{"page":"<link rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-572d6a42.css\" />\n<link rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-f4d0de30.css\" media=\"all\" />\n<div data-title='Visualizing the Riemann hypothesis and analytic continuation' data-url='/boclips/videos/5de51db3832c7977e57bf656' data-video-url='/boclips/videos/5de51db3832c7977e57bf656' id='bo_player_modal'>\n<div class='boclips-resource-page modal-dialog panel-container'>\n<div class='react-notifications-root'></div>\n<div class='rp-header'>\n<div class='rp-type'>\n<i aria-hidden='true' class='fai fa-regular fa-circle-play'></i>\nVideo\n</div>\n<h1 class='rp-title' id='video-title'>\nVisualizing the Riemann hypothesis and analytic continuation\n</h1>\n<div class='rp-actions'>\n<div class='mr-1'>\n<a class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"><span><span>Get Free Access</span><span class=\"\"> for 10 Days</span><span>!</span></span></a>\n</div>\n</div>\n</div>\n<div class='rp-body'>\n<div class='rp-info'>\n<div aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'>&times;</div>\n<i aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'></i>\n<i aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'></i>\n<div class='rp-rating'>\n<span class='resource-pool'>\n<span class='pool-label'>Publisher:</span>\n<span class='pool-name'>\n<span class='text'><a data-publisher-id=\"30354888\" href=\"/search?publisher_ids%5B%5D=30354888\">3Blue1Brown</a></span>\n</span>\n</span>\n</div>\n<div class='rp-description'>\n<span class='short-description'>What is the Riemann zeta function?  What is analytic continuation?  This video lays out the complex analysis needed to answer these questions.</span>\n<span class='full-description hide'>What is the Riemann zeta function?  What is analytic continuation?  This video lays out the complex analysis needed to answer these questions.</span>\n</div>\n<div class='rp-report'>\n</div>\n<div aria-labelledby='resource-details-heading' class='rp-info-section'>\n<h2 class='title' id='resource-details-heading'>Resource Details</h2>\n<div class='rp-resource-details clearfix'>\n<div class='detail'>\n<dl>\n<dt>Curator Rating</dt>\n<dd><span class=\"star-rating\" aria-label=\"5.0 out of 5 stars\" role=\"img\"><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i><i class=\"fa-solid fa-star text-action\" aria-hidden=\"true\"></i></span></dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt class=\"educator-rating-title\">Educator Rating</dt><dd><div class=\"educator-rating-details\" data-path=\"/educator_ratings/rrp_data?resourceable_id=32451&amp;resourceable_type=Boclips%3A%3AVideoMetadata\"><span class=\"not-yet-rated\">Not yet Rated</span></div></dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Media Length</dt>\n<dd>20:27</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Grade</dt><dd title=\"Grade\">12th - Higher Ed</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Subjects</dt><dd><span><a href=\"/search?grade_ids%5B%5D=258&amp;grade_ids%5B%5D=259&amp;search_tab_id=1&amp;subject_ids%5B%5D=365220\">Math</a></span></dd><dd class=\"text-muted\"><i class=\"fa-solid fa-lock mr5\"></i>8 more...</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Media Type</dt><dd><span><a href=\"/search?grade_ids%5B%5D=258&amp;grade_ids%5B%5D=259&amp;search_tab_id=2&amp;type_ids%5B%5D=4543647\">Instructional Videos</a></span></dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Source:</dt>\n<div 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'>\n<span>3Blue1Brown</span>\n<i aria-hidden='true' class='fa-solid fa-circle-info channel-tooltip-icon' id='channel-tooltip'></i>\n</div>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Date</dt>\n<dd>2019</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<i aria-hidden='true' class='fai fa-solid fa-language'></i>\n<dt>Language</dt><dd>English</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Audiences</dt><dd><span><a href=\"/search?audience_ids%5B%5D=371079&amp;grade_ids%5B%5D=258&amp;grade_ids%5B%5D=259&amp;search_tab_id=1\">For Teacher Use</a></span></dd><dd class=\"text-muted\"><i class=\"fa-solid fa-lock mr5\"></i>2 more...