{"id":451,"date":"2011-09-19T14:54:10","date_gmt":"2011-09-19T14:54:10","guid":{"rendered":"http:\/\/blogs.truman.edu\/mathcs\/?p=451"},"modified":"2011-09-19T14:54:10","modified_gmt":"2011-09-19T14:54:10","slug":"math-department-colloquium","status":"publish","type":"post","link":"https:\/\/blogs.truman.edu\/mathcs\/2011\/09\/19\/math-department-colloquium\/","title":{"rendered":"Math Department Colloquium"},"content":{"rendered":"<p>The next Math Colloquium will be held Tuesday, September 20 at 3:30 in VH1224.  David Garth will be speaking on Fractions, Pi, and Quasicrystals.  Refreshments will be provided.<\/p>\n<p>ABSTRACT<\/p>\n<p>A rational number is one that can be expressed as a ratio of two integers.  A real number that is not rational is said to be irrational.  In the field of rational approximation one is interested in approximating an irrational number, like Pi, by a rational number whose denominator is as small as possible.  For example, 22\/7 is a good approximation to Pi, having a single digit denominator that approximates Pi to two decimal digits.  In this talk we will show how to find other such fractions of small denominator that serve to approximate well a given irrational number.  In fact, our method will provide a means for finding all such fractions.  This method has a nice geometric interpretation and will provide an introduction to the theory of continued fractions.  It will also illustrate a surprising application to the study of quasicrystals in solid state physics.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The next Math Colloquium will be held Tuesday, September 20 at 3:30 in VH1224. David Garth will be speaking on Fractions, Pi, and Quasicrystals. Refreshments will be provided. ABSTRACT A rational number is one that can be expressed as a ratio of two integers. A real number that is not rational is said to be [&hellip;]<\/p>\n","protected":false},"author":188,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-451","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":[],"_links":{"self":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts\/451","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/users\/188"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/comments?post=451"}],"version-history":[{"count":1,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts\/451\/revisions"}],"predecessor-version":[{"id":454,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/posts\/451\/revisions\/454"}],"wp:attachment":[{"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/media?parent=451"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/categories?post=451"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.truman.edu\/mathcs\/wp-json\/wp\/v2\/tags?post=451"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}