{"id":492,"date":"2023-05-06T03:24:06","date_gmt":"2023-05-06T03:24:06","guid":{"rendered":"http:\/\/src.cikeys.com\/2023\/?page_id=492"},"modified":"2023-05-06T04:04:32","modified_gmt":"2023-05-06T04:04:32","slug":"quaternions","status":"publish","type":"page","link":"https:\/\/src.cikeys.com\/2023\/conference-schedule\/poster-presentations-session-2\/quaternions\/","title":{"rendered":"Quaternions"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Riad Saad, Eric Strauss, &amp; Dr. Ivona Grzegorczyk<\/h2>\n\n\n\n<!--more-->\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-7387b849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<h3 class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract on quaternions and some applications by Riad Saad:<br>Number systems allow operations of addition, multiplication and division that come with certain properties, such as commutativity, distributivity, etc. We discuss quaternions as a number system and related representations. Then we present an extension of this system to even larger number system called octonions. The quaternions are members of a non-commutative division algebra first invented by William Rowan Hamilton. The quaternion number system can be considered as an extension of the complex number system. Hamilton defined a quaternion as the quotient of two direct lines in a three-dimensional space. Quaternions have various applications in geometry and physics representing three-dimensional rotations. They can be used alongside other methods of rotation, such as Euler angles and rotation matrices, or as an alternative to them, depending on the application. Octonions are a kind of hypercomplex number system and have applications in string theory and quantum logic.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<h3 class=\"wp-block-heading\">Details<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Session 2<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3:00pm \u2013 4:30pm<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Grand Salon<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<div class=\"wp-block-comments\">\n\n\n\n\n\n\t<div id=\"respond\" class=\"comment-respond wp-block-post-comments-form\">\n\t\t<h3 id=\"reply-title\" class=\"comment-reply-title\">Leave a Reply <small><a rel=\"nofollow\" id=\"cancel-comment-reply-link\" href=\"\/2023\/wp-json\/wp\/v2\/pages\/492#respond\" style=\"display:none;\">Cancel reply<\/a><\/small><\/h3><form action=\"https:\/\/src.cikeys.com\/2023\/wp-comments-post.php\" method=\"post\" id=\"commentform\" class=\"comment-form\"><p class=\"comment-notes\"><span id=\"email-notes\">Your email address will not be published.<\/span> <span class=\"required-field-message\">Required fields are marked <span class=\"required\">*<\/span><\/span><\/p><p class=\"comment-form-comment\"><label for=\"comment\">Comment <span class=\"required\">*<\/span><\/label> <textarea id=\"comment\" name=\"comment\" cols=\"45\" rows=\"8\" maxlength=\"65525\" required><\/textarea><\/p><p class=\"comment-form-author\"><label for=\"author\">Name <span class=\"required\">*<\/span><\/label> <input id=\"author\" name=\"author\" type=\"text\" value=\"\" size=\"30\" maxlength=\"245\" autocomplete=\"name\" required \/><\/p>\n<p class=\"comment-form-email\"><label for=\"email\">Email <span class=\"required\">*<\/span><\/label> <input id=\"email\" name=\"email\" type=\"email\" value=\"\" size=\"30\" maxlength=\"100\" aria-describedby=\"email-notes\" autocomplete=\"email\" required \/><\/p>\n<p class=\"comment-form-url\"><label for=\"url\">Website<\/label> <input id=\"url\" name=\"url\" type=\"url\" value=\"\" size=\"30\" maxlength=\"200\" autocomplete=\"url\" \/><\/p>\n<p class=\"comment-form-cookies-consent\"><input id=\"wp-comment-cookies-consent\" name=\"wp-comment-cookies-consent\" type=\"checkbox\" value=\"yes\" \/> <label for=\"wp-comment-cookies-consent\">Save my name, email, and website in this browser for the next time I comment.<\/label><\/p>\n<p class=\"form-submit\"><input name=\"submit\" type=\"submit\" id=\"submit\" class=\"submit\" value=\"Post Comment\" \/> <input type='hidden' name='comment_post_ID' value='492' id='comment_post_ID' \/>\n<input type='hidden' name='comment_parent' id='comment_parent' value='0' \/>\n<\/p><p style=\"display: none !important;\" class=\"akismet-fields-container\" data-prefix=\"ak_\"><label>&#916;<textarea name=\"ak_hp_textarea\" cols=\"45\" rows=\"8\" maxlength=\"100\"><\/textarea><\/label><input type=\"hidden\" id=\"ak_js_1\" name=\"ak_js\" value=\"146\"\/><script>\ndocument.getElementById( \"ak_js_1\" ).setAttribute( \"value\", ( new Date() ).getTime() );\n<\/script>\n<\/p><\/form>\t<\/div><!-- #respond -->\n\t<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Riad Saad, Eric Strauss, &amp; Dr. Ivona Grzegorczyk<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":112,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[5,3,10],"tags":[29],"class_list":["post-492","page","type-page","status-publish","hentry","category-poster","category-presentations","category-session-2-poster","tag-mathematics"],"_links":{"self":[{"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/pages\/492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/comments?post=492"}],"version-history":[{"count":2,"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/pages\/492\/revisions"}],"predecessor-version":[{"id":612,"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/pages\/492\/revisions\/612"}],"up":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/pages\/112"}],"wp:attachment":[{"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/media?parent=492"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/categories?post=492"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/src.cikeys.com\/2023\/wp-json\/wp\/v2\/tags?post=492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}