{"id":20740,"date":"2013-07-04T22:14:02","date_gmt":"2013-07-04T22:14:02","guid":{"rendered":"http:\/\/thomasjpitts.co.uk\/wp\/?p=20740"},"modified":"2013-07-04T22:14:02","modified_gmt":"2013-07-04T22:14:02","slug":"day-185-geeky-maths-things-185","status":"publish","type":"post","link":"https:\/\/thomasjpitts.co.uk\/wordpress\/2013\/07\/04\/day-185-geeky-maths-things-185\/","title":{"rendered":"Day 185: Geeky Maths Things (185)"},"content":{"rendered":"<p>Nothing much interesting happened today. Sports day went well, all is good.<\/p>\n<p>However, 185 is a key number in many ways, so I thought I&#8217;d focus on that tonight.<\/p>\n<ul>\n<li>185 is an\u00a0<a class=\"zem_slink\" title=\"Parity (mathematics)\" href=\"http:\/\/en.wikipedia.org\/wiki\/Parity_%28mathematics%29\" target=\"_blank\" rel=\"wikipedia\">odd number<\/a><\/li>\n<li>185 is a\u00a0<a class=\"zem_slink\" title=\"Composite number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Composite_number\" target=\"_blank\" rel=\"wikipedia\">composite number<\/a><\/li>\n<li>185 is a\u00a0<a class=\"zem_slink\" title=\"Deficient number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Deficient_number\" target=\"_blank\" rel=\"wikipedia\">deficient number<\/a>, as\u00a043\u00a0is less than 185<\/li>\n<li>185 is an\u00a0<a class=\"zem_slink\" title=\"Thue\u2013Morse sequence\" href=\"http:\/\/en.wikipedia.org\/wiki\/Thue%E2%80%93Morse_sequence\" target=\"_blank\" rel=\"wikipedia\">odious number<\/a><\/li>\n<li>185 is a\u00a0<a class=\"zem_slink\" title=\"Square-free integer\" href=\"http:\/\/en.wikipedia.org\/wiki\/Square-free_integer\" target=\"_blank\" rel=\"wikipedia\">square-free number<\/a><\/li>\n<li>185 is the\u00a0sum\u00a0of two\u00a0square numbers\u00a0in two different ways: 13<sup>2<\/sup>+ 4<sup>2<\/sup>\u00a0and 11<sup>2<\/sup>\u00a0+ 8<sup>2<\/sup><\/li>\n<li>185 is the difference of 2\u00a0square numbers: 21<sup>2<\/sup>\u00a0&#8211; 16<sup>2<\/sup><\/li>\n<\/ul>\n<p>Some of these will need explaining!<\/p>\n<p>A\u00a0composite number\u00a0is a\u00a0positive <a class=\"zem_slink\" title=\"Integer (computer science)\" href=\"http:\/\/en.wikipedia.org\/wiki\/Integer_%28computer_science%29\" target=\"_blank\" rel=\"wikipedia\">integer<\/a>\u00a0that has at least one positive\u00a0<a class=\"zem_slink\" title=\"Divisor\" href=\"http:\/\/en.wikipedia.org\/wiki\/Divisor\" target=\"_blank\" rel=\"wikipedia\">divisor<\/a>\u00a0other than one or itself. In other words a composite number is any positive\u00a0integer\u00a0greater than\u00a0one\u00a0that is\u00a0<b>not<\/b>\u00a0a\u00a0<a class=\"zem_slink\" title=\"Prime number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Prime_number\" target=\"_blank\" rel=\"wikipedia\">prime number<\/a>. Basically, by definition, every integer greater than one is either a\u00a0prime number\u00a0or a composite number. The number one is a\u00a0unit;\u00a0it is neither prime nor composite.<\/p>\n<p>Deficient numbers\u00a0work like this: for\u00a0the number 21, the divisors are 1, 3, 7 and 21, and their sum is 32. However, because 32 is less than 2\u00a0\u00d7\u00a021, the number 21 is deficient. Its deficiency is 2\u00a0\u00d7\u00a021\u00a0\u2212\u00a032\u00a0=\u00a010.