{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-af73c33d.css\" media=\"all\" /\u003e\n\u003cdiv data-title='e to the pi i, a nontraditional take (old version)' data-url='/boclips/videos/6207b1070dfde6378ea4dcaa' data-video-url='/boclips/videos/6207b1070dfde6378ea4dcaa' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\ne to the pi i, a nontraditional take (old version)\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30354888\" href=\"/search?publisher_ids%5B%5D=30354888\"\u003e3Blue1Brown\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003eThe enigmatic equation e^{pi i} = -1 is usually explained using Taylor's formula during a calculus class.  This video offers a different perspective, which involves thinking about numbers as actions, and about e^x as something which...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003eThe enigmatic equation e^{pi i} = -1 is usually explained using Taylor's formula during a calculus class.  This video offers a different perspective, which involves thinking about numbers as actions, and about e^x as something which turns one action into another.\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='action-container flex justify-between'\u003e\n\u003cbutton aria-expanded='false' aria-label='Read more description' class='rp-full-description' type='button'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\n\u003cspan id='read_more'\u003eRead More\u003c/span\u003e\n\u003c/button\u003e\n\u003cdiv class='rp-report'\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='resource-details-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='resource-details-heading'\u003eResource Details\u003c/h2\u003e\n\u003cdiv class='rp-resource-details clearfix'\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eCurator Rating\u003c/dt\u003e\n\u003cdd\u003e\u003cspan class=\"star-rating\" aria-label=\"5.0 out of 5 stars\" 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href=\"/search?grade_ids%5B%5D=258\u0026amp;grade_ids%5B%5D=259\u0026amp;search_tab_id=2\u0026amp;type_ids%5B%5D=4543647\"\u003eInstructional Videos\u003c/a\u003e\u003c/span\u003e\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv class='detail'\u003e\n\u003cdl\u003e\n\u003cdt\u003eSource:\u003c/dt\u003e\n\u003cdiv class='preview-source' data-animation='true' data-boundary='.rp-info' data-container='.rp-resource-details' data-html='false' data-title='3Blue1Brown is a channel about visualizing math, with content ranging from calculus to linear algebra, topology, neural networks and even how bitcoin works.' data-trigger='hover focus'\u003e\n\u003cspan\u003e3Blue1Brown\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-circle-info channel-tooltip-icon' id='channel-tooltip'\u003e\u003c/i\u003e\n\u003c/div\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003cdiv 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Use\u003c/dd\u003e\n\u003c/dl\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='additional-materials-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='additional-materials-heading'\u003eAdditional Materials\u003c/h2\u003e\n\u003cdiv class='additional-material'\u003e\n\u003ci aria-hidden='true' class='fai fa-solid fa-lock'\u003e\u003c/i\u003e\n\u003ca class=\"text-muted\" title=\"Video Transcript\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin 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type='button'\u003e\n\u003cspan\u003eShow Less\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-up ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='additional-tags-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='additional-tags-heading'\u003eAdditional Tags\u003c/h2\u003e\n\u003cdiv class='clearfix'\u003e\n\u003cdiv class='details-list keyterms' data-identifier='Boclips::VideoDecorator6207b1070dfde6378ea4dcaa' data-type='keyterms'\u003e3b1b, 3 blue 1 brown, euler\u0026#39;s formula, three brown one blue, three blue one brown, 3 brown 1 blue, e to the pi i, mathematics (field of study), 3brown1blue, complex analysis (field of study), euler\u0026#39;s constant, e (literature subject), make sense, square root, evenly spaced, infinite sum, repeated multiplication, adders, means, sliding, points, applying, side, takes, slides, case, natural, negative, function, line, multiplier, plane, adder, clear, understand, require, write, number, define, actions, thought, tricky\u003c/div\u003e\n\u003cdiv class='keyterms-toggle-buttons' data-identifier='Boclips::VideoDecorator6207b1070dfde6378ea4dcaa'\u003e\n\u003cbutton aria-expanded='false' class='more btn-link' type='button'\u003e\n\u003cspan\u003eShow More\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-down ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003cbutton aria-expanded='true' class='less btn-link' style='display: none;' type='button'\u003e\n\u003cspan\u003eShow Less\u003c/span\u003e\n\u003ci aria-hidden='true' class='fa-solid fa-caret-up ml5'\u003e\u003c/i\u003e\n\u003c/button\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv aria-labelledby='classroom-considerations-heading' class='rp-info-section'\u003e\n\u003ch2 class='title' id='classroom-considerations-heading'\u003eClassroom Considerations\u003c/h2\u003e\n\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eBest For: Explaining a topic\u003c/div\u003e\u003cdiv class='classroom-considerations'\u003e\u003cdiv class='fai fa-solid fa-bell'\u003e\u003c/div\u003eVideo is ad-free\u003c/div\u003e \n\u003c/div\u003e\n\u003cdiv aria-labelledby='educator-ratings-heading' class='rp-info-section'\u003e\n\u003ch2 class='title sr-only' id='educator-ratings-heading'\u003eEducator Ratings\u003c/h2\u003e\n\u003cdiv id=\"educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"all-educator-ratings-root\"\u003e\u003c/div\u003e\u003cdiv id=\"educator-rating-form-root\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-resource'\u003e\n\u003cdiv aria-label='Show resource details' class='rp-show-info' role='button' tabindex='0'\u003e\n\u003ci class='fai fa-solid fa-align-left'\u003e\u003c/i\u003e\nShow resource details\n\u003c/div\u003e\n\u003cdiv aria-label='Video player' class='player' id='player-wrapper' role='region'\u003e\n\u003cdiv class='relative container mx-auto' id='lp-boclips-visitor-thumbnail'\u003e\n\u003ca class=\"block\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"\u003cdiv class=\u0026quot;text-center py-2\u0026quot;\u003e\u003ca class=\u0026quot;bold\u0026quot; href=\u0026quot;/auth/users/sign_in\u0026quot;\u003eSign in\u003c/a\u003e or \u003ca class=\u0026quot;bold text-danger\u0026quot; data-posthog-event=\u0026quot;Signup: LP Signup Activity\u0026quot; data-posthog-location=\u0026quot;body_link_boclips\u0026quot; data-remote=\u0026quot;true\u0026quot; href=\u0026quot;/subscription/new\u0026quot;\u003eJoin Now\u003c/a\u003e\u003c/div\u003e\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" aria-label=\"Play video: e to the pi i, a nontraditional take (old version)\" href=\"/subscription/new\"\u003e\u003cimg class=\"resource-img img-thumbnail img-responsive z-10 lp-boclips-thumbnail w-full h-full lozad\" alt=\"e to the pi i, a nontraditional take (old version)\" title=\"e to the pi i, a nontraditional take (old version)\" onError=\"handleImageNotLoadedError(this)\" data-default-image=\"https://static.lp.lexp.cloud/images/attachment_defaults/resource/large/missing.png\" data-src=\"https://cdnapisec.kaltura.com/p/1776261/thumbnail/entry_id/1_pytmm7qe/width/250/vid_slices/3/vid_slice/1\" width=\"315\" height=\"220\" src=\"data:image/png;base64,R0lGODlhAQABAAD/ACwAAAAAAQABAAACADs\" /\u003e\n\u003cspan aria-hidden='true' class='flex justify-center items-center bg-white rounded-full w-16 h-16 absolute top-1/2 left-1/2 -mt-8 -ml-8 cursor-pointer z-0 border-2 border-primary drop-shadow-md lp-boclips-thumbnail-playBtn'\u003e\n\u003ci class='fa-solid fa-play text-primary text-3xl ml-1 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