{"id":216,"date":"2023-12-09T22:06:20","date_gmt":"2023-12-09T22:06:20","guid":{"rendered":"https:\/\/artchery.org\/wordpress\/?page_id=216"},"modified":"2024-09-28T20:20:15","modified_gmt":"2024-09-28T20:20:15","slug":"aesthetics-geometry-and-the-yumi","status":"publish","type":"page","link":"https:\/\/artchery.org\/wordpress\/index.php\/aesthetics-geometry-and-the-yumi\/","title":{"rendered":"Aesthetics, Geometry and the Yumi"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"216\" class=\"elementor elementor-216\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f005e18 e-con-full e-flex e-con e-parent\" data-id=\"f005e18\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;,&quot;background_background&quot;:&quot;classic&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f067301 elementor-widget__width-inherit elementor-widget elementor-widget-heading\" data-id=\"f067301\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.18.0 - 08-12-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Aesthetics, Geometry and the Yumi<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-39c6cbe e-flex e-con-boxed e-con e-parent\" data-id=\"39c6cbe\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d941bac elementor-widget__width-inherit elementor-widget elementor-widget-text-editor\" data-id=\"d941bac\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.18.0 - 08-12-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><b>During the 2019 seminar in South Carolina, Hashimoto sensei forwarded to me an enigmatic note, shown in Fig. 1.\u00a0 It was a brief review of the Golden Ratio. An attached memo said that it \u201crefers to the proportions of the yumi.\u201d I followed his hint and explored the manifestations of the Golden Ratio in the proportions and the shape of a yumi. My main results are highlighted below. The <a href=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Aesthetics_geometry_and_the_yumi.pdf\">full article<\/a> gives the mathematical and experimental details.<\/b><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8595e04 elementor-widget elementor-widget-image\" data-id=\"8595e04\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.18.0 - 08-12-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"294\" height=\"300\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Hashimoto-note-294x300.jpg\" class=\"attachment-medium size-medium wp-image-247\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Hashimoto-note-294x300.jpg 294w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Hashimoto-note-1002x1024.jpg 1002w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Hashimoto-note-768x785.jpg 768w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Hashimoto-note.jpg 1131w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 1:  The original note from Hashimoto sensei.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-78d3d9d elementor-widget elementor-widget-heading\" data-id=\"78d3d9d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The Golden Ratio:  A mathematical expression of aesthetics<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5789181 elementor-widget elementor-widget-text-editor\" data-id=\"5789181\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>In the fifth century BC, the Greek sculptor and mathematician Phidias proposed the division of a line segment into two with &#8220;the most beautiful&#8221; proportions.\u00a0 As seen in Fig. 2, this division defines not two, but three lengths, in the descending order<\/p><ul><li>a+b &#8211; the total length,<\/li><li>a &#8211; the length of the greater segment,<\/li><li>b &#8211; the length of the lesser segment.<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1ad2bdb elementor-widget elementor-widget-image\" data-id=\"1ad2bdb\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"768\" height=\"88\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/golden-ratio-768x88.jpg\" class=\"attachment-medium_large size-medium_large wp-image-255\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/golden-ratio-768x88.jpg 768w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/golden-ratio-300x34.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/golden-ratio.jpg 1008w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 2:    Three lengths defined by division of a line segment into two.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-2d67b9e e-flex e-con-boxed e-con e-parent\" data-id=\"2d67b9e\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1fa7504 elementor-widget elementor-widget-text-editor\" data-id=\"1fa7504\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Phidias imposed a certain symmetry between these lengths: The total (<i>a+b<\/i>) stands in relation to the greater (<i>a<\/i>), the same as the greater (<i>a<\/i>) to the lesser (<i>b<\/i>). Stated mathematically, the ratios <i>(a+b)\/a<\/i> and <i>a\/b<\/i> must be equal to the same number: the Golden Ratio \u03d5:<\/p><p><i>(a+b)\/a = a\/b = <\/i>\u03d5 \u2248 1.61803&#8230;<\/p><p>The Golden Ratio is a\u00a0 mathematical form arising from pure aesthetics.