As of 2024, humans have calculated 105 trillion digits of \u03c0. But how many do we really need?<\/p>\n\n\n\n
\u2022 Everyday use: 3.14 is enough.
\u2022 Engineering: 3.1416 is usually plenty.
\u2022 ISRO\/NASA: about 15 digits
What if we measure the biggest thing with the tiniest ruler?<\/p>\n\n\n\n
The largest thing that humans can measure is the circumference of observable-universe, whose radius is<\/p>\n\n\n\n
R \u2248 46.5 \\text{billion light-years} \u2248 4.399\\times10^{26} \\text{m}<\/pre><\/div>\n\n\n\ngiving the circumference<\/p>\n\n\n\n
C=2\\pi R\\approx2.764\\times10^{27} \\text{m}<\/pre><\/div>\n\n\n\nThe Planck length<\/strong> is considered the smallest physically meaningful unit of length, beyond it, space and time may not even make sense.<\/p>\n\n\n\n\\ell_P\\approx1.616255\\times10^{-35} \\text{m}<\/pre><\/div>\n\n\n\nSo, relative precision<\/p>\n\n\n\n
\\ell_P\/C\\approx5.85\\times10^{-63}<\/pre><\/div>\n\n\n\nThat is 63 decimal digits. <\/p>\n\n\n\n
Beyond that, the extra digits are pure poetry \u2014 infinite whispers of mathematics<\/em>.<\/p>\n\n\n\n
\n\n\n\nLinks:
\u2022 Observable Universe: https:\/\/en.wikipedia.org\/wiki\/Observable_universe<\/a>
\u2022 Plank: https:\/\/en.wikipedia.org\/wiki\/Planck_units<\/a>
\u2022 Random pi: https:\/\/gsama.cc\/guess-pi\/<\/a><\/p>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"
As of 2024, humans have calculated 105 trillion digits of \u03c0. But how many do we really need? \u2022 Everyday use: 3.14 is enough.\u2022 Engineering: 3.1416 is usually plenty.\u2022 ISRO\/NASA: about 15 digits What if we measure the biggest thing with the tiniest ruler? The largest thing that humans can measure is the circumference of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[11,15,12],"class_list":["post-63","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-math-2","tag-pi","tag-science-2"],"_links":{"self":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts\/63","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=63"}],"version-history":[{"count":7,"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts\/63\/revisions"}],"predecessor-version":[{"id":99,"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts\/63\/revisions\/99"}],"wp:attachment":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=63"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=63"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=63"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}