{"id":28769,"date":"2023-09-12T19:56:44","date_gmt":"2023-09-12T12:56:44","guid":{"rendered":"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi"},"modified":"2023-09-12T19:56:44","modified_gmt":"2023-09-12T12:56:44","slug":"hang-so-la-gi","status":"publish","type":"post","link":"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi","title":{"rendered":"T\u00ecm hi\u1ec3u v\u1ec1 h\u1eb1ng s\u1ed1 v\u00e0 nh\u1eefng v\u00ed d\u1ee5 minh ho\u1ea1"},"content":{"rendered":"<p>H\u1eb1ng s\u1ed1 l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb kh\u00f4ng thay \u0111\u1ed5i trong to\u00e1n h\u1ecdc v\u00e0 khoa h\u1ecdc t\u1ef1 nhi\u00ean. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u1ecbnh ngh\u0129a c\u00e1c quy t\u1eafc v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh trong c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c nhau. H\u1eb1ng s\u1ed1 gi\u00fap ch\u00fang ta hi\u1ec3u v\u00e0 d\u1ef1 \u0111o\u00e1n c\u00e1c hi\u1ec7n t\u01b0\u1ee3ng t\u1ed3n t\u1ea1i xung quanh ch\u00fang ta.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6acda1902a2c0\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-6acda1902a2c0\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#1_Hang_so_la_gi\" title=\"1. H\u1eb1ng s\u1ed1 l\u00e0 g\u00ec?\">1. H\u1eb1ng s\u1ed1 l\u00e0 g\u00ec?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Vi_du_ve_hang_so\" title=\"V\u00ed d\u1ee5 v\u1ec1 h\u1eb1ng s\u1ed1:\">V\u00ed d\u1ee5 v\u1ec1 h\u1eb1ng s\u1ed1:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#2_Hang_so_toan_hoc_va_vi_du\" title=\"2. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.\">2. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Vi_du_ve_hang_so_toan_hoc\" title=\"V\u00ed d\u1ee5 v\u1ec1 h\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc:\">V\u00ed d\u1ee5 v\u1ec1 h\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#3_Hang_so_toan_hoc_va_vi_du\" title=\"3. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.\">3. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Hang_so_Euler_e\" title=\"H\u1eb1ng s\u1ed1 Euler (e)\">H\u1eb1ng s\u1ed1 Euler (e)<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Cong_thuc_tinh_lai_kep\" title=\"C\u00f4ng th\u1ee9c t\u00ednh l\u00e3i k\u00e9p:\">C\u00f4ng th\u1ee9c t\u00ednh l\u00e3i k\u00e9p:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#4_Hang_so_vat_ly_va_vi_du\" title=\"4. H\u1eb1ng s\u1ed1 v\u1eadt l\u00fd v\u00e0 v\u00ed d\u1ee5.\">4. H\u1eb1ng s\u1ed1 v\u1eadt l\u00fd v\u00e0 v\u00ed d\u1ee5.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Toc_do_anh_sang_trong_chan_khong_c\" title=\"T\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng trong ch\u00e2n kh\u00f4ng (c)\">T\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng trong ch\u00e2n kh\u00f4ng (c)<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Cong_thuc_E_mc2\" title=\"C\u00f4ng th\u1ee9c E = mc^2:\">C\u00f4ng th\u1ee9c E = mc^2:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#5_Ung_dung_cua_hang_so_trong_doi_song_va_nghien_cuu_khoa_hoc\" title=\"5. \u1ee8ng d\u1ee5ng c\u1ee7a h\u1eb1ng s\u1ed1 trong \u0111\u1eddi s\u1ed1ng v\u00e0 nghi\u00ean c\u1ee9u khoa h\u1ecdc.\">5. \u1ee8ng d\u1ee5ng c\u1ee7a h\u1eb1ng s\u1ed1 trong \u0111\u1eddi s\u1ed1ng v\u00e0 nghi\u00ean c\u1ee9u khoa h\u1ecdc.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#6_So_%CF%80_va_%CF%86_-_nhung_hang_so_quan_trong_trong_toan_hoc_va_kien_truc\" title=\"6. S\u1ed1 \u03c0 v\u00e0 \u03c6 &#8211; nh\u1eefng h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 ki\u1ebfn tr\u00fac.