Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn<\/p>\n\n\n\n
N\u1ed9i dung ph\u1ea7n H\u00ecnh h\u1ecdc c\u1ee7a m\u00f4n To\u00e1n l\u1edbp 8 bao g\u1ed3m 2 ph\u1ea7n l\u00e0 h\u00ecnh h\u1ecdc ph\u1eb3ng v\u00e0 h\u00ecnh h\u1ecdc kh\u00f4ng gian. Trong \u0111\u00f3, ph\u1ea7n h\u00ecnh h\u1ecdc ph\u1eb3ng chi\u1ebfm dung l\u01b0\u1ee3ng nhi\u1ec1u h\u01a1n m\u1ed9t ch\u00fat v\u1edbi tr\u1ecdng t\u00e2m ki\u1ebfn th\u1ee9c nghi\u00eang v\u1ec1 c\u00e1c h\u00ecnh h\u1ecdc th\u01b0\u1eddng g\u1eb7p, \u0111\u1eb7c \u0111i\u1ec3m nh\u1eadn d\u1ea1ng c\u0169ng nh\u01b0 c\u00e1c ph\u00e9p t\u00ednh to\u00e1n li\u00ean quan. V\u1edbi b\u00e0i h\u00f4m nay, Vietlearn s\u1ebd t\u1ed5ng k\u1ebft gi\u00fap b\u1ea1n ph\u1ea7n ki\u1ebfn th\u1ee9c v\u1ec1 \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u c\u1ee7a To\u00e1n 8. V\u1eady c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> c\u1ea7n n\u1eafm nh\u1eefng g\u00ec sau khi h\u1ecdc b\u00e0i n\u00e0y?<\/p>\n\n\n\n T\u1ed5ng qu\u00e1t n\u1ed9i dung c\u1ea7n h\u1ecdc v\u1ec1 \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u l\u1edbp 8<\/p>\n\n\n\n Tr\u00ean th\u1ef1c t\u1ebf, nh\u1eefng ki\u1ebfn th\u1ee9c v\u1ec1 \u0111a gi\u00e1c hay \u0111a gi\u00e1c \u0111\u1ec1u, b\u1ea1n \u0111\u00e3 \u0111\u01b0\u1ee3c ti\u1ebfp x\u00fac t\u1eeb r\u1ea5t s\u1edbm, ngay t\u1eeb nh\u1eefng n\u0103m c\u00f2n h\u1ecdc \u1edf c\u00e1c l\u1edbp d\u01b0\u1edbi ch\u1ee9 kh\u00f4ng ph\u1ea3i t\u1edbi t\u1eadn l\u1edbp 8 m\u1edbi \u0111\u01b0\u1ee3c h\u1ecdc. Tuy nhi\u00ean, v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh to\u00e1n<\/a> 8 \u0111a gi\u00e1c \u0111a gi\u00e1c \u0111\u1ec1u, h\u1ecdc sinh<\/a> s\u1ebd \u0111\u01b0\u1ee3c h\u1ec7 th\u1ed1ng l\u1ea1i m\u1ed9t c\u00e1ch b\u00e0i b\u1ea3n, \u0111\u1ea7y \u0111\u1ee7 v\u00e0 chu\u1ea9n h\u01a1n t\u1eeb kh\u00e1i ni\u1ec7m cho t\u1edbi \u0111\u1eb7c \u0111i\u1ec3m nh\u1eadn d\u1ea1ng c\u1ee7a \u0111a gi\u00e1c n\u00f3i chung v\u00e0 \u0111a gi\u00e1c \u0111\u1ec1u n\u00f3i ri\u00eang.<\/p>\n\n\n\n Trong khoa h\u1ecdc t\u1ef1 nhi\u00ean n\u00f3i chung v\u00e0 to\u00e1n h\u1ecdc n\u00f3i ri\u00eang, c\u00e1c nghi\u00ean c\u1ee9u v\u1ec1 \u0111a gi\u00e1c r\u1ea5t nhi\u1ec1u. Song song v\u1edbi \u0111i\u1ec1u \u0111\u00f3 l\u00e0 \u0111\u1ec3 bi\u1ebft v\u00e0 hi\u1ec3u \u0111\u01b0\u1ee3c h\u1ebft n\u1ed9i dung v\u1ec1 \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u l\u00e0 kh\u00f4ng d\u1ec5.