{"id":815,"date":"2014-04-28T21:16:00","date_gmt":"2014-04-28T13:16:00","guid":{"rendered":"http:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/2014\/04\/squares-and-infinities\/"},"modified":"2024-02-16T21:11:55","modified_gmt":"2024-02-16T13:11:55","slug":"squares-and-infinities","status":"publish","type":"post","link":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/2014\/04\/squares-and-infinities\/","title":{"rendered":"Squares And Infinities"},"content":{"rendered":"

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So, President was being briefed by his Chiefs Of
\nStaff on the latest conflict. He listened, asked questions, hummed and
\nahed. Then he asked “were there any casualties?”<\/p>\n

The Defense Chief nodded. “Three Brazilian soldiers were killed”<\/p>\n

“Oh my God.” said the President. He clutched the edge of his desk. A
\ntear appeared at the edge of his eye. “My God.”<\/p>\n

The Chiefs glanced at one another, unsure how to respond to the
\nPresident’s obvious grief. Finally he looked up.<\/p>\n

“How many millions in a brazillion?”<\/p>\n

Oh-kay… not sure where that one came from. Ahem.<\/p>\n

So, I got my computer to make a video, showing how to construct a
\nsquare with a ruler and a compass. You can see it here
\n<\/http:>
\n.<\/p>\n

Back to big numbers. A number of years ago, I ran a Big Numbers
\nContest through my website. Kids had to come up with the biggest
\nnumber they could
\n
\n write in a two inch by four inch box. You’d think that out of the
\ninfinity of numbers, there’d be a clear winner. Astoundingly, the
\ncompetition ended in a draw
\n<\/http:>
\n. <\/p>\n

The rules said kids couldn’t write “Infinity”. The obvious reason is
\nthat that would make the contest too easy. The real reason is that
\n“Infinity” isn’t a well-defined number. There are actually different
\nsizes of infinity. <\/p>\n

Some of the paradoxes of infinity were made clear to me by a short
\nstory by Stanislaw Lem, in this book
\n<\/http:>
\n. I read it a long time ago. You may find similar presentations by
\ngoogling Hilbert’s Hotel Paradox. <\/p>\n

Yours,<\/p>\n

Michael Hartley<\/p>\n

—
\nTo see the newletter archives, This
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\nhttp:\/\/www.dr-mikes-math-games-for-kids.com\/newsletter\/?p=forward&uid=5bb87ab629dd196aab24974186e7290a&mid=116<\/p>\n