\">6. S\u1ed1 \u03c0 v\u00e0 \u03c6 &#8211; nh\u1eefng h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 ki\u1ebfn tr\u00fac.<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#So_Pi_%CF%80\" title=\"S\u1ed1 Pi (\u03c0)\">S\u1ed1 Pi (\u03c0)<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Cong_thuc_tinh_dien_tich_cua_mot_duong_tron\" title=\"C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n:\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#So_Vang_%CF%86\" title=\"S\u1ed1 V\u00e0ng (\u03c6)\">S\u1ed1 V\u00e0ng (\u03c6)<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/hang-so-la-gi\/#Vi_du_ve_su_dung_so_Vang_trong_kien_truc\" title=\"V\u00ed d\u1ee5 v\u1ec1 s\u1eed d\u1ee5ng s\u1ed1 V\u00e0ng trong ki\u1ebfn tr\u00fac:\">V\u00ed d\u1ee5 v\u1ec1 s\u1eed d\u1ee5ng s\u1ed1 V\u00e0ng trong ki\u1ebfn tr\u00fac:<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"1_Hang_so_la_gi\"><\/span>1. H\u1eb1ng s\u1ed1 l\u00e0 g\u00ec?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>H\u1eb1ng s\u1ed1 l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb kh\u00f4ng thay \u0111\u1ed5i trong to\u00e0n b\u1ed9 qu\u00e1 tr\u00ecnh t\u00ednh to\u00e1n ho\u1eb7c ph\u00e2n t\u00edch. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u1ea1i di\u1ec7n cho m\u1ed9t gi\u00e1 tr\u1ecb c\u1ed1 \u0111\u1ecbnh v\u00e0 kh\u00f4ng thay \u0111\u1ed5i trong m\u1ed9t h\u1ec7 th\u1ed1ng hay m\u00f4 h\u00ecnh n\u00e0o \u0111\u00f3. H\u1eb1ng s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau nh\u01b0 to\u00e1n h\u1ecdc, v\u1eadt l\u00fd, k\u1ef9 thu\u1eadt v\u00e0 c\u00e1c ng\u00e0nh khoa h\u1ecdc kh\u00e1c.<\/p>\n<p>H\u1eb1ng s\u1ed1 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n b\u1eb1ng c\u00e1c k\u00fd hi\u1ec7u ho\u1eb7c bi\u1ec3u th\u1ee9c c\u1ee5 th\u1ec3 v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb x\u00e1c \u0111\u1ecbnh. M\u1ed9t s\u1ed1 h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 v\u1eadt l\u00fd bao g\u1ed3m pi (\u03c0), e, c (t\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng), G (h\u1eb1ng s\u1ed1 Gravitational) v\u00e0 Avogadro&#8217;s number.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vi_du_ve_hang_so\"><\/span>V\u00ed d\u1ee5 v\u1ec1 h\u1eb1ng s\u1ed1:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>H\u1eb1ng s\u1ed1 Planck (h): \u0110\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 &#8220;h&#8221; v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 6.62607015 \u00d7 10^-34 joule-seconds. H\u1eb1ng s\u1ed1 n\u00e0y xu\u1ea5t hi\u1ec7n trong c\u01a1 s\u1edf c\u1ee7a l\u00fd thuy\u1ebft c\u01a1 quan t\u1eed.<\/li>\n<li>H\u1eb1ng s\u1ed1 t\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng (c): \u0110\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 &#8220;c&#8221; v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 299,792,458 m\u00e9t\/gi\u00e2y. H\u1eb1ng s\u1ed1 n\u00e0y \u0111\u1ea1i di\u1ec7n cho t\u1ed1c \u0111\u1ed9 c\u1ef1c \u0111\u1ea1i m\u00e0 \u00e1nh s\u00e1ng c\u00f3 th\u1ec3 di chuy\u1ec3n trong ch\u00e2n kh\u00f4ng.<\/li>\n<li>H\u1eb1ng s\u1ed1 Avogadro (NA): \u0110\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 &#8220;NA&#8221; v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 6.02214076 \u00d7 10^23 mol^-1. H\u1eb1ng s\u1ed1 n\u00e0y \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 bi\u1ec3u di\u1ec5n s\u1ed1 l\u01b0\u1ee3ng c\u00e1c ph\u00e2n t\u1eed ho\u1eb7c nguy\u00ean t\u1eed trong m\u1ed9t mol c\u1ee7a m\u1ed9t ch\u1ea5t.