Trong cu\u1ed9c s\u1ed1ng h\u1eb1ng ng\u00e0y ta th\u01b0\u1eddng g\u1eb7p nhi\u1ec1u kh\u00e1i ni\u1ec7m m\u01a1 h\u1ed3, v\u00ed nh\u01b0 khi n\u1ea5u c\u01a1m \u0111\u1ed5 n\u01b0\u1edbc nhi\u1ec1u hay \u00edt, khi gi\u1eb7t qu\u1ea7n \u00e1o th\u00eam nhi\u1ec1u hay \u00edt b\u1ed9t gi\u1eb7t. C\u00e1c gi\u1edbi h\u1ea1n \u00edt nhi\u1ec1u n\u00e0y th\u1eadt kh\u00f4ng r\u00f5 r\u00e0ng, th\u1eadt m\u01a1 h\u1ed3. V\u1edbi kinh nghi\u1ec7m ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 ph\u00e2n \u0111\u1ecbnh \u0111\u01b0\u1ee3c m\u1ee9c \u0111\u1ed9 n\u00e0o \u0111\u00f3 nh\u01b0ng khi x\u1eed l\u00ed b\u1eb1ng m\u00e1y t\u00ednh s\u1ebd g\u1eb7p kh\u00f4ng \u00edt kh\u00f3 kh\u0103n. V\u00ec v\u1eady t\u00ecm c\u00f4ng c\u1ee5 to\u00e1n h\u1ecdc th\u00edch h\u1ee3p cho vi\u1ec7c x\u1eed l\u00ed c\u00e1c s\u1ef1 vi\u1ec7c m\u01a1 h\u1ed3 t\u1ef1 nhi\u00ean tr\u1edf th\u00e0nh \u0111i\u1ec3m n\u00f3ng c\u1ee7a c\u00e1c nghi\u00ean c\u1ee9u to\u00e1n h\u1ecdc.<\/p>\n\n\n\n
T\u1eeb n\u0103m 1937, Black \u0111\u00e3 t\u1eebng b\u00e0n \u0111\u1ebfn hi\u1ec7n t\u01b0\u1ee3ng m\u01a1 h\u1ed3 tr\u00ean ph\u01b0\u01a1ng di\u1ec7n l\u00f4gic. V\u00e0o n\u0103m 1951, trong m\u1ed9t lu\u1eadn v\u0103n, m\u1ed9t ng\u01b0\u1eddi Ph\u00e1p \u0111\u00e3 t\u1eebng \u0111\u01b0a ra thu\u1eadt ng\u1eef \u201ct\u1eadp h\u1ee3p m\u01a1 h\u1ed3\u201d hay \u201ct\u1eadp m\u1edd\u201d. N\u0103m 1965, gi\u00e1o s\u01b0 Zadeh thu\u1ed9c ph\u00e2n hi\u1ec7u \u0111\u1ea1i h\u1ecdc Berkley \u1edf bang California n\u01b0\u1edbc M\u1ef9 \u0111\u00e3 c\u00f4ng b\u1ed1 lu\u1eadn v\u0103n v\u1ec1 \u201ct\u1eadp m\u1edd\u201d. T\u1eeb \u0111\u00f3 m\u1ed9t ng\u00e0nh to\u00e1n h\u1ecdc m\u1edbi: to\u00e1n h\u1ecdc m\u01a1 h\u1ed3 hay to\u00e1n h\u1ecdc m\u1edd b\u1eaft \u0111\u1ea7u ph\u00e1t tri\u1ec3n m\u1ea1nh m\u1ebd.<\/p>\n\n\n\n
To\u00e1n h\u1ecdc m\u1edd l\u00e0 ng\u00e0nh khoa h\u1ecdc d\u00f9ng c\u00f4ng c\u1ee5 to\u00e1n h\u1ecdc \u0111\u1ec3 nghi\u00ean c\u1ee9u c\u00e1c s\u1ef1 v\u1eadt m\u01a1 h\u1ed3. To\u00e1n h\u1ecdc l\u00e0 ng\u00e0nh khoa h\u1ecdc ch\u00ednh x\u00e1c, c\u00f2n to\u00e1n h\u1ecdc m\u1edd kh\u00f4ng h\u1ec1 gi\u1ea3m \u0111i t\u00ed n\u00e0o t\u00ednh ch\u00ednh x\u00e1c c\u1ee7a to\u00e1n h\u1ecdc.<\/p>\n\n\n\n
