{"id":2116,"date":"2009-03-14T08:24:25","date_gmt":"2009-03-14T00:24:25","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=2116"},"modified":"2009-03-14T16:32:33","modified_gmt":"2009-03-14T08:32:33","slug":"pi-day-today-314-buffons-needle","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/mathematics\/pi-day-today-314-buffons-needle-2116","title":{"rendered":"Pi Day today (3\/14) - Buffon’s Needle"},"content":{"rendered":"

Today we celebrate Pi Day. The first 3 digits of pi are 3.14 and today's date, when written in the US style, is 3\/14.<\/p>\n

Some people get really carried away and have a special even at 1:59 PM, since the next 3 digits of pi are 159. However, if they were really keen, they would do it at 1:59 AM — it seems more respectful that way... \ud83d\ude42<\/p>\n

Did you realize that you can get an estimate of pi that involves probability and dropping needles on a table?<\/p>\n

Buffon's Needle<\/h2>\n

Say you have a needle that is 5 cm long. You draw a set of parallel lines 5 cm apart on a piece of paper, and begin dropping the needle onto the paper.<\/p>\n

\"Buffon's<\/p>\n

When the needle lands, it either touches one of the parallel lines, or it doesn't.<\/p>\n

It turns out that the probability of the needle landing on one of the lines is 2\/pi. From there, we can get a value of pi, as follows:<\/p>\n

pi = (2 × the number of drops) \/ (number of line touches)<\/p>\n

The problem was first posed by Georges-Louis Leclerc, Comte de Buffon in 1777.<\/p>\n

You can see some analysis of this problem and Java applets to see how it works here: Buffon's Needle An Analysis and Simulation<\/a> (which has a good explanation, but a weak applet) and here: Buffon's Needle<\/a> (which has a good applet, but brief explanation).<\/p>\n

See the 1 Comment<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"

\"Buffon<\/a>Today is Pi Day and to mark the day, we take a look at Buffon's Needle, which is a technique for finding the value of pi that involves needles and probability.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2116"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=2116"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/2116\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=2116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=2116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=2116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}