{"id":1467,"date":"2025-06-14T20:55:49","date_gmt":"2025-06-14T11:55:49","guid":{"rendered":"https:\/\/daba-no-heya.com\/?p=1467"},"modified":"2025-06-14T20:55:49","modified_gmt":"2025-06-14T11:55:49","slug":"post-1467","status":"publish","type":"post","link":"https:\/\/daba-no-heya.com\/?p=1467","title":{"rendered":"\u7403\u306e\u8868\u9762\u7a4d\u3092\u6c42\u3081\u308b"},"content":{"rendered":"\n<p>\u307e\u305a\u3001\u534a\u5f84$r$\u306e\u7403\u306b\u3064\u3044\u3066\u3001\u6975\u5ea7\u6a19\u8868\u793a\u3092\u7528\u3044\u3066\u5fae\u5c0f\u306a\u8868\u9762\u7a4d$dS$\u3092\u6c42\u3081\u307e\u3059\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"651\" height=\"638\" src=\"https:\/\/daba-no-heya.com\/wp-content\/uploads\/2025\/06\/sphere.png\" alt=\"\" class=\"wp-image-1472\" srcset=\"https:\/\/daba-no-heya.com\/wp-content\/uploads\/2025\/06\/sphere.png 651w, https:\/\/daba-no-heya.com\/wp-content\/uploads\/2025\/06\/sphere-300x294.png 300w\" sizes=\"auto, (max-width: 651px) 100vw, 651px\" \/><\/figure>\n\n\n\n<p>\u534a\u5f84$r$\u306e\u5186\u5468\u306e\u9577\u3055\u306f$2\\pi r$\u3067\u3001\u3053\u306e\u3046\u3061$\\theta$ (rad)\u306e\u5f27\u306e\u9577\u3055\u306f<\/p>\n\n\n\n<p>$$2\\pi r\\cdot\\frac{\\theta}{2\\pi}=r\\theta$$<\/p>\n\n\n\n<p>\u3053\u306e\u3053\u3068\u3088\u308a$dS$\u306e$\\theta$\u65b9\u5411\u306e\u9577\u3055\u306f$rd\\theta$\u3001$\\phi$\u65b9\u5411\u306e\u9577\u3055\u306f$r\\sin\\theta d\\phi$\u306b\u306a\u308b\u306e\u3067\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>dS&amp;=rd\\theta\\cdot r\\sin\\theta d\\phi \\\\<br>&amp;=r^2\\sin\\theta d\\theta d\\phi<br>\\end{align}<br>$$<\/p>\n\n\n\n<p>\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$dS$\u3092\u9762\u7a4d\u5206\u3059\u308c\u3070\u7403\u306e\u8868\u9762\u7a4d\u304c\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>\\int_S dS&amp;=\\int_0^{2\\pi}\\left(\\int_0^\\pi r^2 \\sin\\theta d\\theta \\right) d\\phi \\\\<br>&amp;=r^2 \\int_0^{2\\pi}\\left(\\int_0^\\pi \\sin\\theta d\\theta \\right) d\\phi<br>\\end{align}<br>$$<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>\\int_0^\\pi\\sin\\theta d\\theta&amp;=\\left[ -\\cos\\theta \\right]_0^\\pi \\\\<br>&amp;=-\\cos\\pi+\\cos 0 \\\\<br>&amp;=1+1 \\\\<br>&amp;=2<br>\\end{align}<br>$$<\/p>\n\n\n\n<p>\u3088\u308a\u3001<\/p>\n\n\n\n<p>$$<br>\\begin{align}<br>\\int_S dS&amp;=r^2\\int_0^{2\\pi}\\left(\\int_0^\\pi \\sin\\theta d\\theta \\right) d\\phi \\\\<br>&amp;=r^2\\int_0^{2\\pi}2d\\phi \\\\<br>&amp;=4\\pi r^2<br>\\end{align}<br>$$<\/p>\n\n\n\n<p>\u3057\u305f\u304c\u3063\u3066\u3001\u534a\u5f84$r$\u306e\u7403\u306e\u8868\u9762\u7a4d\u306f$4\\pi r^2$\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u307e\u305a\u3001\u534a\u5f84$r$\u306e\u7403\u306b\u3064\u3044\u3066\u3001\u6975\u5ea7\u6a19\u8868\u793a\u3092\u7528\u3044\u3066\u5fae\u5c0f\u306a\u8868\u9762\u7a4d$dS$\u3092\u6c42\u3081\u307e\u3059\u3002 \u534a\u5f84$r$\u306e\u5186\u5468\u306e\u9577\u3055\u306f$2\\pi r$\u3067\u3001\u3053\u306e\u3046\u3061$\\theta$ (rad)\u306e\u5f27\u306e\u9577\u3055\u306f $$2\\pi r\\cdot\\frac{\\th [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30],"tags":[],"class_list":["post-1467","post","type-post","status-publish","format-standard","hentry","category-30"],"_links":{"self":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1467","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1467"}],"version-history":[{"count":7,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1467\/revisions"}],"predecessor-version":[{"id":1477,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=\/wp\/v2\/posts\/1467\/revisions\/1477"}],"wp:attachment":[{"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1467"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1467"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/daba-no-heya.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1467"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}