<\/p>\n\n\n\n Kh\u00e1i qu\u00e1t chung v\u1ec1 n\u1ed9i dung b\u00e0i h\u1ecdc \u0111a gi\u00e1c \u0111a gi\u00e1c \u0111\u1ec1u l\u1edbp 8<\/p>\n\n\n\n V\u1edbi th\u1eddi l\u01b0\u1ee3ng \u00edt \u1ecfi tr\u00ean l\u1edbp c\u00f9ng v\u1edbi v\u00f4 v\u00e0n n\u1ed9i dung c\u1ee7a nhi\u1ec1u m\u00f4n h\u1ecdc kh\u00e1c th\u00ec c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> kh\u00f4ng th\u1ec3 n\u00e0o h\u1ecdc h\u1ebft \u0111\u01b0\u1ee3c ph\u1ea7n ki\u1ebfn th\u1ee9c kh\u1ed5ng l\u1ed3 nh\u01b0 v\u1eady. V\u00ec th\u1ebf, n\u1ebfu th\u1ea5y h\u1ee9ng th\u00fa, b\u1ea1n c\u00f3 th\u1ec3 t\u00ecm hi\u1ec3u th\u00eam v\u1ec1 \u0111a gi\u00e1c. C\u00f2n t\u1ea1i \u0111\u00e2y, Vietlearn s\u1ebd ch\u1ec9 g\u00f3i g\u1ecdn l\u1ea1i ph\u1ea7n ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n<\/a> c\u1ee7a \u0111a gi\u00e1c \u0111a gi\u00e1c \u0111\u1ec1u l\u1edbp 8 th\u00f4i.<\/p>\n\n\n\n \u0110\u1ecbnh ngh\u0129a v\u1ec1 \u0111a gi\u00e1c<\/p>\n\n\n\n \u0110a gi\u00e1c \u0111\u01b0\u1ee3c chia l\u00e0m 2 lo\u1ea1i c\u01a1 b\u1ea3n l\u00e0 \u0111a gi\u00e1c l\u1ed3i v\u00e0 \u0111a gi\u00e1c l\u00f5m. H\u1ea7u h\u1ebft c\u00e1c h\u00ecnh h\u1ecdc \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a gi\u00e1c m\u00e0 c\u00e1c b\u1ea1n \u0111ang h\u1ecdc trong ch\u01b0\u01a1ng tr\u00ecnh ph\u1ed5 th\u00f4ng hi\u1ec7n nay \u0111\u1ec1u l\u00e0 \u0111a gi\u00e1c l\u1ed3i. Hay n\u00f3i c\u00e1ch kh\u00e1c, ch\u00fang ta s\u1ebd kh\u00f4ng nghi\u00ean c\u1ee9u s\u00e2u v\u00e0 \u0111\u1ec1 c\u1eadp nhi\u1ec1u t\u1edbi n\u1ed9i dung v\u1ec1 \u0111a gi\u00e1c l\u00f5m trong nh\u1eefng n\u1ed9i dung b\u00e0i h\u1ecdc sau n\u00e0y.<\/p>\n\n\n\n Trong h\u00ecnh h\u1ecdc ph\u1eb3ng, \u0111a gi\u00e1c \u0111\u01b0\u1ee3c hi\u1ec3u l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng g\u1ea5p kh\u00fac ph\u1eb3ng kh\u00e9p k\u00edn, t\u1ee9c l\u00e0 s\u1ebd bao g\u1ed3m c\u00e1c \u0111o\u1ea1n th\u1eb3ng n\u1ed1i li\u1ec1n v\u00e0 kh\u00e9p k\u00edn l\u1ea1i v\u1edbi nhau. Nh\u01b0 v\u1eady, \u0111\u1ec3 t\u1ea1o n\u00ean m\u1ed9t \u0111a gi\u00e1c th\u00ec t\u1ed1i thi\u1ec3u s\u1ed1 c\u1ea1nh ph\u1ea3i l\u00e0 3 tr\u1edf l\u00ean.