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Mar. 12, 2014

Estimate Pi by Dropping Sticks

by Chau Tu

Click to enlarge images
Pi Day is just around the corner (March 14, or 3.14), and we here at SciFri came across a fun simulator that estimates the number in a blog post by Tommy Ogden, a Ph.D student in theoretical physics at Durham University in England.
 
The simulator is based on an experiment called Buffon’s needle, one of the oldest problems in the field of geometrical probability, according to The Mathematica Journal. In the 18th century, French philosopher Georges-Louis Leclerc, Comte de Buffon determined that you can approximate pi by dropping needles on a grid of parallel lines (whose spacing is greater than the length of a needle) and calculating the probability that they will cross a line. The probability is directly related to pi. 
 
Ultimately, you can calculate pi using this formula: 
{"input":{"width":490,"photo":"pi","row":"4874","table":"DOCUMENT"}}
 
Ready to find pi? Use Ogden's simulator below, where you can "drop" thousands of sticks and test the formula yourself. How close can you get to pi, with how many sticks? Send us your results by commenting below or tweeting us @scifri with the hashtag #MyPi.
 
If you want to get truly interactive, print out this worksheet and drop 2.5-inch toothpicks on it. Let us know how close you get!  Please note that an updated version of this worksheet was added at about 6:30 p.m. on March 13, 2014 to reflect a change in the formula.

Bonus: You can even try the experiment using hot dogs!

 

RELATED SCIENCE FRIDAY LINKs
About Chau Tu

Chau is SciFri's web producer. She spends a lot of her time drinking coffee, seeking out street art, listening to music, and defending Los Angeles. Follow her @chaubtu

The views expressed are those of the author and are not necessarily those of Science Friday.
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                                                 ^
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Code:
line 1: package tmpevalpackage;
line 2: sub doEval { 
line 3: 	my($parent);
line 4: 	
line 5: 	if($LayoutManager::url_resolved_values{'SEGMENT.nickname'}) {
line 6: 		$parent = $LayoutManager::url_resolved_values{'SEGMENT.nickname'};
line 7: 	}
line 8: 	elsif($LayoutManager::url_resolved_values{'VIDEO.nickname'}) {
line 9: 		$parent = $LayoutManager::url_resolved_values{'VIDEO.nickname'};
line 10: 	}
line 11: 	elsif($LayoutManager::url_resolved_values{'DOCUMENT.nickname'}) {
line 12: 		$parent = $LayoutManager::url_resolved_values{'DOCUMENT.nickname'}
line 13: 	}
line 14: 	
line 15: 	if($parent) {
line 16: 		my(@books) = &Database::SelectClause('BOOK',"parent = $parent");
line 17: 		if(!@books) {
line 18: 			$parent = '';
line 19: 		}
line 20: 	}
line 21: 	
line 22: 	if(!$parent) {
line 23: 		my(@sel) = &Database::SelectClause('GLOBAL','record all ""');
line 24: 		if(@sel) {
line 25: 			$parent = 'GLOBAL.' . $sel[0];
line 26: 		}
line 27: 			$main::ENV{'reading_header'} = "FEATURED READING";
line 28: 	}
line 29: 	
line 30: 	 = '';
line 31: 	
line 32: 	if($parent) {
line 33: 		my(@books) = &Database::SelectClause('BOOK',"parent = $parent");
line 34: 		0 = 0;
line 35: 		my $dots;
line 36: 		foreach(@books) {
line 37: 			my(%data);
line 38: 			&Database::GetRow($_,'BOOK',\%data);
line 39: 			my($status,$title,$author,$url,$image,$width,$height) = &SciFri::Schema::getAmazonItem($data{'isbn'});
line 40: 			if($data{'title'}) {
line 41: 				$title = $data{'title'};
line 42: 			}
line 43: 			if($data{'author'}) {
line 44: 				$author = $data{'author'};
line 45: 			}
line 46: 			if($status eq 'ok') {
line 47: 				 .= "<div class=\"box-2x1-item box-slide\" data-href=\"$url\">";
line 48: 				 .= "	<div class=\"box-2x1-item-photo\">";
line 49: 				 .= "		<div class=\"image-wrapper\" data-jsclass=\"imageWrapper\" data-align=\"right\">";
line 50: 				 .= "			<img src=\"$image\" data-width=\"$width\" data-height=\"$height\">";
line 51: 				 .= "		</div>";
line 52: 				 .= "	</div>";
line 53: 				 .= "	<h4>$title</h4>";
line 54: 				if($author) {
line 55: 					 .= "	<p>by $author</p>";
line 56: 				}
line 57: 				 .= "	<div class=\"box-2x1-more-button\"><a href=\"$url\"><img src=\"/images/v1/icon_text_more_white.png\" width=47 height=15 border=0></a></div>";
line 58: 				 .= "</div>";
line 59: 				++0;
line 60: 			}
line 61: 		}
line 62: 	}
line 63: 	if($parent eq "GLOBAL.1") { $main::ENV{'reading_header'} = "FEATURED READING"; }
line 64: 	else { $main::ENV{'reading_header'} = "RELATED READING"; }
line 65:  };
line 66: &doEval();
line 67: 1;

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