<\/p><p>Phidias originally applied the Golden Ratio to set proportions in human figure sculptures of the Parthenon temple. Once released into world culture, the Golden Ratio strongly insinuates itself in artistic and architectural works over the two and a half millennia since Phidias. Here is an example in Kyudo, very much in the original spirit of Phidias: On page 132 of the Kyudo Kyohan, there is an idealized line drawing of Kai. Superimposed upon it, there is the central vertical axis of the Kyudoka, and the three horizontal lines of shoulders, hips and feet, as in the Sanjumonji (three crosses). In the figure, the elevation of the shoulder line above the feet is 76.5 mm, and the elevation of the hip line, 47.5 mm. The ratio of these elevations is 1.611, close to the Golden Ratio \u03d5 \u2248 1.61803&#8230;<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bafeda7 elementor-widget elementor-widget-heading\" data-id=\"bafeda7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Golden Ratio in Yumi <\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-aeef9f4 elementor-widget elementor-widget-text-editor\" data-id=\"aeef9f4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Let\u2019s examine the proportion between yumi lengths above the top of the grip (a), below (b) and total (a+b).<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-d05180d e-flex e-con-boxed e-con e-parent\" data-id=\"d05180d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c587696 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"c587696\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"152\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop-1024x152.jpg\" class=\"attachment-large size-large wp-image-229\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop-1024x152.jpg 1024w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop-300x45.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop-768x114.jpg 768w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop.jpg 1464w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 3: Golden Ratio tested in five Yonsum yumi.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2f106a4 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"2f106a4\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"374\" height=\"249\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop-table.jpg\" class=\"attachment-large size-large wp-image-271\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop-table.jpg 374w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/prop-table-300x200.jpg 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-fc451a8 e-flex e-con-boxed e-con e-parent\" data-id=\"fc451a8\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d0e7126 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"d0e7126\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"89\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/kaniwara1-1024x89.jpg\" class=\"attachment-large size-large wp-image-278\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/kaniwara1-1024x89.jpg 1024w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/kaniwara1-300x26.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/kaniwara1-768x67.jpg 768w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/kaniwara1-1536x133.jpg 1536w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/kaniwara1.jpg 1566w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 4: Kaniwara: an ancient Chinese aesthetics of dividing a line into six segments. Seven white nodes are considered Yang and six black segments are considered Ying.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0d45164 elementor-widget elementor-widget-text-editor\" data-id=\"0d45164\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The table in Fig. 3 shows the measurements of lengths <i>a<\/i> and <i>b<\/i>, performed on five Don Symanski Yonsun yumi. The third and fourth columns report the ratios <i>(a+b)\/a<\/i> and <i>a\/b<\/i>: they all are close to the Golden Ratio \u03d5 =~ 1.61803&#8230; We obtain an even better agreement when we compute geometric means: 1.621 for the third column and 1.613 in the fourth column. Thus, the grip placement according to the Golden Ratio is very nearly realized for the five yumi.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-81bb216 elementor-widget elementor-widget-text-editor\" data-id=\"81bb216\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Was grip placement according to the Golden Ratio consciously articulated by some yumishi long ago?\u00a0 I have no idea.\u00a0 There are other ancient mathematical expressions of aesthetics with closer proximity to Kyudo.\u00a0 Hashimoto sensei shared with me an\u00a0 ancient Chinese aesthetics called &#8220;Kaniwara.&#8221;\u00a0\u00a0 Divide a line segment into six equal portions, illustrated in Fig. 4. The seven endpoints of segments marked by white dots are &#8220;Yang.&#8221;\u00a0 The six intervals between adjacent pairs of endpoints, marked in black, are &#8220;Yin.&#8221;\u00a0 Now look at the bamboo nodes of the yumi in Fig. 5.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ed9817a elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"ed9817a\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"664\" height=\"76\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/firstyumi.jpg\" class=\"attachment-large size-large wp-image-1184\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/firstyumi.jpg 664w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/03\/firstyumi-300x34.jpg 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 5:  White dots are back nodes.  Black dots are belly nodes.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f06e683 elementor-widget elementor-widget-text-editor\" data-id=\"f06e683\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The back of the yumi that faces the target is &#8220;Yang&#8221;, with seven &#8220;Yang&#8221; nodes, also marked by white dots.\u00a0\u00a0 The belly of the yumi facing the archer is &#8220;Yin,&#8221; and halfway between any pair of of &#8220;Yang&#8221; nodes on the back, there are &#8220;Yin&#8221; nodes on the belly, six of them in all.\u00a0 The fourth belly node from the top marks the top of the grip.