{"id":8004,"date":"2012-03-18T21:47:40","date_gmt":"2012-03-19T02:47:40","guid":{"rendered":"http:\/\/blog.kenperlin.com\/?p=8004"},"modified":"2012-03-18T21:47:40","modified_gmt":"2012-03-19T02:47:40","slug":"the-importance-of-circles","status":"publish","type":"post","link":"http:\/\/blog.kenperlin.com\/?p=8004","title":{"rendered":"The importance of circles"},"content":{"rendered":"

In order to understand the power of Euler’s identity eiπ<\/sup> + 1 = 0, you need to unlearn some pretty fundamental things you were taught in school.<\/p>\n

We are all taught that light and sound travels in waves, that alternating current is described by sine waves, as well as tides, water waves, guitar strings, bouncing springs, pendulums and anything other kind of regular periodic movement.<\/p>\n

The problem with this mental model is that it misses the most important thing: None of these things are best described by something moving in a sine wave. Rather, they are best described by something moving in a circle. Deep down, they are all pretty much equivalent to tying a rock to a rope and swinging it over your head in a circle.<\/p>\n

I know this seems counterintuitive. After all, we can actually see<\/i> the bob of the pendulum move left and right. The movement doesn’t look anything like a circle. The problem is that the circle isn’t visible — but even so, it is essential.<\/p>\n

In the case of a pendulum, one axis of the circle is displacement and the other axis is speed. Any<\/i> time you see periodic movement, you are actually looking at something that holds energy by spinning in a circle. Unfortunately one or more of the dimensions of that circle is often invisible to the naked eye.<\/p>\n

Once you absorb this idea, Euler’s identity takes on much more significance. It’s the key to understanding light, sound, vibrating strings, bouncing springs, and pretty much everything that sends information around the Universe.<\/p>\n","protected":false},"excerpt":{"rendered":"

In order to understand the power of Euler’s identity eiπ + 1 = 0, you need to unlearn some pretty fundamental things you were taught in school. We are all taught that light and sound travels in waves, that alternating current is described by sine waves, as well as tides, water waves, guitar strings, bouncing … Continue reading “The importance of circles”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/8004"}],"collection":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=8004"}],"version-history":[{"count":1,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/8004\/revisions"}],"predecessor-version":[{"id":8005,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/8004\/revisions\/8005"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=8004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=8004"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=8004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}