<\/p>\n\n\n\n Th\u1ebf n\u00e0o l\u00e0 \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u?<\/p>\n\n\n\n \u0110a gi\u00e1c l\u1ed3i l\u00e0 nh\u1eefng \u0111a gi\u00e1c m\u00e0 trong \u0111\u00f3 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh t\u1ea1o n\u00ean \u0111\u1ec1u ph\u1ea3i n\u1eb1m chung tr\u00ean 1 n\u1eeda m\u1eb7t ph\u1eb3ng l\u1ea5y b\u1edd l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a b\u1ea5t k\u1ef3 m\u1ed9t c\u1ea1nh n\u00e0o c\u1ee7a \u0111a gi\u00e1c \u0111\u00f3. C\u00f2n \u0111\u1ecbnh ngh\u0129a v\u1ec1 \u0111a gi\u00e1c l\u00f5m s\u1ebd ng\u01b0\u1ee3c l\u1ea1i v\u1edbi \u0111a gi\u00e1c l\u1ed3i, khi m\u1ed9t trong s\u1ed1 c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng ch\u1ee9a 1 c\u1ea1nh c\u1ee7a \u0111a gi\u00e1c khi\u1ebfn h\u00ecnh \u0111\u00f3 ph\u00e2n chia ra 2 n\u1eeda m\u1eb7t ph\u1eb3ng th\u00ec ta g\u1ecdi h\u00ecnh \u1ea5y l\u00e0 \u0111a gi\u00e1c l\u00f5m.<\/p>\n\n\n\n \u0110\u1ecbnh ngh\u0129a v\u1ec1 \u0111a gi\u00e1c \u0111\u1ec1u<\/p>\n\n\n\n T\u01b0\u01a1ng t\u1ef1 nh\u01b0 \u0111\u1ecbnh ngh\u0129a v\u1ec1 tam gi\u00e1c \u0111\u1ec1u th\u00ec \u0111a gi\u00e1c \u0111\u1ec1u c\u0169ng l\u00e0 \u0111a gi\u00e1c m\u00e0 trong \u0111\u00f3 t\u1ea5t c\u1ea3 c\u00e1c c\u1ea1nh d\u00e0i b\u1eb1ng nhau v\u00e0 t\u1ea5t c\u1ea3 c\u00e1c g\u00f3c n\u1eb1m trong \u0111a gi\u00e1c \u0111\u00f3 c\u0169ng ph\u1ea3i c\u00f3 s\u1ed1 \u0111o b\u1eb1ng nhau.<\/p>\n\n\n\n Nh\u1eefng h\u00ecnh h\u1ecdc n\u00e0o \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u?<\/p>\n\n\n\n V\u1edbi ph\u1ea7n \u0111\u1ecbnh ngh\u0129a \u0111\u01b0\u1ee3c gi\u1ea3i \u0111\u00e1p \u1edf tr\u00ean v\u1ec1 \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u, ch\u1eafc ch\u1eafn ph\u1ea7n l\u1edbn c\u00e1c b\u1ea1n \u0111\u1ec1u c\u00f3 th\u1ec3 bi\u1ebft \u0111\u01b0\u1ee3c nh\u1eefng h\u00ecnh \u0111\u1eb7c bi\u1ec7t quen thu\u1ed9c v\u1edbi ch\u00fang ta trong m\u00f4n to\u00e1n t\u1eeb tr\u01b0\u1edbc t\u1edbi nay c\u00f3 ph\u1ea3i l\u00e0 \u0111a gi\u00e1c hay kh\u00f4ng r\u1ed3i.<\/p>\n\n\n\n \u0110\u00fang v\u1eady, nh\u1eefng h\u00ecnh nh\u01b0 tam gi\u00e1c, h\u00ecnh ch\u1eef nh\u1eadt, h\u00ecnh thang,\u2026 \u0111\u1ec1u \u0111\u01b0\u1ee3c g\u1ecdi chung l\u00e0 \u0111a gi\u00e1c. T\u01b0\u01a1ng t\u1ef1, tam gi\u00e1c \u0111\u1ec1u, h\u00ecnh vu\u00f4ng,\u2026 \u0111\u1ec1u \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a gi\u00e1c \u0111\u1ec1u.