\u00a0 If all spacing between nodes are equal, then the ratio of lengths above and below the grip is 1.5, not too far from the Golden ratio \u03d5 \u2248 1.61803.\u00a0 In practice, the node spacing increases gradually as you ascend a bamboo stalk.\u00a0 Naturally, yumishi orient the back and belly bamboos in the upward direction, and the ratio of lengths increases somewhat.\u00a0 In practice, the Golden Ratio of length proportions is very nearly achieved.\u00a0 (More on this in the <a href=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Aesthetics_geometry_and_the_yumi.pdf\">full article)<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3f2105b e-flex e-con-boxed e-con e-parent\" data-id=\"3f2105b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-56abc1c elementor-widget elementor-widget-heading\" data-id=\"56abc1c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Curve proportions<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-6132e48 e-flex e-con-boxed e-con e-parent\" data-id=\"6132e48\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-7d4edc6 elementor-widget elementor-widget-text-editor\" data-id=\"7d4edc6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Imagine facing a braced\u00a0 yumi so you gaze along its back.\u00a0\u00a0 In Fig. 6, with the yumi oriented horizontally, you are looking\u00a0 from above.\u00a0 From this perspective, the top and bottom curves are concave. This appears to be a natural choice consistent with most archery traditions everywhere and throughout the ages. The curve containing the grip is concave as well, as if yumishi wanted to impart some extra Ikasu (&#8220;life&#8221;) about the grip. The mathematics of curves dictates that concave and convex curves must alternate, so there must be at least one convex curve above the grip, and at least one other below.\u00a0 The yumi displays a sequence of five curves: concave, convex, concave, convex, concave. Each pair of adjacent curves is connected at the inflection points; in the figure, the approximate positions of the four inflection points are marked by hollow dots.<\/p><p>Just as we examine these proportions of yumi lengths above and below the grip, we examine geometric proportions of the curves in relation to each other.\u00a0 First, we examine the proportions seen in actual yumi.\u00a0 Then we propose a mathematical expression of these proportions which closely reproduces what we see in typical yumi.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-238ff77 e-flex e-con-boxed e-con e-parent\" data-id=\"238ff77\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-2db945d elementor-widget elementor-widget-image\" data-id=\"2db945d\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"818\" height=\"107\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi3.jpg\" class=\"attachment-large size-large wp-image-317\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi3.jpg 818w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi3-300x39.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi3-768x100.jpg 768w\" sizes=\"(max-width: 818px) 100vw, 818px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 6:   The five curves of a yumi, seperated by four inflection points (hollow dots). The length h of the arrow indicates the elevation of a curve midpoint relative to the cord line.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a1f778c elementor-widget elementor-widget-heading\" data-id=\"a1f778c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Consensus Shape of a Well-Proportioned Yumi <\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-95f50d6 elementor-widget elementor-widget-text-editor\" data-id=\"95f50d6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>We quantify yumi curves by their lengths and depths.<\/p><ul><li>The length of a curve is measured by a cloth tape measure hugging the back of the yumi between endpoints.<\/li><li>The depth, or elevation <i>h<\/i> of each curve is the displacement of the curve\u2019s midpoint relative to its chord. The chord between endpoints is realized physically by a connecting thread (see the Fig. 5). We measure the distance from the midpoint of the thread to the back of the yumi. The elevation is assumed positive for convex curves, negative for concave curves.<\/li><\/ul><p>The blue curves in Fig.\u00a0 6 depict individual shapes of the five Don Symanski yumi: Photographs are imported into a graphics program and the blue curves are obtained by tracing along the back bamboo.\u00a0 The red curve represents an &#8220;consensus&#8221; shape,\u00a0 based on averaging the lengths and depths of the curves of\u00a0 the five individual yumi.\u00a0 Three yumi follow this &#8220;average&#8221; shape well. Two are outliers: one is weak above the grip, the other is strong.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f5d3b93 elementor-widget__width-initial elementor-widget elementor-widget-image\" data-id=\"f5d3b93\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"834\" height=\"119\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi4.jpg\" class=\"attachment-large size-large wp-image-916\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi4.jpg 834w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi4-300x43.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/yumi4-768x110.jpg 768w\" sizes=\"(max-width: 834px) 100vw, 834px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 7: Blue curves are individual shapes of five yumi; the red curve is the consensus shape. <\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-035e86d elementor-widget elementor-widget-heading\" data-id=\"035e86d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">The Golden Ratio \"hidden\" in curve proportions<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3b62ab4 elementor-widget elementor-widget-text-editor\" data-id=\"3b62ab4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>A yumi is not mirror symmetric about a vertical axis through the grip.