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\n
\n <\/title><\/p>\n<style type=\"text\/css\">\nbody { font-size : 11px; font-family: Verdana, Arial, Helvetica, sans-serif; }\na { font-size: 11px; color: #ff6600; font-style: normal; font-family: verdana, sans-serif; text-decoration: none; }\na:visited { color: #666666; }\na:hover { text-decoration: underline; }\np { font-weight: normal; font-size: 12px; color: #000000; font-style: normal; font-family: verdana, sans-serif; text-decoration: none; }\nh1 {font-weight: bold; font-size: 20px; color: #000000; font-style: normal; font-family: verdana, sans-serif; text-decoration: none;}\nh2 {font-weight: bold; font-size: 18px; color: #000000; font-style: normal; font-family: verdana, sans-serif; text-decoration: none;}\nh3 {font-weight: bold; font-size: 16px; color: #000000; font-style: normal; font-family: verdana, sans-serif; text-decoration: none; margin:0px; padding:0px;}\nh4 {font-weight: bold; font-size: 14px; color: #000000; font-style: normal; font-family: verdana, sans-serif; text-decoration: none; margin:0px; padding:0px;}\nhr {width : 100%; height : 1px; color: #000000; size:1px;}\n.forwardform {margin: 0 0 0 0; padding: 0 0 0 0;}\n.forwardinput {margin: 0 0 0 0; padding: 0 0 0 0;}\n.forwardsubmit {margin: 0 0 0 0; padding: 0 0 0 0;}\ndiv.emailfooter { font-size : 11px; font-family: Verdana, Arial, Helvetica, sans-serif; }\ndiv.emailfooter a { font-size: 11px; color: #ff6600; font-style: normal; font-family: verdana, sans-serif; text-decoration: none; }\n<\/style>\n<p><\/head><body><\/p>\n<p>So, President was being briefed by his Chiefs Of Staff on the latest conflict. He listened, asked questions, hummed and ahed. Then he asked "were there any casualties?"<\/p>\n<p>The Defense Chief nodded. "Three Brazilian soldiers were killed"<\/p>\n<p>"Oh my God." said the President. He clutched the edge of his desk. A tear appeared at the edge of his eye. "My God."<\/p>\n<p>The Chiefs glanced at one another, unsure how to respond to the President’s obvious grief. Finally he looked up.<\/p>\n<p>"How many millions in a brazillion?"<\/p>\n<p>Oh-kay… not sure where that one came from. Ahem.<\/p>\n<p>So, I got my computer to make a video, showing how to construct a square with a ruler and a compass. You can <a href=\"http:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/2014\/04\/constructing-a-square-inside-a-circle\/\">see it here<\/a>.<\/p>\n<p>Back to big numbers. A number of years ago, I ran a Big Numbers Contest through my website. Kids had to come up with the <a href=\"http:\/\/www.dr-mikes-math-games-for-kids.com\/big-numbers-competition.html\">biggest number they could<\/a> write in a two inch by four inch box. You’d think that out of the infinity of numbers, there’d be a clear winner. Astoundingly, the <a href=\"http:\/\/www.dr-mikes-math-games-for-kids.com\/big-numbers-competition-results.html\">competition ended in a draw<\/a>. <\/p>\n<p>The rules said kids couldn’t write "Infinity". The obvious reason is that that would make the contest too easy. The real reason is that "Infinity" isn’t a well-defined number. There are actually different sizes of infinity. <\/p>\n<p>Some of the paradoxes of infinity were made clear to me by a short story by Stanislaw Lem, in <a href=\"http:\/\/www.amazon.com\/gp\/product\/012721951X\/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=012721951X&linkCode=as2&tag=dmmgfk-20\">this book<\/a>. I read it a long time ago. You may find similar presentations by googling Hilbert’s Hotel Paradox. <\/p>\n<p>Yours,<br \/>\nMichael Hartley<\/p>\n<p> <\/p>\n<p> <\/p>\n<div class=\"emailfooter\">—<br \/>\nTo see the newletter archives, <a href=\"http:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/category\/newsletter-archives\/?utm_source=dmmgfk&utm_medium=email&utm_content=dmmgfk-archives&utm_campaign=dmmgfk\">This Link<\/a><br \/>\nIf you do not want to receive any more newsletters, <a href=\"http:\/\/www.dr-mikes-math-games-for-kids.com\/newsletter\/?p=unsubscribe&uid=5bb87ab629dd196aab24974186e7290a\">this link<\/a><br \/>\nTo update your preferences and to unsubscribe visit <a href=\"http:\/\/www.dr-mikes-math-games-for-kids.com\/newsletter\/?p=preferences&uid=5bb87ab629dd196aab24974186e7290a\">this link<\/a><br \/>\nForward a Message to Someone <a href=\"http:\/\/www.dr-mikes-math-games-for-kids.com\/newsletter\/?p=forward&uid=5bb87ab629dd196aab24974186e7290a&mid=116\">this link<\/a><\/div>\n<p align=left><a href=\"http:\/\/www.phplist.com\"><img decoding=\"async\" src=\"cid:32a8041081a4b06a7f94acfd9d6fc7a3\" width=70 height=30 title=\"Powered by PHPlist version 2.10.13, © tincan ltd\" alt=\"Powered by PHPlist2.10.13, &copy tincan ltd\" border=\"0\"\/><\/a><\/p>\n<p><\/body><\/html><\/p>\n<p>–b2_1f605e91eb2d2a7e3555a71c738163ac–<br \/>\n–b1_1f605e91eb2d2a7e3555a71c738163ac<br \/>\nContent-Type: image\/png; 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boundary=”b2_1f605e91eb2d2a7e3555a71c738163ac” –b2_1f605e91eb2d2a7e3555a71c738163ac Content-Type: text\/plain; charset = “UTF-8” Content-Transfer-Encoding: 8bit So, President was being briefed by his Chiefs Of Staff on the latest conflict. He listened, asked questions, hummed and ahed. Then he asked “were there any casualties?” The Defense Chief nodded. “Three Brazilian soldiers were killed” “Oh my God.” said the President. … <a href=\"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/2014\/04\/squares-and-infinities\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Squares And Infinities<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[153],"tags":[],"_links":{"self":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/815"}],"collection":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/comments?post=815"}],"version-history":[{"count":1,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/815\/revisions"}],"predecessor-version":[{"id":1292,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/posts\/815\/revisions\/1292"}],"wp:attachment":[{"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/media?parent=815"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/categories?post=815"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.dr-mikes-math-games-for-kids.com\/blog\/wp-json\/wp\/v2\/tags?post=815"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}