area of the circle = Pi R^2 and the area of he square = 4 R^2. If you divide the area of the circle by the area of the square you get Pi/4.

Pi can be estimated as:
Pi = 4 x (dots in the circle) / (dots in the square - including those in the circle)

Statistics
Place: 22 out of 92
Avg (all users): 5.9444
Avg (commenters): 7.1250
Avg (participants): 5.7111
Avg (non-participants): 5.9952
Views since voting: 1045
Views during voting: 509
Votes: 252
Comments: 8
Favorites: 1 (view)


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AuthorThread
 Comments Made During the Challenge
05/07/2007 04:07:55 PM
I just love the idea of this, but I'm afraid many people won't immediately get the cleverness of it. I hope for your sake they do a little research into the title and grade it appropriately! Personally I was laughing the moment I saw it.
  Photographer found comment helpful.
05/06/2007 04:36:21 AM
?
05/04/2007 10:56:05 AM
Well, so far, Montecarlo says Pi = 4, cause there ain't no spots on the tile. Apart from that, this is a good image. Nice lighting. The biggest technical problem is colour bleeding, possibly from using chroma noise reduction? An off-board flash should get this effect without having to push the ISO too high, and a lower ISO won't need so much NR. Focus is a little soft, probably from NR again. Highlight on front of tile is also distracting. Despite all this, it's a nice image, and I'm scoring it well. :)
  Photographer found comment helpful.
05/03/2007 10:07:06 PM
haha brilliant! perfectly captures pi without being explicit.. most other entries just photograph a projection of 3.141... a 10 :)
  Photographer found comment helpful.
05/03/2007 04:58:12 PM
This is a thought-provoking, well executed image. Nice job.
  Photographer found comment helpful.
05/02/2007 12:20:16 PM
had to google that - but very nice concept :)
  Photographer found comment helpful.
05/02/2007 09:48:15 AM
This is kinda cool - captures motion. But I don't get the title reference or how it relates to pi
  Photographer found comment helpful.
05/02/2007 04:30:47 AM
Lovely DOF & Bokeh. I get it, but how many others will !?
  Photographer found comment helpful.


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