\u00a0\u00a0 Nevertheless we can formulate an analog of mirror symmetry in which curve proportions above the grip are the same as curve proportions below.\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-ab4c295 e-flex e-con-boxed e-con e-parent\" data-id=\"ab4c295\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-4351681 elementor-widget elementor-widget-image\" data-id=\"4351681\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"984\" height=\"211\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/mirr_symm_prop.jpg\" class=\"attachment-large size-large wp-image-1459\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/mirr_symm_prop.jpg 984w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/mirr_symm_prop-300x64.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/mirr_symm_prop-768x165.jpg 768w\" sizes=\"(max-width: 984px) 100vw, 984px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 8:  \"Mirror symmetry\" of proportions between curve lengths.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0923692 elementor-widget elementor-widget-text-editor\" data-id=\"0923692\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Figure 8 visually summarizes this scheme of &#8220;mirror symmetric&#8221; curve proportions.\u00a0\u00a0 As in Fig. 6, the hollow dots mark inflection points separating curves and the black dot marks the top of the grip.\u00a0 The symbol l denotes the length of the bottom concave curve.\u00a0 There is a progressive increase of lengths by a common factor R as we ascend from the bottom concave curve to the top convex curve.\u00a0 The progressive increase does not extend all the way to the top concave curve:\u00a0 It&#8217;s length is not R<sup>4<\/sup>l but\u00a0 rather R<sup>2<\/sup>l.\u00a0 In this way we impose a mirror symmetry of proportions between the top two and bottom two curves:\u00a0 The lower convex curve is longer than the bottom concave curve by the factor R , and so is the upper convex curve longer than the top concave curve by the same factor R as well. \u00a0 The upper convex and concave curves are longer than their lower counterparts by the factor R<sup>2<\/sup>.\u00a0 The mirror symmetry of curve proportions above and below also dictates that the length of middle concave curve above the grip is also R<sup>2<\/sup> times the length below.<\/p><p>The factor R is related to the Golden ratio \u03d5:\u00a0 The proceeding construction implies that the total length a above the grip is R<sup>2<\/sup> times the length b below. In this way we identify R<sup>2<\/sup> with \u03d5, so<\/p><p>R<sup>2<\/sup> = a\/b = \u03d5,<\/p><p>and then<\/p><p>R = \u03d5<sup>1\/2<\/sup> \u2248 1.27202.<\/p><p>The proportions of curve lengths are now uniquely determined.<\/p><p>Assigning curve depths is more subtle.\u00a0 Details are discussed in the <a href=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/Aesthetics_geometry_and_the_yumi.pdf\">full article<\/a>. In particular, the upper concave and convex curves are geometrically similar to their lower counterparts.\u00a0 The &#8220;above&#8221; depths are larger than the &#8220;below&#8221; depths by the Golden Ratio.\u00a0 After imposing\u00a0 symmetry constraints on the depths, there is still freedom to choose the depth of the big convex curve above the grip and the (small) depth of the middle curve.\u00a0\u00a0 Two further common sense requirements limit the choices:\u00a0\u00a0 (i)\u00a0 With the tsuru oriented horizontally as in Fig. 6, the yumi should be above the tsuru along its whole length.\u00a0 The tsuru should not wrap itself on either strike plate.\u00a0 (ii)\u00a0 The brace height (Ha) should be close to the standard 15 cm.\u00a0 Given all the curve lengths and depths, we can geometrically construct the yumi shape.\u00a0\u00a0<\/p><p>The green\u00a0 curve in the top panel of Fig. 9 is a shape with the &#8220;mirror symmetry&#8221; proportions as described above.\u00a0 The red curve is the &#8220;consensus&#8221; shape, the same as in Fig. 7.\u00a0 The bottom panel is a photograph of a Shibata XX yumi after restoration by Don Symanski.\u00a0 He offers it as an example of a well proportioned yumi.\u00a0 The green curve representing the &#8220;mirror symmetry&#8221; shape tracks the Shibata yumi over the whole length of the top limb, and for some ways along the bottom as well.\u00a0 The divergence of the bottom two curves raises a significant point: For the Shibata yumi and for most yumi in general, the tsuru is not tangent to the yumi limb at the bottom tip.\u00a0\u00a0 Maybe yumishi don&#8217;t want Tsurune happening at both tips.\u00a0 I don&#8217;t know.\u00a0 But I do know that the tangency of the mirror symmetry shape at the bottom tip to the tsuru follows from imposing the same curve proportions below the grip as above.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-62f6424 e-flex e-con-boxed e-con e-parent\" data-id=\"62f6424\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-1fe98c2 elementor-widget elementor-widget-image\" data-id=\"1fe98c2\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1009\" height=\"367\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/compare_shapes.jpg\" class=\"attachment-large size-large wp-image-1526\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/compare_shapes.jpg 1009w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/compare_shapes-300x109.