{"id":5924,"date":"2015-12-23T14:09:03","date_gmt":"2015-12-23T13:09:03","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=5924"},"modified":"2015-12-23T14:12:58","modified_gmt":"2015-12-23T13:12:58","slug":"the-happy-holidays-number","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=5924","title":{"rendered":"The ‘Happy Holidays’ number"},"content":{"rendered":"

Some numbers have something to say. Take the following, rather huge number, for example:<\/p>\n

185325291040682644803531312384041336595151018761127807725763308064246070395230764956468856341399670487
514610052487586323067575687914642829757636555138456145938430191876551756992329818006401775522301219016
237245425891544032218544390861818271526845858747648909382915665997160517028671058273052955697138350617
856171748990490346558484883522495310587304606877332488244886849690319641412147118669050542398759303832
627672479768452329971883073420877438596419179762421854464516060347269129680634374662501202129049727949
71185874579656679344857677824<\/p>\n

This number wants to tell you ‘Happy Holidays’, it just needs a little code to help it out. \u00a0In Maple<\/a>, this code is:<\/p>\n

n := 18532529104068264480353131238404133659515101876112780772576330806424607039523076495646885634139967048751461005248758632306757568791464282975763655513845614593843019187655175699232981800640177552230121901623724542589154403221854439086181827152684585874764890938291566599716051702867105827305295569713835061785617174899049034655848488352249531058730460687733248824488684969031964141214711866905054239875930383262767247976845232997188307342087743859641917976242185446451606034726912968063437466250120212904972794971185874579656679344857677824:\r\nmodnew := proc (x, y) options operator, arrow; x-y*floor(x\/y) end proc:\r\ntupper := piecewise(1\/2 < floor(modnew(floor((1\/17)*y)*2^(-17*floor(x)-modnew(floor(y), 17)), 2)), 0, 1):\r\npoints := [seq([seq(tupper(x, y), y = n+16 .. n, -1)], x = 105 .. 0, -1)]:\r\nplots:-listdensityplot(points, scaling = constrained, view = [0 .. 106, 0 .. 17], style = patchnogrid, size = [800, 800]);\r\n<\/pre>\n
The result is the following plot<\/p>\n
\"Screen<\/a><\/p>\n
Thanks to Samir<\/a> for this one!<\/p>\n
The mathematics is based on a generalisation of Tupper’s self-referential formula<\/a>.<\/p>\n
There’s more than one way to send a message with an equation, however. Here’s an image of one I discovered a few years ago — The equation that says Hi<\/a><\/p>\n
\"\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
Some numbers have something to say. Take the following, rather huge number, for example: 18532529104068264480353131238404133659515101876112780772576330806424607039523076495646885634139967048751461005248758632306757568791464282975763655513845614593843019187655175699232981800640177552230121901623724542589154403221854439086181827152684585874764890938291566599716051702867105827305295569713835061785617174899049034655848488352249531058730460687733248824488684969031964141214711866905054239875930383262767247976845232997188307342087743859641917976242185446451606034726912968063437466250120212904972794971185874579656679344857677824 This number wants to tell you ‘Happy Holidays’, it just needs a little code to help it out. \u00a0In Maple, this code is: n := 18532529104068264480353131238404133659515101876112780772576330806424607039523076495646885634139967048751461005248758632306757568791464282975763655513845614593843019187655175699232981800640177552230121901623724542589154403221854439086181827152684585874764890938291566599716051702867105827305295569713835061785617174899049034655848488352249531058730460687733248824488684969031964141214711866905054239875930383262767247976845232997188307342087743859641917976242185446451606034726912968063437466250120212904972794971185874579656679344857677824: modnew := proc (x, y) options operator, arrow; x-y*floor(x\/y) end proc: tupper := piecewise(1\/2 […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[6,45,25,4],"tags":[],"class_list":["post-5924","post","type-post","status-publish","format-standard","hentry","category-general-math","category-just-for-fun","category-maple","category-math-software"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-1xy","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/5924","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5924"}],"version-history":[{"count":4,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/5924\/revisions"}],"predecessor-version":[{"id":5927,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/5924\/revisions\/5927"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}