<\/p>\n\n\n\n H\u00ecnh minh h\u1ecda c\u00e1c \u0111a gi\u00e1c \u0111\u1ec1u si\u00eau \u201cquen thu\u1ed9c\u201d<\/p>\n\n\n\n V\u00e0 s\u1ef1 th\u1eadt l\u00e0 h\u00ecnh t\u1ee9 gi\u00e1c b\u1ea1n h\u1ecdc \u1edf nh\u1eefng b\u00e0i tr\u01b0\u1edbc c\u0169ng \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111a gi\u00e1c lu\u00f4n. Ngo\u00e0i ra, trong cu\u1ed9c s\u1ed1ng b\u1ea1n c\u0169ng s\u1ebd hay b\u1eaft g\u1eb7p m\u1ed9t s\u1ed1 h\u00ecnh nh\u01b0 ng\u0169 gi\u00e1c \u0111\u1ec1u, l\u1ee5c gi\u00e1c \u0111\u1ec1u, b\u00e1t gi\u00e1c \u0111\u1ec1u,\u2026<\/p>\n\n\n\n M\u1ed9t s\u1ed1 c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n li\u00ean quan \u0111\u1ebfn \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u<\/p>\n\n\n\n \u1ede b\u00e0i gi\u1ea3ng v\u1ec1 \u0111a gi\u00e1c \u0111a gi\u00e1c \u0111\u1ec1u l\u1edbp 8 n\u00e0y, b\u00ean c\u1ea1nh c\u00e1c c\u00f4ng th\u1ee9c v\u1ec1 di\u1ec7n t\u00edch th\u00ec b\u1ea1n c\u1ea7n b\u1ed5 sung th\u00eam m\u1ed9t s\u1ed1 c\u00f4ng th\u1ee9c kh\u00e1c nh\u1eb1m ph\u1ee5c v\u1ee5 cho qu\u00e1 tr\u00ecnh gi\u1ea3i m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp sau n\u00e0y.<\/p>\n\n\n\n T\u00ednh t\u1ed5ng s\u1ed1 \u0111o g\u00f3c c\u1ee7a m\u1ed9t \u0111a gi\u00e1c c\u00f3 n c\u1ea1nh (n\u22653)<\/p>\n\n\n\n S\u1ed1 \u0111o c\u1ee7a m\u1ed9t g\u00f3c trong \u0111a gi\u00e1c n c\u1ea1nh l\u00e0:<\/p>\n\n\n\n T\u1ed5ng s\u1ed1 \u0111o t\u1ea5t c\u1ea3 c\u00e1c g\u00f3c trong \u0111a gi\u00e1c c\u00f3 n c\u1ea1nh l\u00e0: (n-2).180<\/p>\n\n\n\n T\u00ednh s\u1ed1 \u0111\u01b0\u1eddng ch\u00e9o c\u00f3 trong m\u1ed9t \u0111a gi\u00e1c n c\u1ea1nh (n\u22653)<\/p>\n\n\n\n C\u00f4ng th\u1ee9c t\u00ednh s\u1ed1 \u0111\u01b0\u1eddng ch\u00e9o trong \u0111a gi\u00e1c c\u00f3 n c\u1ea1nh l\u00e0:<\/p>\n\n\n\n Ph\u01b0\u01a1ng ph\u00e1p t\u00ednh di\u1ec7n t\u00edch \u0111a gi\u00e1c<\/p>\n\n\n\n \u0110\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch \u0111a gi\u00e1c, c\u00e1ch \u0111\u01a1n gi\u1ea3n nh\u1ea5t l\u00e0 b\u1ea1n quy v\u1ec1 c\u00e1c h\u00ecnh \u0111\u1eb7c bi\u1ec7t nh\u1ecf r\u1ed3i t\u00ednh theo c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch \u0111\u00e3 \u0111\u01b0\u1ee3c h\u1ecdc. C\u1ee5 th\u1ec3 l\u00e0 b\u1ea1n c\u00f3 th\u1ec3 chia th\u00e0nh c\u00e1c h\u00ecnh tam gi\u00e1c, h\u00ecnh vu\u00f4ng ho\u1eb7c ch\u1eef nh\u1eadt b\u00ean trong sao cho linh ho\u1ea1t v\u00e0 d\u1ec5 t\u00ednh nh\u1ea5t.