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/compare_shapes-768x279.jpg 768w\" sizes=\"(max-width: 1009px) 100vw, 1009px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 9: Top panel:  Comparison of the \"mirror symmetry\" shape (green curve) with the \"consensus\" shape (red curve.  Bottom panel:  Comparison of the mirror symmetry shape with the Shibata XX yumi.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-544c834 e-flex e-con-boxed e-con e-parent\" data-id=\"544c834\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-6979c3b elementor-widget elementor-widget-text-editor\" data-id=\"6979c3b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Figure 10 is a photograph of a Rokusun yumi made by the author.\u00a0 Its design shape\u00a0 embodies &#8220;broken mirror symmetry.&#8221;\u00a0 Length proportions of curves stay the same.\u00a0 Only curve elevations\u00a0 change:\u00a0 By straightening the bottom curve, the tsuru is lifted off of the bottom strike plate.\u00a0 The middle curve is made deeper in an attempt to preserve the brace height (Ha).<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0b889c7 elementor-widget elementor-widget-image\" data-id=\"0b889c7\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t<figure class=\"wp-caption\">\n\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"122\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Roku-mirr-1024x122.jpg\" class=\"attachment-large size-large wp-image-1527\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Roku-mirr-1024x122.jpg 1024w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Roku-mirr-300x36.jpg 300w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Roku-mirr-768x91.jpg 768w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2024\/04\/Roku-mirr.jpg 1087w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t<figcaption class=\"widget-image-caption wp-caption-text\">Fig. 10:  Comparison of the \"mirror symmetry\" shape with a Rokusun made by the author.<\/figcaption>\n\t\t\t\t\t\t\t\t\t\t<\/figure>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-494aa0c e-flex e-con-boxed e-con e-parent\" data-id=\"494aa0c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3ed92a9 elementor-widget elementor-widget-heading\" data-id=\"3ed92a9\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Zanshin<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7ec6962 elementor-widget elementor-widget-text-editor\" data-id=\"7ec6962\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>The aesthetics of the yumi is expressed by its realizations of symmmetries.\u00a0 In the broadest sense, symmetries refer to aspects of phenomena which remain the same under a change of perspective. Is this why we so readily respond to to them, our hearts recognizing them before our minds catch up?\u00a0 It is tempting to construe symmetries as anchors or reference points in what the meditation teacher Ryushin sensei calls &#8220;radical impermanence.&#8221; \u00a0 What is that?\u00a0 It is not &#8220;things change.&#8221;\u00a0 Rather, there are no things, only processes.\u00a0 None are complete unto themselves because they all co-arise. \u00a0 There are no anchors or reference points.\u00a0 And yet, a feeling and longing remain.\u00a0<\/p><p>The beauty of Don Symanski&#8217;s restoration of the Shibata XX yumi is not mathematical perfection.\u00a0 It is unlikely that either yumishi whose hands shaped it impressed any conscious let alone mathematical scheme of symmetry upon it.\u00a0 It stands in proximity to mathematical symmetry, but not quite.\u00a0 I&#8217;ve heard it said (I wish I could rmember the source):\u00a0 Artists honor symmetries not in their perfection, but in the subtle breach<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-1562acb e-flex e-con-boxed e-con e-parent\" data-id=\"1562acb\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\" data-core-v316-plus=\"true\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c3e692f elementor-widget elementor-widget-image\" data-id=\"c3e692f\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"547\" height=\"32\" src=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/watakuri.jpg\" class=\"attachment-large size-large wp-image-80\" alt=\"\" srcset=\"https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/watakuri.jpg 547w, https:\/\/artchery.org\/wordpress\/wp-content\/uploads\/2023\/12\/watakuri-300x18.jpg 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Aesthetics, Geometry and the Yumi During the 2019 seminar in South Carolina, Hashimoto sensei forwarded to me an enigmatic note, shown in Fig. 1.\u00a0 It was a brief review of the Golden Ratio. An attached memo said that it \u201crefers to the proportions of the yumi.\u201d I followed his hint and explored the manifestations of &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/artchery.org\/wordpress\/index.php\/aesthetics-geometry-and-the-yumi\/\"> <span class=\"screen-reader-text\">Aesthetics, Geometry and the Yumi<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"no-sidebar","site-content-layout":"","ast-site-content-layout":"full-width-container","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-216","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages\/216","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/comments?post=216"}],"version-history":[{"count":300,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages\/216\/revisions"}],"predecessor-version":[{"id":2733,"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/pages\/216\/revisions\/2733"}],"wp:attachment":[{"href":"https:\/\/artchery.org\/wordpress\/index.php\/wp-json\/wp\/v2\/media?parent=216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}