{"id":2859,"date":"2019-03-03T09:31:17","date_gmt":"2019-03-03T08:31:17","guid":{"rendered":"https:\/\/www.bravecroc.de\/paradoxer-umfang\/"},"modified":"2020-11-27T13:19:58","modified_gmt":"2020-11-27T12:19:58","slug":"paradoxer-umfang","status":"publish","type":"post","link":"https:\/\/www.bravecroc.de\/en\/paradoxer-umfang\/","title":{"rendered":"Paradoxical perimeter"},"content":{"rendered":"[vc_row type=&#8221;full_width_background&#8221; full_screen_row_position=&#8221;middle&#8221; column_margin=&#8221;default&#8221; column_direction=&#8221;default&#8221; column_direction_tablet=&#8221;default&#8221; column_direction_phone=&#8221;default&#8221; bg_color=&#8221;#b52827&#8243; scene_position=&#8221;center&#8221; text_color=&#8221;custom&#8221; custom_text_color=&#8221;#ffffff&#8221; text_align=&#8221;left&#8221; row_border_radius=&#8221;none&#8221; row_border_radius_applies=&#8221;bg&#8221; zindex=&#8221;99999&#8243; overlay_strength=&#8221;0.3&#8243; gradient_direction=&#8221;left_to_right&#8221; 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css=&#8221;.vc_custom_1606478390018{padding-top: 5px !important;}&#8221;]Facts[\/vc_column_text][vc_custom_heading text=&#8221;Paradoxical perimeter&#8221; font_container=&#8221;tag:h1|font_size:26px|text_align:left|color:%23ffffff|line_height:26px&#8221; use_theme_fonts=&#8221;yes&#8221;][divider line_type=&#8221;Small Line&#8221; line_alignment=&#8221;default&#8221; line_thickness=&#8221;2&#8243; divider_color=&#8221;extra-color-1&#8243; custom_height=&#8221;10&#8243; custom_line_width=&#8221;45&#8243;][vc_column_text el_class=&#8221;blog-datum&#8221;]2019-03-03[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][vc_row type=&#8221;full_width_background&#8221; full_screen_row_position=&#8221;middle&#8221; column_margin=&#8221;default&#8221; column_direction=&#8221;default&#8221; column_direction_tablet=&#8221;default&#8221; column_direction_phone=&#8221;default&#8221; scene_position=&#8221;center&#8221; top_padding=&#8221;2%&#8221; bottom_padding=&#8221;2%&#8221; 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overlay_strength=&#8221;0.3&#8243; width=&#8221;2\/3&#8243; tablet_width_inherit=&#8221;default&#8221; tablet_text_alignment=&#8221;default&#8221; phone_text_alignment=&#8221;default&#8221; column_border_width=&#8221;none&#8221; column_border_style=&#8221;solid&#8221; bg_image_animation=&#8221;none&#8221;][vc_row_inner content_placement=&#8221;bottom&#8221; column_margin=&#8221;default&#8221; column_direction=&#8221;default&#8221; column_direction_tablet=&#8221;default&#8221; column_direction_phone=&#8221;default&#8221; text_align=&#8221;left&#8221;][vc_column_inner column_padding=&#8221;no-extra-padding&#8221; column_padding_tablet=&#8221;inherit&#8221; column_padding_phone=&#8221;inherit&#8221; column_padding_position=&#8221;all&#8221; background_color_opacity=&#8221;1&#8243; background_hover_color_opacity=&#8221;1&#8243; column_shadow=&#8221;none&#8221; column_border_radius=&#8221;none&#8221; column_link_target=&#8221;_self&#8221; gradient_direction=&#8221;left_to_right&#8221; overlay_strength=&#8221;0.3&#8243; width=&#8221;1\/2&#8243; tablet_width_inherit=&#8221;default&#8221; column_border_width=&#8221;none&#8221; column_border_style=&#8221;solid&#8221; bg_image_animation=&#8221;none&#8221;]<div class=\"nectar-fancy-ul\" data-list-icon=\"fa fa-stop\" data-animation=\"false\" data-animation-delay=\"0\" data-color=\"extra-color-2\" data-spacing=\"default\" data-alignment=\"left\"> Imagine the earth would be a perfect sphere and around this sphere runs a band at the equator, directly on the sphere.<\/p>\n<p>The band is now cut at one point and a piece of band 3 m long is inserted. In a miraculous way, the band rises evenly over the equator and floats perfectly above it.<\/p>\n<h5>Question<\/h5>\n<p>How large could the distance between the band and the earth be? Does a finger, hand or arm fit between the band and the earth? Do we have to worry about the safety distances according to ISO 13857? ISO 13857 specifies that for such a slit-shaped opening:<\/p>\n<ul>\n<li>for fingers not more than 6 mm,<\/li>\n<li>for hands not more than 30 mm and<\/li>\n<li>for arms no longer 120 mm.