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"2_Hang_so_toan_hoc_va_vi_du\"><\/span>2. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc l\u00e0 nh\u1eefng gi\u00e1 tr\u1ecb kh\u00f4ng thay \u0111\u1ed5i trong c\u00e1c ph\u00e9p t\u00ednh to\u00e1n v\u00e0 c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc. Ch\u00fang \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 bi\u1ec3u di\u1ec5n m\u1ed9t gi\u00e1 tr\u1ecb c\u1ed1 \u0111\u1ecbnh v\u00e0 kh\u00f4ng thay \u0111\u1ed5i trong c\u00e1c ph\u00e9p t\u00ednh hay c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vi_du_ve_hang_so_toan_hoc\"><\/span>V\u00ed d\u1ee5 v\u1ec1 h\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>S\u1ed1 Pi (\u03c0): S\u1ed1 Pi l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 kh\u00f4ng \u00e2m \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 \u03c0 v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 3.14159. N\u00f3 xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc v\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch, chu vi c\u1ee7a c\u00e1c h\u00ecnh tr\u00f2n v\u00e0 li\u00ean quan \u0111\u1ebfn c\u00e1c kh\u00e1i ni\u1ec7m nh\u01b0 b\u00e1n k\u00ednh, \u0111\u01b0\u1eddng k\u00ednh.<\/li>\n<li>S\u1ed1 Euler (e): S\u1ed1 Euler l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 kh\u00f4ng \u00e2m \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 e v\u00e0 c\u00f3 gi\u00e1 tr\u1ecb x\u1ea5p x\u1ec9 2.71828. N\u00f3 xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc nh\u01b0 ph\u00e2n t\u00edch s\u1ed1, \u0111\u1ea1i s\u1ed1, x\u00e1c su\u1ea5t v\u00e0 l\u00fd thuy\u1ebft \u0111\u1ed3 th\u1ecb.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"3_Hang_so_toan_hoc_va_vi_du\"><\/span>3. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"3. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/tim_hieu_ve_hang_so_va_nhung_vi_du_minh_hoa.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"3. H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u00ed d\u1ee5.\"\/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Hang_so_Euler_e\"><\/span>H\u1eb1ng s\u1ed1 Euler (e)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>H\u1eb1ng s\u1ed1 Euler, k\u00fd hi\u1ec7u l\u00e0 e, l\u00e0 m\u1ed9t trong nh\u1eefng h\u1eb1ng s\u1ed1 quan tr\u1ecdng nh\u1ea5t trong to\u00e1n h\u1ecdc. N\u00f3 \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 gi\u1edbi h\u1ea1n c\u1ee7a t\u1ed5ng (1 + 1\/n)^n khi n ti\u1ebfn t\u1edbi v\u00f4 c\u00f9ng. Gi\u00e1 tr\u1ecb c\u1ee7a h\u1eb1ng s\u1ed1 Euler x\u1ea5p x\u1ec9 kho\u1ea3ng 2.71828. H\u1eb1ng s\u1ed1 n\u00e0y xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u l\u0129nh v\u1ef1c c\u1ee7a to\u00e1n h\u1ecdc, nh\u01b0 t\u00ednh to\u00e1n l\u00e3i k\u00e9p, ph\u00e2n r\u00e3 radioactiv v\u00e0 c\u00e1c c\u00f4ng th\u1ee9c li\u00ean quan \u0111\u1ebfn chu\u1ed7i s\u1ed1.<\/p>\n<p>V\u00ed d\u1ee5: Trong c\u00f4ng th\u1ee9c t\u00ednh l\u00e3i k\u00e9p, ta s\u1eed d\u1ee5ng h\u1eb1ng s\u1ed1 Euler \u0111\u1ec3 t\u00ednh l\u00e3i su\u1ea5t li\u00ean t\u1ee5c theo th\u1eddi gian. C\u00f4ng th\u1ee9c n\u00e0y c\u00f3 d\u1ea1ng A = P*e^(rt), trong \u0111\u00f3 A l\u00e0 s\u1ed1 ti\u1ec1n cu\u1ed1i c\u00f9ng sau t th\u1eddi gian, P l\u00e0 s\u1ed1 ti\u1ec1n ban \u0111\u1ea7u, r l\u00e0 l\u00e3i su\u1ea5t h\u00e0ng n\u0103m v\u00e0 t l\u00e0 th\u1eddi gian t\u00ednh b\u1eb1ng n\u0103m.