<\/p>\n\n\n\n Chia \u0111a gi\u00e1c th\u00e0nh c\u00e1c h\u00ecnh nh\u1ecf \u0111\u1ec3 t\u00ednh di\u1ec7n t\u00edch<\/p>\n\n\n\n Tr\u00ean \u0111\u00e2y l\u00e0 ph\u1ea7n l\u00fd thuy\u1ebft tr\u1ecdng t\u00e2m v\u1ec1 \u0111a gi\u00e1c.\u0111a gi\u00e1c \u0111\u1ec1u trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n<\/a> h\u00ecnh 8 m\u00e0 c\u00e1c b\u1ea1n h\u1ecdc sinh<\/a> c\u1ea7n n\u1eafm v\u1eefng. Ngo\u00e0i ra, n\u1ebfu b\u1ea1n mu\u1ed1n tham kh\u1ea3o th\u00eam c\u00e1c n\u1ed9i dung kh\u00e1c c\u1ee7a m\u00f4n h\u1ecdc, h\u00e3y t\u00ecm ki\u1ebfm t\u1ea1i Vietlearn.vn nh\u00e9.<\/p>\n\n\n\n <\/p>\n\n\n\n Ph\u00e9p \u0111\u1ed1i x\u1ee9ng t\u00e2m<\/p>\n\n\n\n T\u1ee9 gi\u00e1c l\u00e0 g\u00ec? Nh\u1eefng h\u00ecnh t\u1ee9 gi\u00e1c<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":" Ghi ch\u00fa: T\u00e0i li\u1ec7u tr\u00edch d\u1eabn N\u1ed9i dung ph\u1ea7n H\u00ecnh h\u1ecdc c\u1ee7a m\u00f4n To\u00e1n l\u1edbp 8 bao g\u1ed3m 2 ph\u1ea7n l\u00e0 h\u00ecnh h\u1ecdc ph\u1eb3ng v\u00e0 h\u00ecnh h\u1ecdc kh\u00f4ng gian. Trong \u0111\u00f3, ph\u1ea7n h\u00ecnh h\u1ecdc ph\u1eb3ng chi\u1ebfm dung l\u01b0\u1ee3ng nhi\u1ec1u h\u01a1n m\u1ed9t ch\u00fat v\u1edbi tr\u1ecdng t\u00e2m ki\u1ebfn th\u1ee9c nghi\u00eang v\u1ec1 c\u00e1c h\u00ecnh h\u1ecdc th\u01b0\u1eddng g\u1eb7p, \u0111\u1eb7c […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_disable_autopaging":false},"categories":[9,4],"tags":[],"class_list":["post-1107","post","type-post","status-publish","format-standard","hentry","category-toan-hoc","category-trung-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1107","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/comments?post=1107"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/1107\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=1107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=1107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=1107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}