{"id":501194,"date":"2026-06-23T13:34:00","date_gmt":"2026-06-23T13:34:00","guid":{"rendered":"https:\/\/livelycity.com\/switzerland\/prove-that-e-ipi-1-mathematics-stack-exchange\/"},"modified":"2026-06-23T13:34:00","modified_gmt":"2026-06-23T13:34:00","slug":"prove-that-e-ipi-1-mathematics-stack-exchange","status":"publish","type":"post","link":"https:\/\/livelycity.com\/switzerland\/prove-that-e-ipi-1-mathematics-stack-exchange\/","title":{"rendered":"Prove that $e^ {ipi} = -1$ &#8211; Mathematics Stack Exchange"},"content":{"rendered":"<p>The $pi$ itself is defined as the total angle which connects $1$ to $-1$ along the arch. Summarizing, we can say that because the circle can be defined through the action of the group of shifts which preserve the distance between a point and another point, the relation between \u03c0 and e arises.<\/p>\n<p>\u00a0<a href=\"https:\/\/math.stackexchange.com\/questions\/341214\/prove-that-ei-pi-1\" target=\"_blank\" class=\"\">https:\/\/math.stackexchange.com\/questions\/341214\/prove-that-ei-pi-1<\/a>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The $pi$ itself is defined as the total angle which connects $1$ to $-1$ along the arch. Summarizing, we can say that because the circle&#8230;<\/p>\n","protected":false},"author":0,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-501194","post","type-post","status-publish","format-standard","hentry","category-zurich","wpcat-8-id"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/posts\/501194","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/comments?post=501194"}],"version-history":[{"count":0,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/posts\/501194\/revisions"}],"wp:attachment":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/media?parent=501194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/categories?post=501194"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/tags?post=501194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}