<\/li>\n<\/ul>\n <\/div>[\/vc_column_inner][vc_column_inner column_padding=&#8221;no-extra-padding&#8221; column_padding_tablet=&#8221;inherit&#8221; column_padding_phone=&#8221;inherit&#8221; column_padding_position=&#8221;all&#8221; background_color_opacity=&#8221;1&#8243; background_hover_color_opacity=&#8221;1&#8243; column_shadow=&#8221;none&#8221; column_border_radius=&#8221;none&#8221; column_link_target=&#8221;_self&#8221; gradient_direction=&#8221;left_to_right&#8221; overlay_strength=&#8221;0.3&#8243; width=&#8221;1\/2&#8243; tablet_width_inherit=&#8221;default&#8221; column_border_width=&#8221;none&#8221; column_border_style=&#8221;solid&#8221; bg_image_animation=&#8221;none&#8221;][image_with_animation image_url=&#8221;2117&#8243; animation=&#8221;Fade In&#8221; hover_animation=&#8221;none&#8221; alignment=&#8221;center&#8221; border_radius=&#8221;none&#8221; box_shadow=&#8221;none&#8221; image_loading=&#8221;default&#8221; max_width=&#8221;75%&#8221; max_width_mobile=&#8221;default&#8221;][\/vc_column_inner][\/vc_row_inner][vc_column_text]And how does the distance with such a 3 m supplement behave with diameters other than the earth diameter?<\/p>\n<p>In comparison to the total length of the band that lies around the earth, 3 m is very little. Certainly there will be a gap, but probably rather a very small one, our intuition says.<\/p>\n<p>.[\/vc_column_text][vc_row_inner content_placement=&#8221;bottom&#8221; column_margin=&#8221;default&#8221; column_direction=&#8221;default&#8221; column_direction_tablet=&#8221;default&#8221; column_direction_phone=&#8221;default&#8221; text_align=&#8221;left&#8221;][vc_column_inner column_padding=&#8221;no-extra-padding&#8221; column_padding_tablet=&#8221;inherit&#8221; column_padding_phone=&#8221;inherit&#8221; column_padding_position=&#8221;all&#8221; background_color_opacity=&#8221;1&#8243; background_hover_color_opacity=&#8221;1&#8243; column_shadow=&#8221;none&#8221; column_border_radius=&#8221;none&#8221; column_link_target=&#8221;_self&#8221; gradient_direction=&#8221;left_to_right&#8221; overlay_strength=&#8221;0.3&#8243; width=&#8221;1\/2&#8243; tablet_width_inherit=&#8221;default&#8221; column_border_width=&#8221;none&#8221; column_border_style=&#8221;solid&#8221; bg_image_animation=&#8221;none&#8221;][vc_column_text]\n<h5>Method<\/h5>\n<p>The radius of the extended band results from the radius of the earth r + the distance D between earth and band. Multiplied by 2\u03c0 you get the perimeter of the floating band. The perimeter of the floating band is also defined by the perimeter of the earth + 3 m.<\/p>\n<p>Let&#8217;s put these two insights into an equation and adjust it according to the distance D:[\/vc_column_text][\/vc_column_inner][vc_column_inner column_padding=&#8221;no-extra-padding&#8221; column_padding_tablet=&#8221;inherit&#8221; column_padding_phone=&#8221;inherit&#8221; column_padding_position=&#8221;all&#8221; background_color_opacity=&#8221;1&#8243; background_hover_color_opacity=&#8221;1&#8243; column_shadow=&#8221;none&#8221; column_border_radius=&#8221;none&#8221; column_link_target=&#8221;_self&#8221; gradient_direction=&#8221;left_to_right&#8221; overlay_strength=&#8221;0.3&#8243; width=&#8221;1\/2&#8243; tablet_width_inherit=&#8221;default&#8221; column_border_width=&#8221;none&#8221; column_border_style=&#8221;solid&#8221; bg_image_animation=&#8221;none&#8221;][image_with_animation image_url=&#8221;2119&#8243; animation=&#8221;Fade In&#8221; hover_animation=&#8221;none&#8221; alignment=&#8221;center&#8221; border_radius=&#8221;none&#8221; box_shadow=&#8221;none&#8221; image_loading=&#8221;default&#8221; max_width=&#8221;75%&#8221; max_width_mobile=&#8221;default&#8221;][\/vc_column_inner][\/vc_row_inner][vc_column_text]\n<h5>Solution<\/h5>\n<p>According to this, the distance D between tape and earth is 0.47746482927568600730665129011754 m, i.e. approx. 0.48 m. 0.48 m is not a problematic distance according to ISO 13857 and yet much more than usually assumed.