<\/p>\n<p>An\u00a0odious\u00a0number is a <a class=\"zem_slink\" title=\"Sign (mathematics)\" href=\"http:\/\/en.wikipedia.org\/wiki\/Sign_%28mathematics%29\" target=\"_blank\" rel=\"wikipedia\">non-negative number<\/a> that has an odd number of 1s in its <a class=\"zem_slink\" title=\"Binary number\" href=\"http:\/\/en.wikipedia.org\/wiki\/Binary_number\" target=\"_blank\" rel=\"wikipedia\">binary representation<\/a>. It could also be part of the Thue-Morse sequence, shown below:<\/p>\n<figure id=\"attachment_20743\" aria-describedby=\"caption-attachment-20743\" style=\"width: 318px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/i0.wp.com\/thomasjpitts.co.uk\/wp\/wp-content\/uploads\/2013\/07\/Morse-Thue_sequence.gif\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"20743\" data-permalink=\"https:\/\/thomasjpitts.co.uk\/wordpress\/morse-thue_sequence\/\" data-orig-file=\"https:\/\/i0.wp.com\/thomasjpitts.co.uk\/wordpress\/wp-content\/uploads\/2013\/07\/Morse-Thue_sequence.gif?fit=318%2C57&amp;ssl=1\" data-orig-size=\"318,57\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"Morse-Thue_sequence\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;This graphic demonstrates the repeating and complementary makeup of the Thue\u2013Morse sequence.&lt;\/p&gt;\n\" data-large-file=\"https:\/\/i0.wp.com\/thomasjpitts.co.uk\/wordpress\/wp-content\/uploads\/2013\/07\/Morse-Thue_sequence.gif?fit=318%2C57&amp;ssl=1\" class=\"size-full wp-image-20743\" alt=\"This graphic demonstrates the repeating and complementary makeup of the Thue\u2013Morse sequence.\" src=\"https:\/\/i0.wp.com\/thomasjpitts.co.uk\/wp\/wp-content\/uploads\/2013\/07\/Morse-Thue_sequence.gif?resize=318%2C57\" width=\"318\" height=\"57\" \/><\/a><figcaption id=\"caption-attachment-20743\" class=\"wp-caption-text\">This graphic demonstrates the repeating and complementary makeup of the Thue\u2013Morse sequence.<\/figcaption><\/figure>\n<p>A\u00a0square-free,\u00a0integer\u00a0is one\u00a0divisible\u00a0by no\u00a0perfect square, except 1. For example, 10 is square-free but 18 is not, as it is divisible by 9 = 3<sup>2<\/sup>.<\/p>\n<p>185 is a good number for stats!<\/p>\n<div class=\"zemanta-pixie\" style=\"margin-top: 10px; height: 15px;\"><a class=\"zemanta-pixie-a\" title=\"Enhanced by Zemanta\" href=\"http:\/\/www.zemanta.com\/?px\"><img data-recalc-dims=\"1\" decoding=\"async\" class=\"zemanta-pixie-img\" style=\"border: none; float: right;\" alt=\"Enhanced by Zemanta\" src=\"https:\/\/i0.wp.com\/img.zemanta.com\/zemified_e.png?w=1165\" \/><\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Nothing much interesting happened today. Sports day went well, all is good. However, 185 is a key number in many ways, so I thought I&#8217;d focus on that tonight. 185 is an\u00a0odd number 185 is a\u00a0composite number 185 is a\u00a0deficient number, as\u00a043\u00a0is less than 185 185 is an\u00a0odious number 185 is a\u00a0square-free number 185 is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"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","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[2,3,18],"tags":[753,950,1524,1909,2199,2296,2440,2721],"class_list":["post-20740","post","type-post","status-publish","format-standard","hentry","category-2","category-awesomeness","category-maths","tag-composite-number","tag-divisor","tag-integers","tag-math","tag-number-theory","tag-parity-mathematics","tag-prime-number","tag-sieve-of-eratosthenes","has-post-title","has-post-date","has-post-category","has-post-tag","has-post-comment","has-post-author",""],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p6OeSW-5ow","jetpack-related-posts":[],"builder_content":"","_links":{"self":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/20740","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/comments?post=20740"}],"version-history":[{"count":0,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/posts\/20740\/revisions"}],"wp:attachment":[{"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/media?parent=20740"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/categories?post=20740"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thomasjpitts.co.uk\/wordpress\/wp-json\/wp\/v2\/tags?post=20740"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}