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Cong_thuc_tinh_lai_kep\"><\/span>C\u00f4ng th\u1ee9c t\u00ednh l\u00e3i k\u00e9p:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>A: S\u1ed1 ti\u1ec1n cu\u1ed1i c\u00f9ng sau t th\u1eddi gian<\/li>\n<li>P: S\u1ed1 ti\u1ec1n ban \u0111\u1ea7u<\/li>\n<li>e: H\u1eb1ng s\u1ed1 Euler<\/li>\n<li>r: L\u00e3i su\u1ea5t h\u00e0ng n\u0103m<\/li>\n<li>t: Th\u1eddi gian t\u00ednh b\u1eb1ng n\u0103m<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"4_Hang_so_vat_ly_va_vi_du\"><\/span>4. H\u1eb1ng s\u1ed1 v\u1eadt l\u00fd v\u00e0 v\u00ed d\u1ee5.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Toc_do_anh_sang_trong_chan_khong_c\"><\/span>T\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng trong ch\u00e2n kh\u00f4ng (c)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>T\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng trong ch\u00e2n kh\u00f4ng, k\u00fd hi\u1ec7u l\u00e0 c, l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 v\u1eadt l\u00fd quan tr\u1ecdng. Gi\u00e1 tr\u1ecb c\u1ee7a t\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng trong ch\u00e2n kh\u00f4ng \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh l\u00e0 kho\u1ea3ng 299,792,458 m\u00e9t\/gi\u00e2y. H\u1eb1ng s\u1ed1 n\u00e0y c\u00f3 vai tr\u00f2 quan tr\u1ecdng trong c\u00e1c l\u0129nh v\u1ef1c nh\u01b0 v\u1eadt l\u00fd h\u1ea1t nh\u00e2n, \u0111i\u1ec7n t\u1eeb v\u00e0 thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i.<\/p>\n<p>V\u00ed d\u1ee5: Trong thuy\u1ebft t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a Albert Einstein, t\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng trong ch\u00e2n kh\u00f4ng \u0111\u01b0\u1ee3c coi l\u00e0 gi\u1edbi h\u1ea1n t\u1ed1i \u0111a m\u00e0 b\u1ea5t k\u1ef3 v\u1eadt th\u1ec3 n\u00e0o c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng c\u00f3 th\u1ec3 di chuy\u1ec3n. C\u00f4ng th\u1ee9c E = mc^2 cho bi\u1ebft r\u1eb1ng n\u0103ng l\u01b0\u1ee3ng (E) c\u1ee7a m\u1ed9t v\u1eadt c\u00f3 kh\u1ed1i l\u01b0\u1ee3ng (m) li\u00ean quan tr\u1ef1c ti\u1ebfp \u0111\u1ebfn b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a t\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng (c).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Cong_thuc_E_mc2\"><\/span>C\u00f4ng th\u1ee9c E = mc^2:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>E: N\u0103ng l\u01b0\u1ee3ng<\/li>\n<li>m: Kh\u1ed1i l\u01b0\u1ee3ng<\/li>\n<li>c: T\u1ed1c \u0111\u1ed9 \u00e1nh s\u00e1ng trong ch\u00e2n kh\u00f4ng<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"5_Ung_dung_cua_hang_so_trong_doi_song_va_nghien_cuu_khoa_hoc\"><\/span>5. \u1ee8ng d\u1ee5ng c\u1ee7a h\u1eb1ng s\u1ed1 trong \u0111\u1eddi s\u1ed1ng v\u00e0 nghi\u00ean c\u1ee9u khoa h\u1ecdc.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>H\u1eb1ng s\u1ed1 to\u00e1n h\u1ecdc v\u00e0 v\u1eadt l\u00fd c\u00f3 r\u1ea5t nhi\u1ec1u \u1ee9ng d\u1ee5ng trong \u0111\u1eddi s\u1ed1ng v\u00e0 nghi\u00ean c\u1ee9u khoa h\u1ecdc. Ch\u00fang \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 th\u1ef1c t\u1ebf v\u00e0 x\u00e2y d\u1ef1ng c\u00e1c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc cho hi\u1ec3u bi\u1ebft v\u1ec1 th\u1ebf gi\u1edbi xung quanh ch\u00fang ta.