</dd>\n</dl>\n</div>\n<div class='detail'>\n<dl>\n<dt>Usage Permissions</dt><dd>Fine Print: Educational Use</dd>\n</dl>\n</div>\n</div>\n</div>\n<div aria-labelledby='additional-materials-heading' class='rp-info-section'>\n<h2 class='title' id='additional-materials-heading'>Additional Materials</h2>\n<div class='additional-material'>\n<i aria-hidden='true' class='fai fa-solid fa-lock'></i>\n<a class=\"text-muted\" title=\"Video Transcript\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"<div class=&quot;text-center py-2&quot;><a class=&quot;bold&quot; href=&quot;/auth/users/sign_in&quot;>Sign in</a> or <a class=&quot;bold text-danger&quot; data-posthog-event=&quot;Signup: LP Signup Activity&quot; data-posthog-location=&quot;body_link_boclips&quot; data-remote=&quot;true&quot; href=&quot;/subscription/new&quot;>Join Now</a></div>\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\">Video Transcript</a>\n</div>\n<div class='additional-material'>\n<i aria-hidden='true' class='fai fa-solid fa-lock'></i>\n<a class=\"text-muted\" title=\"Video Preview\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"<div class=&quot;text-center py-2&quot;><a class=&quot;bold&quot; href=&quot;/auth/users/sign_in&quot;>Sign in</a> or <a class=&quot;bold text-danger&quot; data-posthog-event=&quot;Signup: LP Signup Activity&quot; data-posthog-location=&quot;body_link_boclips&quot; data-remote=&quot;true&quot; href=&quot;/subscription/new&quot;>Join Now</a></div>\" data-title=\"Get Full Access\" data-container=\"body\" rel=\"popover\" tabindex=\"0\" href=\"/subscription/new\">Video Preview</a>\n</div>\n</div>\n<div aria-labelledby='concepts-heading' class='rp-info-section'>\n<h2 class='title' id='concepts-heading'>Concepts</h2>\n<div class='clearfix'>\n<div class='details-list concepts' data-identifier='Boclips::VideoDecorator5de51db3832c7977e57bf656' data-type='concepts'>complex plane, unit circle, natural numbers, prime numbers, numbers, complex numbers</div>\n<div class='concepts-toggle-buttons' data-identifier='Boclips::VideoDecorator5de51db3832c7977e57bf656'>\n<button aria-expanded='false' class='more btn-link' type='button'>\n<span>Show More</span>\n<i aria-hidden='true' class='fa-solid fa-caret-down ml5'></i>\n</button>\n<button aria-expanded='true' class='less btn-link' style='display: none;' type='button'>\n<span>Show Less</span>\n<i aria-hidden='true' class='fa-solid fa-caret-up ml5'></i>\n</button>\n</div>\n</div>\n</div>\n<div aria-labelledby='additional-tags-heading' class='rp-info-section'>\n<h2 class='title' id='additional-tags-heading'>Additional Tags</h2>\n<div class='clearfix'>\n<div class='details-list keyterms' data-identifier='Boclips::VideoDecorator5de51db3832c7977e57bf656' data-type='keyterms'>riemann hypothesis, critical line, extended function, complex number, jigsaw puzzle, riemann zeta function, gridlines turn, angle preserving, moving, left half, complex, remains unchanged, grid, imaginary part, math, complex functions, infinite sum, complex analysis, mathematics, transformed version, complex analysis., analytic continuation, zeta function, real part, zeta, analytic, single point, analytic function, trivial zeros, original sum, preserves angles, function</div>\n<div class='keyterms-toggle-buttons' data-identifier='Boclips::VideoDecorator5de51db3832c7977e57bf656'>\n<button aria-expanded='false' class='more btn-link' type='button'>\n<span>Show More</span>\n<i aria-hidden='true' class='fa-solid fa-caret-down ml5'></i>\n</button>\n<button aria-expanded='true' class='less btn-link' style='display: none;' type='button'>\n<span>Show Less</span>\n<i aria-hidden='true' class='fa-solid fa-caret-up ml5'></i>\n</button>\n</div>\n</div>\n</div>\n<div aria-labelledby='classroom-considerations-heading' class='rp-info-section'>\n<h2 class='title' id='classroom-considerations-heading'>Classroom Considerations</h2>\n<div class='classroom-considerations'><div class='fai fa-solid fa-bell'></div>Best For: Explaining a topic</div><div class='classroom-considerations'><div class='fai fa-solid fa-bell'></div>Video is ad-free</div> \n</div>\n<div aria-labelledby='educator-ratings-heading' class='rp-info-section'>\n<h2 class='title sr-only' id='educator-ratings-heading'>Educator Ratings</h2>\n<div id=\"educator-ratings-root\"></div><div id=\"all-educator-ratings-root\"></div><div id=\"educator-rating-form-root\"></div>\n</div>\n</div>\n<div class='rp-resource'>\n<div aria-label='Show resource details' class='rp-show-info' role='button' tabindex='0'>\n<i class='fai fa-solid fa-align-left'></i>\nShow resource details\n</div>\n<div aria-label='Video player' class='player ie' id='player-wrapper' role='region'>\n<div class='relative container mx-auto' id='lp-boclips-visitor-thumbnail'>\n<a class=\"block\" data-html=\"true\" data-placement=\"bottom\" data-trigger=\"click\" data-content=\"<div class=&quot;text-center py-2&quot;><a class=&quot;bold&quot; 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