{"id":254,"date":"2019-06-26T23:12:10","date_gmt":"2019-06-26T23:12:10","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=254"},"modified":"2019-11-18T22:18:05","modified_gmt":"2019-11-18T22:18:05","slug":"buffon-needle-problem","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/buffon-needle-problem\/","title":{"rendered":"Buffon Needle Problem"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"alignright\"><img loading=\"lazy\" decoding=\"async\" width=\"311\" height=\"183\" data-attachment-id=\"1372\" data-permalink=\"https:\/\/math.hmc.edu\/funfacts\/buffon-needle-problem\/10003-6-1\/\" data-orig-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/11\/10003.6.1.gif\" data-orig-size=\"311,183\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"10003.6.1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/11\/10003.6.1-300x177.gif\" data-large-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/11\/10003.6.1.gif\" src=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/11\/10003.6.1.gif\" alt=\"\" class=\"wp-image-1372\"\/><\/figure><\/div>\n\n\n\n<p>A plane is ruled with parallel lines 1 cm apart. A needle of length 1 cm is dropped randomly on the plane. What is the probability that the needle will be lying across one of the lines?<\/p>\n\n\n\n<p>Answer: 2\/Pi.<\/p>\n\n\n\n<p>This gives an interesting way to calculate Pi! If you throw down a large number of needles, the fraction of needles which lie across a line will get closer to 2\/Pi the more needles that you throw. So, you can just throw down needles and count them to get an estimate for Pi!<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Draw a picture and a few &#8220;random&#8221; needles. As a challenge, ask students to prove this formula using&nbsp;calculus, and assuming that needle centers and needle angles are uniformly distributed.<\/p>\n\n\n\n<p><strong>The&nbsp;Math&nbsp;Behind&nbsp;the&nbsp;Fact:<\/strong><br>This method of calculating Pi is very slow. There are faster formulas, see&nbsp;pi formula. However, the idea of using a probabilistic means to get answers like this is very powerful, and is the basis of something called the Monte Carlo method in&nbsp;probability&nbsp;theory.<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong>\u00a0<br>Su, Francis E., et al. &#8220;Buffon Needle Problem.&#8221;\u00a0<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts>.<\/p>\n\n\n\n<p><strong>Fun Fact suggested by:<\/strong><br>Francis Su<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A plane is ruled with parallel lines 1 cm apart. A needle of length 1 cm is dropped randomly on&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[3,30,45],"class_list":["post-254","page","type-page","status-publish","hentry","tag-easy","tag-pi-formula","tag-probability"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/254","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=254"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/254\/revisions"}],"predecessor-version":[{"id":1373,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/254\/revisions\/1373"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=254"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}