To\u00e1n h\u1ecdc m\u1edd th\u1eed d\u00f9ng t\u00ednh \u0111\u1ecbnh l\u01b0\u1ee3ng, t\u00ednh ch\u00ednh x\u00e1c \u0111\u1ec3 x\u1eed l\u00ed t\u00ednh m\u01a1 h\u1ed3, m\u1edf r\u1ed9ng ph\u1ea1m vi \u1ee9ng d\u1ee5ng c\u1ee7a to\u00e1n h\u1ecdc. T\u1eadp h\u1ee3p m\u1edd l\u00e0 kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n c\u1ee7a to\u00e1n h\u1ecdc m\u1edd. \u0110i\u1ec3m kh\u00e1c bi\u1ec7t c\u1ee7a c\u00e1c t\u1eadp h\u1ee3p m\u1edd (hay c\u00f2n g\u1ecdi l\u00e0 t\u1eadp m\u1edd) l\u00e0 c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p m\u1edd c\u00f3 t\u00ednh ch\u1ea5t m\u01a1 h\u1ed3 \u1edf m\u1ee9c \u0111\u1ed9 n\u00e0o \u0111\u00f3. Tr\u00ean c\u01a1 s\u1edf c\u1ee7a t\u1eadp m\u1edd ta c\u00f3 th\u1ec3 th\u1ea3o lu\u1eadn v\u1ec1 quan h\u1ec7 m\u1edd, ma tr\u1eadn m\u1edd v\u00e0 s\u1ed1 m\u1edd.<\/p>\n\n\n\n
To\u00e1n h\u1ecdc m\u1edd ph\u00e1t tri\u1ec3n d\u1ef1a v\u00e0o c\u01a1 s\u1edf c\u1ee7a to\u00e1n h\u1ecdc truy\u1ec1n th\u1ed1ng. To\u00e1n h\u1ecdc m\u1edd kh\u00f4ng ph\u1ea3i l\u00e0 to\u00e1n h\u1ecdc truy\u1ec1n th\u1ed1ng nh\u01b0ng c\u00f3 m\u1ed1i li\u00ean h\u1ec7 v\u1edbi to\u00e1n h\u1ecdc truy\u1ec1n th\u1ed1ng. D\u01b0\u1edbi \u0111\u00e2y ta s\u1ebd xem x\u00e9t m\u1ed9t v\u00ed d\u1ee5.<\/p>\n\n\n\n
Trong h\u00ecnh h\u1ecdc c\u00f3 \u0111\u1ecbnh ngh\u0129a v\u1ec1 v\u00f2ng tr\u00f2n \u201cH\u00ecnh tr\u00f2n l\u00e0 t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m tr\u00ean m\u1eb7t ph\u1eb3ng c\u00f3 kho\u1ea3ng c\u00e1ch kh\u00f4ng thay \u0111\u1ed5i t\u1edbi m\u1ed9t \u0111i\u1ec3m c\u1ed1 \u0111\u1ecbnh trong v\u00f2ng tr\u00f2n\u201d. Th\u1ebf nh\u01b0ng trong cu\u1ed9c s\u1ed1ng h\u1eb1ng ng\u00e0y t\u00ecm \u0111\u01b0\u1ee3c m\u1ed9t h\u00ecnh tr\u00f2n ho\u00e0n to\u00e0n ph\u00f9 h\u1ee3p v\u1edbi \u0111\u1ecbnh ngh\u0129a to\u00e1n h\u1ecdc l\u00e0 r\u1ea5t kh\u00f3. Ng\u01b0\u1eddi ta th\u01b0\u1eddng n\u00f3i \u201cM\u1eb7t tr\u0103ng tr\u00f2n\u201d, \u201cQu\u1ea3 tr\u1ee9ng tr\u00f2n\u201d, \u201cG\u01b0\u01a1ng m\u1eb7t tr\u00f2n\u201d v.v\u2026 \u0111\u1ec1u l\u00e0 c\u00e1c kh\u00e1i ni\u1ec7m m\u01a1 h\u1ed3. N\u1ebfu c\u00f3 ai \u0111\u00f3 \u0111\u01b0a cho b\u1ea1n m\u1ed9t t\u1ea5m \u1ea3nh trong \u0111\u00f3 c\u00f3 \u1ea3nh c\u1ee7a nhi\u1ec1u ng\u01b0\u1eddi, ng\u01b0\u1eddi ta y\u00eau c\u1ea7u b\u1ea1n ch\u1ecdn trong s\u1ed1 \u0111\u00f3 m\u1ed9t g\u01b0\u01a1ng m\u1eb7t tr\u00f2n nh\u1ea5t. N\u1ebfu ch\u1ec9 d\u00f9ng tr\u1ef1c gi\u00e1c th\u1eadt kh\u00f3 th\u1ef1c hi\u1ec7n \u0111\u01b0\u1ee3c. Ch\u1ec9 c\u00f3 d\u00f9ng m\u00e1y t\u00ednh k\u1ebft h\u1ee3p v\u1edbi c\u00e1c d\u1ee5ng c\u1ee5 \u0111o \u0111\u1ea1c may ra c\u00f3 th\u1ec3 ho\u00e0n th\u00e0nh \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n
