{"id":6943,"date":"2012-01-16T16:41:51","date_gmt":"2012-01-16T08:41:51","guid":{"rendered":"http:\/\/www.intmath.com\/blog\/?p=6943"},"modified":"2014-12-05T09:04:43","modified_gmt":"2014-12-05T01:04:43","slug":"biorhythm-graphs","status":"publish","type":"post","link":"https:\/\/www.intmath.com\/blog\/learn-math\/biorhythm-graphs-6943","title":{"rendered":"Biorhythm Graphs - background"},"content":{"rendered":"<p>I re-developed my <a href=\"https:\/\/www.intmath.com\/trigonometric-graphs\/biorhythm-graphs.php\">Biorhythm Graphs<\/a> page (for various technical reasons). You can input anyone's birthday and you can see what their state will be (or was) on any day (well, that's the theory). <\/p>\n<p>Biorhythms are interesting, but not at all scientific. They are a quirky example of <a href=\"https:\/\/www.intmath.com\/trigonometric-graphs\/6-composite-trigonometric-graphs.php\">Composite Trigonometric Graphs<\/a>, since they involve 3 sine curves starting at (0,0) on your birthday, and having 3 different periods. <\/p>\n<div class=\"imgCenter\">\n<p><img loading=\"lazy\" src=\"\/blog\/wp-content\/images\/2012\/01\/biorhythm-graphs-bday.png\" width=\"362\" height=\"299\" alt=\"Biorhythm graph - birthday\" \/><br \/>\nBiorhythm cycles - starting from birth<\/p>\n<\/div>\n<p>They work on the principle that our bodies, minds and emotions go through various cycles throughout the month, leading us to have pre-determined &quot;good days&quot; and &quot;not-so-good&quot; days. I have assumed the &quot;best&quot; days (colored green on my graph) will be the days when all 3 cycles add to give us the largest amplitude, and the &quot;worst&quot; days (colored red) will be when all 3 cycles push us into the depths of despair. <\/p>\n<p>According to the <a href=\"http:\/\/skepdic.com\/biorhyth.html\">Skeptik's Dictionary<\/a>, biorhythms were  first &quot;observed&quot; by the Berlin physician Wilhelm Fliess (a good friend of psychologist Sigmund Freud's) in the 19th century. <\/p>\n<p>Fliess originally proposed a 23-day &quot;male&quot; cycle and a 28-day &quot;female&quot; cycle. An Austrian engineering teacher proposed a 33-day &quot;mind&quot; cycle, based on his observations of how well his students performed over time. <\/p>\n<p>They are now known as the <strong>physical<\/strong>, <strong>emotional<\/strong> and <strong>intellectual<\/strong> cycles. Apparently:<\/p>\n<blockquote>\n<p>There is the 38-day <em class=\"textem\">intuitional cycle<\/em>, the 43-day <em class=\"textem\">aesthetic cycle<\/em>, and      the 53-day <em class=\"textem\">spiritual cycle<\/em>.<\/p>\n<\/blockquote>\n<p>Head on over and put in your dates here:<\/p>\n<p><a href=\"https:\/\/www.intmath.com\/trigonometric-graphs\/biorhythm-graphs.php\">Biorhythm Graphs<\/a><\/p>\n<h2>Math behind the graphs<\/h2>\n<p><strong>Periods: <\/strong>To get graphs having wavelengths of 23, 28 and 33 days, I used these sine curves:<\/p>\n<ul>\n<li>Physical: <span class=\"intmath\"><em>y<\/em> = sin(2&pi;<em>x<\/em>\/23)<\/span><\/li>\n<li>Emotional: <span class=\"intmath\"><em>y<\/em> = sin(2&pi;<em>x<\/em>\/28)<\/span><\/li>\n<li>Intellectual: <span class=\"intmath\"><em>y<\/em> = sin(2&pi;<em>x<\/em>\/33)<\/span><\/li>\n<\/ul>\n<p>The <strong>period<\/strong> of the general graph <span class=\"intmath\"><em>y<\/em> = sin(<em>bx<\/em>)<\/span> is <span class=\"intmath\">2&pi;\/<em>b<\/em><\/span>. In the first graph, <span class=\"intmath\"><em>b<\/em> = 2&pi;\/23<\/span>, so the period is <span class=\"intmath\">2&pi;\/[2&pi;\/23] = 23<\/span>.<\/p>\n<p><strong>Composite graph: <\/strong>A &quot;composite&quot; graph   is the result of adding the <em>y<\/em>-values for 2 or more given graphs. <\/p>\n<p><strong>Bars: <\/strong>For the green and red bars used for the &quot;good days&quot; and &quot;not-so-good&quot; days, I used  <a href=\"https:\/\/www.intmath.com\/blog\/mathematics\/riemann-sums-4715\">Reimann Sum<\/a> rectangles. These are used to approximate the area under a curve. (See also this <a href=\"https:\/\/www.intmath.com\/integration\/riemann-sums.php\">Riemann Sums java applet<\/a>.) <\/p>\n<h2>Conclusion<\/h2>\n<p>Don't take biorhythms seriously! However, hopefully you've learned some math from this example.<\/p>\n<p>The link again: <a href=\"https:\/\/www.intmath.com\/trigonometric-graphs\/biorhythm-graphs.php\">Interactive Biorhythm Graphs<\/a><\/p>\n<p class=\"alt\">See the <a href=\"https:\/\/www.intmath.com\/blog\/learn-math\/biorhythm-graphs-6943#comments\" id=\"comms\">8 Comments<\/a> below.<\/p>\n","protected":false},"excerpt":{"rendered":"<p><a href=\"https:\/\/www.intmath.com\/blog\/learn-math\/biorhythm-graphs-6943\"><img loading=\"lazy\" alt=\"Biorhythm graphs are an interesting - but unscientific - application of sine curves\" src=\"\/blog\/wp-content\/images\/2012\/01\/biorhythm-graphs.png\" title=\"Biorhythm graphs are an interesting - but unscientific - application of sine curves\" width=\"128\" height=\"100\" class=\"imgRt\" \/><\/a><br \/>\nBiorhythm graphs are an interesting - but unscientific - application of sine curves.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mo_disable_npp":""},"categories":[102],"tags":[125,134,109,127],"_links":{"self":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/6943"}],"collection":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/comments?post=6943"}],"version-history":[{"count":0,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/posts\/6943\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/media?parent=6943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/categories?post=6943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.intmath.com\/blog\/wp-json\/wp\/v2\/tags?post=6943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}