<\/p>\n<p>V\u00ed d\u1ee5: H\u1eb1ng s\u1ed1 Pi (\u03c0) \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong t\u00ednh to\u00e1n h\u00ecnh h\u1ecdc, t\u00ednh di\u1ec7n t\u00edch v\u00e0 chu vi c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng tr\u00f2n. N\u00f3 c\u0169ng xu\u1ea5t hi\u1ec7n trong c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t v\u00e0 th\u1ec3 t\u00edch c\u1ee7a c\u00e1c h\u00ecnh c\u1ea7u.<\/p>\n<p>C\u00e1c nh\u00e0 khoa h\u1ecdc c\u0169ng s\u1eed d\u1ee5ng c\u00e1c h\u1eb1ng s\u1ed1 \u0111\u1ec3 x\u00e2y d\u1ef1ng c\u00e1c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc cho hi\u1ec3u bi\u1ebft v\u1ec1 t\u1ef1 nhi\u00ean v\u00e0 v\u0169 tr\u1ee5. V\u00ed d\u1ee5, H\u1eb1ng s\u1ed1 Planck (h) \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong l\u0129nh v\u1ef1c c\u01a1 quan t\u1eed \u0111\u1ec3 m\u00f4 t\u1ea3 l\u01b0\u1ee3ng t\u1eed ho\u00e1 c\u1ee7a n\u0103ng l\u01b0\u1ee3ng.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"6_So_%CF%80_va_%CF%86_-_nhung_hang_so_quan_trong_trong_toan_hoc_va_kien_truc\"><\/span>6. S\u1ed1 \u03c0 v\u00e0 \u03c6 &#8211; nh\u1eefng h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 ki\u1ebfn tr\u00fac.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"6. S\u1ed1 \u03c0 v\u00e0 \u03c6 - nh\u1eefng h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 ki\u1ebfn tr\u00fac.\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/tim_hieu_ve_hang_so_va_nhung_vi_du_minh_hoa-1.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"6. S\u1ed1 \u03c0 v\u00e0 \u03c6 - nh\u1eefng h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 ki\u1ebfn tr\u00fac.\"\/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"So_Pi_%CF%80\"><\/span>S\u1ed1 Pi (\u03c0)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 Pi, k\u00fd hi\u1ec7u l\u00e0 \u03c0, l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc. N\u00f3 \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 t\u1ec9 l\u1ec7 gi\u1eefa chu vi c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a n\u00f3. Gi\u00e1 tr\u1ecb c\u1ee7a s\u1ed1 Pi x\u1ea5p x\u1ec9 kho\u1ea3ng 3.14159. S\u1ed1 Pi xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u c\u00f4ng th\u1ee9c v\u00e0 t\u00ednh to\u00e1n li\u00ean quan \u0111\u1ebfn h\u00ecnh h\u1ecdc, t\u00edch ph\u00e2n v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh.<\/p>\n<p>V\u00ed d\u1ee5: Trong c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n, ta s\u1eed d\u1ee5ng s\u1ed1 Pi \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t. C\u00f4ng th\u1ee9c n\u00e0y c\u00f3 d\u1ea1ng A = \u03c0r^2, trong \u0111\u00f3 A l\u00e0 di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t c\u1ee7a \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 r l\u00e0 b\u00e1n k\u00ednh c\u1ee7a n\u00f3.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Cong_thuc_tinh_dien_tich_cua_mot_duong_tron\"><\/span>C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>A: Di\u1ec7n t\u00edch b\u1ec1 m\u1eb7t<\/li>\n<li>\u03c0: S\u1ed1 Pi<\/li>\n<li>r: B\u00e1n k\u00ednh<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"So_Vang_%CF%86\"><\/span>S\u1ed1 V\u00e0ng (\u03c6)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>S\u1ed1 V\u00e0ng, k\u00fd hi\u1ec7u l\u00e0 \u03c6 (phi), c\u0169ng l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 ki\u1ebfn tr\u00fac. N\u00f3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng c\u00e1ch l\u1ea5y t\u1ec9 l\u1ec7 c\u1ee7a hai ph\u1ea7n t\u1eed trong m\u1ed9t d\u00e3y s\u1ed1 Fibonacci li\u00ean ti\u1ebfp. Gi\u00e1 tr\u1ecb c\u1ee7a s\u1ed1 V\u00e0ng x\u1ea5p x\u1ec9 kho\u1ea3ng 1.61803. S\u1ed1 V\u00e0ng xu\u1ea5t hi\u1ec7n trong nhi\u1ec1u c\u00f4ng th\u1ee9c v\u00e0 thi\u1ebft k\u1ebf ki\u1ebfn tr\u00fac \u0111\u1ec3 t\u1ea1o ra c\u00e1c t\u1ef7 l\u1ec7 h\u00e0i h\u00f2a v\u00e0 \u0111\u1eb9p m\u1eaft.