Trong to\u00e1n h\u1ecdc truy\u1ec1n th\u1ed1ng c\u00f3 \u0111\u1ecbnh l\u00ed: V\u1edbi c\u00e1c h\u00ecnh c\u00f3 c\u00f9ng chu vi th\u00ec h\u00ecnh tr\u00f2n c\u00f3 di\u1ec7n t\u00edch l\u1edbn nh\u1ea5t. Ta bi\u1ebft c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n l\u00e0 S = \u03c0R2, c\u00f4ng th\u1ee9c t\u00ednh \u0111\u01b0\u1eddng chu vi l\u00e0 l = 2\u03c0R (R l\u00e0 b\u00e1n k\u00ednh c\u1ee7a h\u00ecnh tr\u00f2n). Ta t\u00ednh t\u1ec9 s\u1ed1 c\u1ee7a di\u1ec7n t\u00edch h\u00ecnh tr\u00f2n v\u1edbi b\u00ecnh ph\u01b0\u01a1ng \u0111\u01b0\u1eddng chu vi h\u00ecnh tr\u00f2n s\u1ebd l\u00e0 S\/l2 = 1\/4\u03c0. V\u1edbi c\u00e1c h\u00ecnh kh\u00e1c th\u00ec t\u1ec9 s\u1ed1 gi\u1eefa di\u1ec7n t\u00edch v\u00e0 b\u00ecnh ph\u01b0\u01a1ng chu vi s\u1ebd nh\u1ecf h\u01a1n h\u1eb1ng s\u1ed1 n\u00e0y.<\/p>\n\n\n\n
V\u1edbi m\u1ed9t h\u00ecnh ti\u1ebfp c\u1eadn v\u1edbi v\u00f2ng tr\u00f2n th\u00ec t\u1ec9 s\u1ed1 S\/l2 s\u1ebd ti\u1ebfn d\u1ea7n \u0111\u1ebfn s\u1ed1 1\/4\u03c0. Nh\u01b0 v\u1eady ta c\u00f3 th\u1ec3 d\u00f9ng 4\u03c0S\/l2 \u0111\u1ec3 bi\u1ec3u di\u1ec5n m\u1ee9c \u0111\u1ed9 tr\u00f2n c\u1ee7a m\u1ed9t h\u00ecnh. B\u00e2y gi\u1edd v\u1edbi c\u00e1c h\u00ecnh ng\u01b0\u1eddi trong t\u1ea5m \u1ea3nh ta ch\u1ec9 c\u1ea7n \u0111o di\u1ec7n t\u00edch v\u00e0 \u0111\u01b0\u1eddng chu vi c\u1ee7a c\u00e1c g\u01b0\u01a1ng m\u1eb7t ta c\u00f3 th\u1ec3 \u0111\u00e1nh gi\u00e1 m\u1ee9c \u0111\u1ed9 tr\u00f2n c\u1ee7a c\u00e1c g\u01b0\u01a1ng m\u1eb7t theo gi\u00e1 tr\u1ecb t\u1ec9 s\u1ed1 4\u03c0S\/l2. C\u00e1c t\u1ec9 s\u1ed1 n\u00e0y s\u1ebd c\u00f3 gi\u00e1 tr\u1ecb trong kho\u1ea3ng 0 – 1. N\u1ebfu t\u1ec9 s\u1ed1 c\u00e0ng g\u1ea7n v\u1edbi 1 th\u00ec g\u01b0\u01a1ng m\u1eb7t c\u00e0ng tr\u00f2n. D\u00f9ng ph\u01b0\u01a1ng ph\u00e1p n\u00e0y m\u00e1y t\u00ednh c\u00f3 th\u1ec3 ch\u1ecdn \u0111\u01b0\u1ee3c g\u01b0\u01a1ng m\u1eb7t tr\u00f2n nh\u1ea5t trong c\u00e1c g\u01b0\u01a1ng m\u1eb7t trong t\u1ea5m \u1ea3nh.<\/p>\n\n\n\n
To\u00e1n h\u1ecdc m\u1edd \u0111\u00e3 \u0111\u01b0a ra ph\u01b0\u01a1ng ph\u00e1p mi\u00eau t\u1ea3 \u0111\u1ecbnh l\u01b0\u1ee3ng cho ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean \u0111\u1ec3 ng\u00f4n ng\u1eef t\u1ef1 nhi\u00ean chuy\u1ec3n ho\u00e1 th\u00e0nh ng\u00f4n ng\u1eef m\u00e1y, nh\u1edd \u0111\u00f3 n\u00e2ng cao \u0111\u1ed9 linh ho\u1ea1t c\u1ee7a m\u00e1y t\u00ednh. To\u00e1n h\u1ecdc m\u1edd k\u1ebft h\u1ee3p v\u1edbi m\u00e1y t\u00ednh \u0111\u00e3 c\u00f3 \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i v\u00e0 \u0111\u1ea1t nhi\u1ec1u k\u1ebft qu\u1ea3. V\u00ed d\u1ee5 Pabis v\u00e0 c\u00e1c c\u1ed9ng s\u1ef1 \u1edf n\u01b0\u1edbc Anh \u0111\u00e3 d\u00f9ng to\u00e1n h\u1ecdc m\u1edd \u0111\u1ec3 ch\u1ebf t\u1ea1o c\u00e1c thi\u1ebft b\u1ecb \u0111i\u1ec1u khi\u1ec3n \u0111i\u1ec3m n\u00fat giao th\u00f4ng ng\u00e3 m\u01b0\u1eddi. Pael c\u1ee7a \u1ea5n \u0110\u1ed9 v\u00e0 c\u00e1c \u0111\u1ed3ng s\u1ef1 \u0111\u00e3 d\u00f9ng to\u00e1n h\u1ecdc m\u1edd \u0111\u1ec3 ph\u00e2n bi\u1ec7t l\u1eddi n\u00f3i c\u1ee7a ng\u01b0\u1eddi n\u00f3i. Ng\u01b0\u1eddi Nh\u1eadt B\u1ea3n \u0111\u00e3 d\u00f9ng to\u00e1n h\u1ecdc m\u1edd \u0111\u1ec3 ch\u1ea9n \u0111o\u00e1n b\u1ec7nh c\u1ed5 tr\u01b0\u1edbng, \u0111\u1ec3 \u0111i\u1ec1u khi\u1ec3n t\u00e0u \u0111i\u1ec7n ng\u1ea7m, m\u00e1y gi\u1eb7t qu\u1ea7n \u00e1o, m\u00e1y h\u00fat b\u1ee5i, m\u00e1y \u0111i\u1ec1u ho\u00e0 kh\u00f4ng kh\u00ed, n\u1ed3i c\u01a1m \u0111i\u1ec7n v.v\u2026 Ng\u01b0\u1eddi Trung Qu\u1ed1c \u0111\u00e3 d\u00f9ng to\u00e1n h\u1ecdc m\u1edd \u0111\u1ec3 d\u00f9ng v\u00e0o vi\u1ec7c d\u1ef1 b\u00e1o kh\u00ed t\u01b0\u1ee3ng, ch\u1ea9n \u0111o\u00e1n y h\u1ecdc, trong c\u00f4ng t\u00e1c t\u00ecnh b\u00e1o, ch\u1ea9n \u0111o\u00e1n b\u1ec7nh c\u1ed5 tr\u01b0\u1edbng, c\u00f4ng t\u00e1c quy ho\u1ea1ch, \u0111i\u1ec1u khi\u1ec3n nhi\u1ec7t \u0111\u1ed9 l\u00f2, qu\u1ea3n l\u00ed kinh doanh\u2026<\/p>\n\n\n\n
To\u00e1n h\u1ecdc m\u1edd kh\u00f4ng ch\u1ec9 l\u00e0 kh\u00f4ng m\u01a1 h\u1ed3 m\u00e0 c\u00f2n d\u00f9ng ph\u01b0\u01a1ng ph\u00e1p ch\u00ednh x\u00e1c \u0111\u1ec3 nghi\u00ean c\u1ee9u s\u1ef1 v\u1eadt m\u01a1 h\u1ed3, l\u00e0 m\u1ed9t m\u00f4n khoa h\u1ecdc c\u00f3 nhi\u1ec1u \u1ee9ng d\u1ee5ng l\u00ed th\u00fa.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: To\u00e1n h\u1ecdc m\u1edd.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Trong cu\u1ed9c s\u1ed1ng h\u1eb1ng ng\u00e0y ta th\u01b0\u1eddng g\u1eb7p nhi\u1ec1u kh\u00e1i ni\u1ec7m m\u01a1 h\u1ed3, v\u00ed nh\u01b0 khi n\u1ea5u c\u01a1m \u0111\u1ed5 n\u01b0\u1edbc nhi\u1ec1u hay \u00edt, khi gi\u1eb7t qu\u1ea7n \u00e1o th\u00eam nhi\u1ec1u hay \u00edt b\u1ed9t gi\u1eb7t. C\u00e1c gi\u1edbi h\u1ea1n \u00edt nhi\u1ec1u n\u00e0y th\u1eadt kh\u00f4ng r\u00f5 r\u00e0ng, th\u1eadt m\u01a1 h\u1ed3. V\u1edbi kinh nghi\u1ec7m ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 ph\u00e2n \u0111\u1ecbnh […]<\/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":[15,9],"tags":[],"class_list":["post-7712","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-toan-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7712","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=7712"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7712\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7712"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7712"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}