{"id":743,"date":"2025-12-15T09:37:31","date_gmt":"2025-12-15T16:37:31","guid":{"rendered":"https:\/\/joshuadahl.net\/blog\/?p=743"},"modified":"2025-12-15T09:37:32","modified_gmt":"2025-12-15T16:37:32","slug":"way","status":"publish","type":"post","link":"https:\/\/joshuadahl.net\/blog\/way\/","title":{"rendered":"Way"},"content":{"rendered":"\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Moana - I Am Moana with Lyrics (Song of the Ancestors) by Auli&#039;i Cravalho\" width=\"688\" height=\"387\" src=\"https:\/\/www.youtube.com\/embed\/2Q27aHJMWnk?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p>Moana felt she had a destiny to save her village, and the calling was to the ocean. She felt that in order to thrive and solve future problems the village would face she would have to seek out the demigod Maui and have him restore what was stolen in order to end the strife for Moana and her people. She takes with her, her chicken Hei Hei, and the stone of te fiti that she received from the ocean.She does not know the way to where the stone must go, however her ancestors are her guide she will succeed, and with Moana being a Disney movie of course she does.<\/p>\n\n\n\n<p>Usually when you use way in a sentence you are describing a methodology or direction. How do I get to grandma\u2019s house? I will show you the way, the way to connect two points together, get you from where you are currently at to grandma\u2019s house. The way can also be a discipline, for instance bushido, the way of the warrior. How does the warrior live, they live the way of the warrior, kind of self defined I suppose I would need to elaborate more on what a warrior is expected to do, kick ass would work, the details are stylistic.&nbsp;<\/p>\n\n\n\n<p>The way things are are. That is not a profound statement, it is just what it is. We can observe the nature of the world and understand the way in which it works. One of the observed methodologies we have devised is mathematics and music. You can\u2019t have music without math, and you appreciate math because of music. In math there is a study of probability, how likely something could happen. Statistically the possibility of something happening is based on what are the possible outcomes and then from the number of permutations the probability of what can take place is found by using the choose function which is&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/joshuadahl.net\/blog\/wp-content\/uploads\/2025\/12\/image.png\"><img loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"47\" src=\"https:\/\/joshuadahl.net\/blog\/wp-content\/uploads\/2025\/12\/image.png\" alt=\"\" class=\"wp-image-744\"\/><\/a><\/figure>\n\n\n\n<p>This reads as n choose k, the easiest example of this is finding the possible hands in a poker game. The deck consists of 52 cards and you deal 5 at a time, there are 52 choose 5 hands in the game.<\/p>\n\n\n\n<p>The combinations that take place were written down into a triangle that incorporates the Fibonacci sequence in its construction. During the 13th century, <a href=\"https:\/\/en.wikipedia.org\/wiki\/Yang_Hui\">Yang Hui<\/a> (1238\u20131298) defined the triangle, and it is known as <strong>Yang Hui&#8217;s triangle<\/strong> or better known as the Pascal triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/joshuadahl.net\/blog\/wp-content\/uploads\/2025\/12\/image-1.png\"><img loading=\"lazy\" decoding=\"async\" width=\"538\" height=\"258\" src=\"https:\/\/joshuadahl.net\/blog\/wp-content\/uploads\/2025\/12\/image-1.png\" alt=\"\" class=\"wp-image-745\" srcset=\"https:\/\/joshuadahl.net\/blog\/wp-content\/uploads\/2025\/12\/image-1.png 538w, https:\/\/joshuadahl.net\/blog\/wp-content\/uploads\/2025\/12\/image-1-300x144.png 300w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/a><\/figure>\n\n\n\n<p>The triangle shows how to perform binomial expansion. Imagine that you had to multiply this out<\/p>\n\n\n\n<p>(x+3)<sup>4&nbsp;<\/sup><\/p>\n\n\n\n<p>That would take a lot of work, however using Pascal\u2019s triangle this becomes a breeze.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Identify the n and terms: n=4 terms x and 3<\/li>\n\n\n\n<li>Get the coefficients from Pascal\u2019s triangle for row 4 => 1,4,6,4,1<\/li>\n\n\n\n<li>Apply the power pattern<\/li>\n<\/ol>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Term 1: 1*x<sup>4<\/sup>*3<sup>0<\/sup><\/li>\n\n\n\n<li>Term 2: 4*x<sup>3<\/sup>*3<sup>1<\/sup><\/li>\n\n\n\n<li>Term 3: 6*x<sup>2<\/sup>*3<sup>2<\/sup><\/li>\n\n\n\n<li>Term 4: 4*x<sup>1<\/sup>*3<sup>3<\/sup><\/li>\n\n\n\n<li>Term 5: 1*x<sup>0<\/sup>*3<sup>4<\/sup><\/li>\n<\/ol>\n\n\n\n<ol start=\"4\" class=\"wp-block-list\">\n<li>Simplify the results: x<sup>4<\/sup>+12x<sup>3<\/sup>+72x<sup>2<\/sup>+108x+81<\/li>\n<\/ol>\n\n\n\n<p>That saved a bunch of time. Everything is much easier when you know the way.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Moana felt she had a destiny to save her village, and the calling was to the ocean. She felt that&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-743","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/posts\/743","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/comments?post=743"}],"version-history":[{"count":1,"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/posts\/743\/revisions"}],"predecessor-version":[{"id":746,"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/posts\/743\/revisions\/746"}],"wp:attachment":[{"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/media?parent=743"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/categories?post=743"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/joshuadahl.net\/blog\/wp-json\/wp\/v2\/tags?post=743"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}