<\/p>\n<p>But is it a question of the radius of the sphere? No, the radius of the earth, or of the considered sphere is no longer part of the calculation and therefore has no influence on the distance of the band to the sphere. So if such a band is placed around a tennis ball and supplemented by 3 m, the distance is exactly the same. Similarly, a band would be placed around the sun and supplemented accordingly.[\/vc_column_text]<div class=\"nectar-fancy-ul\" data-list-icon=\"fa fa-stop\" data-animation=\"false\" data-animation-delay=\"0\" data-color=\"extra-color-2\" data-spacing=\"default\" data-alignment=\"left\"> \n<h5>Die Illustration zu diesem Paradoxon entstand im Corel DESIGNER<\/h5>\n<ul>\n<li>Kugel<br \/>\nKreis mit angepasstem radialen Farbverlauf \u00fcber das Andockfenster\u00a0<em>Eigenschaften<\/em> und dem Hilfsmittel\u00a0<em>Interaktive F\u00fcllung<\/em>, direkt am Objekt<\/li>\n<li>Band<br \/>\nKreis\u00a0<em>projiziert <\/em>in der Ansicht von oben,\u00a0<em>extrudiert\u00a0<\/em>und Extrusionsgruppe aufgel\u00f6st, um ein Teil vor und ein Teil hinter der Kugel zu positionieren, Eigenschaften angepasst<\/li>\n<li>Bema\u00dfung<br \/>\n<em>Bema\u00dfungshilfsmittel<\/em>, teilweise aufgel\u00f6st und angepasst, Bema\u00dfungshilfslinie der eigef\u00fcgten 3\u00a0m durch kopieren des Kurvensegmentes des Bandes erstellt, \u201e+3m\u201c mit dem Hilfsmittel <em>H\u00fclle\u00a0<\/em>frei an die Perspektive angepasst<\/li>\n<li>Formel<br \/>\n<em>Formeleditor<\/em><\/li>\n<\/ul>\n<h5>The illustration of this paradox was created in Corel DESIGNER<\/h5>\n<ul>\n<li>sphere<br \/>\nCircle with adjusted radial gradient via the <em>Properties<\/em> docker and the tool <em>Interactive filling<\/em>, directly on the object<\/li>\n<li>Band<br \/>\nCircle projected in top view, extruded and extrusion group resolved to place one part in front and one part behind the sphere, properties adjusted<\/li>\n<li>Dimensioning<br \/>\n<em>Dimension tool<\/em>, partially resolved and adjusted, dimension auxiliary line of the inserted 3 m created by copying the curve segment of the band, &#8220;+3m&#8221; freely adjusted to the perspective with the tool <em>Envelope<\/em>.<\/li>\n<li>Formula<br \/>\n<em>Equation Editor<\/em><\/li>\n<\/ul>\n <\/div>[\/vc_column][vc_column column_padding=&#8221;no-extra-padding&#8221; column_padding_tablet=&#8221;inherit&#8221; column_padding_phone=&#8221;inherit&#8221; column_padding_position=&#8221;all&#8221; background_color_opacity=&#8221;1&#8243; background_hover_color_opacity=&#8221;1&#8243; column_shadow=&#8221;none&#8221; column_border_radius=&#8221;none&#8221; column_link_target=&#8221;_self&#8221; gradient_direction=&#8221;left_to_right&#8221; overlay_strength=&#8221;0.3&#8243; width=&#8221;1\/3&#8243; tablet_width_inherit=&#8221;default&#8221; tablet_text_alignment=&#8221;default&#8221; phone_text_alignment=&#8221;default&#8221; column_border_width=&#8221;none&#8221; column_border_style=&#8221;solid&#8221; bg_image_animation=&#8221;none&#8221;][vc_widget_sidebar enable_sticky=&#8221;true&#8221; sidebar_id=&#8221;blog-sidebar&#8221;][\/vc_column][\/vc_row]\n","protected":false},"excerpt":{"rendered":"<p>Imagine the earth would be a perfect sphere and around this sphere runs a band at the equator, directly on the sphere. The band is now cut at one point and a piece of band 3 m long is inserted. In a miraculous way, the band rises evenly over the equator and floats perfectly above it. <\/p>\n","protected":false},"author":3,"featured_media":2116,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[22],"tags":[],"class_list":{"0":"post-2859","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-facts"},"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Paradoxical perimeter - www.bravecroc.de<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.bravecroc.de\/en\/paradoxer-umfang\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Paradoxical perimeter - www.bravecroc.de\" \/>\n<meta property=\"og:description\" content=\"Imagine the earth would be a perfect sphere and around this sphere runs a band at the equator, directly on the sphere. The band is now cut at one point and a piece of band 3 m long is inserted. 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