Since today is the 27th day of the month, I find my thoughts drifting toward mathematical patterns. That’s because 27 happens to be 3 raised to the power of 3.<\/p>\n
Which suggests the idea of raising a number to the power of itself. If we do this with integers, we get a series that starts: 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 10000000000 …<\/p>\n
But we don’t need to do this with integers only. We might just as well raise 1.5 to the power of 1.5 (in which case we get a result between 1.8 and 1.9).<\/p>\n
If we try it with negative numbers, for example -1.5, things start to get more complex. And what if we start with complex numbers?<\/p>\n
If we consider the entire complex number plane, this operation gets very interesting. If you are mathematically inclined, you might want to explore the question: What is the shape formed by raising every complex number to the power of itself?<\/p>\n","protected":false},"excerpt":{"rendered":"
Since today is the 27th day of the month, I find my thoughts drifting toward mathematical patterns. That’s because 27 happens to be 3 raised to the power of 3. Which suggests the idea of raising a number to the power of itself. If we do this with integers, we get a series that starts: … Continue reading “Power play”<\/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\/20170"}],"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=20170"}],"version-history":[{"count":2,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/20170\/revisions"}],"predecessor-version":[{"id":20216,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=\/wp\/v2\/posts\/20170\/revisions\/20216"}],"wp:attachment":[{"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=20170"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=20170"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blog.kenperlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=20170"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}