Hmmm, pi is a little bumpier than I thought. (It could just be that my statistical intuition is off, though.)<\/p>\n
Each bar plot below represents the number of occurrences of a digit in the decimal expansion of pi. The y-axis is an index, and the frequency x is counted over the range of digits y*20 to y*20+400. I thought 400 would be a long enough length to make these graphs pretty flat. Higher lengths make it flatter, of course, but still not to the degree that seems ‘right’ to me.<\/p>\n
I guess I could calibrate my perception by using a uniformly distributed sequence of digits…<\/p>\n
Pi digit frequencies<\/a><\/p>\n Update<\/strong>: huh. I guess it is just me. Here’s the same sort of graph but with uniformly random digits (at least, assuming that RAND’s book<\/a>, which I lazily selected as my source, is indeed uniform). Looks equally bumpy to me. Ah well, I’ll leave the post up as a reminder of my folly…<\/p>\n
![Pi digit frequencies<\/a><\/p>\nUpdate<\/strong>: huh. I guess it is just me. Here’s the same sort of graph but with uniformly random digits (at least, assuming that RAND’s book<\/a>, which I lazily selected as my source, is indeed uniform). Looks equally bumpy to me. Ah well, I’ll leave the post up as a reminder of my folly…<\/p>\nRandom digit frequencies<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"Hmmm, pi is a little bumpier than I thought. (It could just be that my statistical intuition is off, though.) Each bar plot below represents the number of occurrences of a digit in the decimal expansion of pi. The y-axis is an index, and the frequency x is counted over the range of digits y*20 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-397","post","type-post","status-publish","format-standard","hentry","category-general","author-admin"],"_links":{"self":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts\/397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/comments?post=397"}],"version-history":[{"count":0,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts\/397\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/media?parent=397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/categories?post=397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/tags?post=397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/www.ourada.org\/blog\/wp-content\/uploads\/2009\/12\/pigraph.png\"){kind=link}
![Random digit frequencies<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"Hmmm, pi is a little bumpier than I thought. (It could just be that my statistical intuition is off, though.) Each bar plot below represents the number of occurrences of a digit in the decimal expansion of pi. The y-axis is an index, and the frequency x is counted over the range of digits y*20 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-397","post","type-post","status-publish","format-standard","hentry","category-general","author-admin"],"_links":{"self":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts\/397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/comments?post=397"}],"version-history":[{"count":0,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/posts\/397\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/media?parent=397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/categories?post=397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.ourada.org\/blog\/wp-json\/wp\/v2\/tags?post=397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}](\"http:\/\/www.ourada.org\/blog\/wp-content\/uploads\/2009\/12\/randgraph.png\"){kind=link}