{"id":4262,"date":"2018-10-18T11:25:06","date_gmt":"2018-10-18T11:25:06","guid":{"rendered":"https:\/\/www.novonon.com\/blog\/2018\/10\/18\/powers-of-the-golden-ratio-are-close-to-integers\/"},"modified":"2018-10-18T11:25:06","modified_gmt":"2018-10-18T11:25:06","slug":"powers-of-the-golden-ratio-are-close-to-integers","status":"publish","type":"post","link":"https:\/\/www.novonon.com\/blog\/2018\/10\/18\/powers-of-the-golden-ratio-are-close-to-integers\/","title":{"rendered":"Powers of the golden ratio are close to integers"},"content":{"rendered":"

<\/p>\n

This really is just the weirdest damn thing. It’s not the least bit clear to me why this would be true.<\/p>\n

\n

This morning I was reading Terry Tao\u2019s <\/span>overview<\/a> <\/span>of the work of Yves Meyer and ran across this line:<\/p>\n

\n

The powers \u03c6, \u03c62<\/sup>, \u03c63<\/sup>, \u2026 of the golden ratio lie unexpectedly close to integers: for instance, \u03c611<\/sup> <\/span>= 199.005\u2026 is unusually close to 199.<\/p>\n<\/blockquote>\n

I\u2019d never heard that before, so I wrote a little code to see just how close golden powers are to integers.<\/p>\n

Here\u2019s a plot of the difference between \u03c6n<\/i><\/sup> <\/span>and the nearest integer:<\/p>\n

<\/p><\/blockquote>\n

https:\/\/www.johndcook.com\/blog\/2017\/03\/22\/golden-powers-are-nearly-integers\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

This really is just the weirdest damn thing. It’s not the least bit clear to me why this would be true. This morning I was reading Terry Tao\u2019s overview of the work of Yves Meyer and ran across this line: The powers \u03c6, \u03c62, \u03c63, \u2026 of the golden ratio lie unexpectedly close to integers: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-4262","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3pfIY-16K","jetpack_sharing_enabled":true,"jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/posts\/4262","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/comments?post=4262"}],"version-history":[{"count":0,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/posts\/4262\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/media?parent=4262"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/categories?post=4262"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.novonon.com\/blog\/wp-json\/wp\/v2\/tags?post=4262"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}