<\/p>\n<p>V\u00ed d\u1ee5: Trong ki\u1ebfn tr\u00fac, s\u1ed1 V\u00e0ng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u1ea1o ra c\u00e1c t\u1ef7 l\u1ec7 h\u00e0i h\u00f2a trong thi\u1ebft k\u1ebf c\u00e1c c\u00f4ng tr\u00ecnh nh\u01b0 t\u00f2a nh\u00e0, c\u00e2y c\u1ea7u v\u00e0 t\u00e1c ph\u1ea9m ngh\u1ec7 thu\u1eadt. C\u00e1c t\u1ef7 l\u1ec7 n\u00e0y \u0111\u01b0\u1ee3c coi l\u00e0 th\u1ea9m m\u1ef9 v\u00e0 c\u00f3 kh\u1ea3 n\u0103ng g\u00e2y \u1ea5n t\u01b0\u1ee3ng t\u00edch c\u1ef1c cho ng\u01b0\u1eddi nh\u00ecn.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du_ve_su_dung_so_Vang_trong_kien_truc\"><\/span>V\u00ed d\u1ee5 v\u1ec1 s\u1eed d\u1ee5ng s\u1ed1 V\u00e0ng trong ki\u1ebfn tr\u00fac:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>T\u1ef7 l\u1ec7 chi\u1ec1u cao v\u00e0 chi\u1ec1u r\u1ed9ng c\u1ee7a c\u00e1c c\u1eeda s\u1ed5 trong m\u1ed9t t\u00f2a nh\u00e0<\/li>\n<li>T\u1ef7 l\u1ec7 chi\u1ec1u d\u00e0i v\u00e0 chi\u1ec1u r\u1ed9ng c\u1ee7a c\u00e1c ph\u00f2ng trong m\u1ed9t c\u0103n h\u1ed9<\/li>\n<li>T\u1ef7 l\u1ec7 k\u00edch th\u01b0\u1edbc c\u1ee7a c\u00e1c th\u00e0nh ph\u1ea7n trong m\u1ed9t b\u1ee9c tranh ho\u1eb7c t\u00e1c ph\u1ea9m \u0111i\u00eau kh\u1eafc<\/li>\n<\/ul>\n<p>H\u1eb1ng s\u1ed1 l\u00e0 c\u00e1c gi\u00e1 tr\u1ecb kh\u00f4ng thay \u0111\u1ed5i trong qu\u00e1 tr\u00ecnh t\u00ednh to\u00e1n hay ph\u00e2n t\u00edch m\u1ed9t h\u1ec7 th\u1ed1ng. Ch\u00fang \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong nhi\u1ec1u l\u0129nh v\u1ef1c, t\u1eeb to\u00e1n h\u1ecdc \u0111\u1ebfn khoa h\u1ecdc t\u1ef1 nhi\u00ean v\u00e0 k\u1ef9 thu\u1eadt. Vi\u1ec7c hi\u1ec3u v\u00e0 s\u1eed d\u1ee5ng h\u1eb1ng s\u1ed1 m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c l\u00e0 \u0111i\u1ec1u c\u1ea7n thi\u1ebft \u0111\u1ec3 th\u00e0nh c\u00f4ng trong c\u00e1c l\u0129nh v\u1ef1c n\u00e0y.<br \/>\n<iframe loading=\"lazy\" title=\"C - B\u00e0i 7: H\u1eb1ng s\u1ed1.\" width=\"790\" height=\"444\" src=\"https:\/\/www.youtube.com\/embed\/mhVsAfF9UfM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>H\u1eb1ng s\u1ed1 l\u00e0 m\u1ed9t gi\u00e1 tr\u1ecb kh\u00f4ng thay \u0111\u1ed5i trong to\u00e1n h\u1ecdc v\u00e0 khoa h\u1ecdc t\u1ef1 nhi\u00ean. N\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u0111\u1ecbnh ngh\u0129a c\u00e1c quy t\u1eafc&#8230; <\/p>\n","protected":false},"author":1,"featured_media":28767,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[],"class_list":["post-28769","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-khai-niem-1"],"_links":{"self":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/28769","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/comments?post=28769"}],"version-history":[{"count":0,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/posts\/28769\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media\/28767"}],"wp:attachment":[{"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/media?parent=28769"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/categories?post=28769"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-json\/wp\/v2\/tags?post=28769"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}