\u201c\u0110\u1ee9ng nghi\u00eam, quay tr\u00e1i, quay ph\u1ea3i, quay \u0111\u1eb1ng sau\u201d l\u00e0 b\u1ed1n \u0111\u1ed9ng t\u00e1c kh\u00f4ng ph\u1ea3i l\u00e0 con s\u1ed1, kh\u00f4ng ph\u1ea3i l\u00e0 h\u00ecnh v\u1ebd v\u00ec sao l\u1ea1i tr\u1edf th\u00e0nh \u0111\u1ed1i t\u01b0\u1ee3ng c\u1ee7a to\u00e1n h\u1ecdc? Nhi\u1ec1u ng\u01b0\u1eddi kh\u00f4ng r\u00f5 t\u1ea1i sao.<\/p>\n\n\n\n
Tr\u01b0\u1edbc h\u1ebft ta th\u1eed ph\u00e2n t\u00edch m\u1ed1i quan h\u1ec7 n\u1ed9i t\u1ea1i c\u1ee7a b\u1ed1n \u0111\u1ed9ng t\u00e1c!<\/p>\n\n\n\n
\u0110\u1ec3 d\u1ec5 d\u00e0ng theo d\u00f5i, ta d\u00f9ng c\u00e1c k\u00ed hi\u1ec7u I, R, L, H \u0111\u1ec3 bi\u1ec3u di\u1ec5n b\u1ed1n \u0111\u1ed9ng t\u00e1c: \u0111\u1ee9ng nghi\u00eam, quay tr\u00e1i, quay ph\u1ea3i, quay \u0111\u1eb1ng sau theo th\u1ee9 t\u1ef1. Ta l\u1eadp t\u1eadp h\u1ee3p M = {I, R, L, H}. N\u1ebfu ban \u0111\u1ea7u ta cho quay ph\u1ea3i, sau \u0111\u00f3 ta cho quay tr\u00e1i, k\u1ebft qu\u1ea3 l\u00e0 \u0111\u01b0\u1ee3c t\u01b0 th\u1ebf nh\u01b0 ban \u0111\u1ea7u (nh\u01b0 khi ch\u01b0a th\u1ef1c hi\u1ec7n \u0111\u1ed9ng t\u00e1c quay) t\u1ee9c \u0111\u1ed9ng t\u00e1c \u0111\u1ee9ng nghi\u00eam nh\u01b0 ban \u0111\u1ea7u.<\/p>\n\n\n\n
N\u1ebfu ta d\u00f9ng \u201co\u201d bi\u1ec3u di\u1ec5n vi\u1ec7c th\u1ef1c hi\u1ec7n hai \u0111\u1ed9ng t\u00e1c li\u00ean ti\u1ebfp. Nh\u01b0 v\u1eady ta s\u1ebd c\u00f3 LoR = I. T\u01b0\u01a1ng t\u1ef1 RoL bi\u1ec3u di\u1ec5n tr\u01b0\u1edbc th\u1ef1c hi\u1ec7n quay tr\u00e1i, sau th\u1ef1c hi\u1ec7n quay ph\u1ea3i, k\u1ebft qu\u1ea3 \u0111\u01b0\u1ee3c I. Ho L bi\u1ec3u di\u1ec5n tr\u01b0\u1edbc h\u1ebft th\u1ef1c hi\u1ec7n \u0111\u1ed9ng t\u00e1c quay tr\u00e1i, sau \u0111\u00f3 th\u1ef1c hi\u1ec7n \u0111\u1ed9ng t\u00e1c quay \u0111\u1eb1ng sau, k\u1ebft qu\u1ea3 \u0111\u01b0\u1ee3c R. Ti\u1ebfp t\u1ee5c c\u00e1ch suy lu\u1eadn t\u01b0\u01a1ng t\u1ef1, ta c\u00f3 th\u1ec3 nh\u1eadn \u0111\u01b0\u1ee3c b\u1ea3ng s\u01a1 \u0111\u1ed3 quan h\u1ec7 sau \u0111\u00e2y. Theo \u0111\u1ecbnh ngh\u0129a, ph\u00e9p t\u00ednh \u201co\u201d cho c\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a t\u1eadp h\u1ee3p M, b\u1ed1n ph\u1ea7n t\u1eed c\u1ee7a c\u00e1c t\u1eadp h\u1ee3p c\u00f3 m\u1ed1i li\u00ean quan:<\/p>\n\n\n\n
Tr\u01b0\u1edbc h\u1ebft, v\u1edbi b\u1ea5t k\u00ec ph\u1ea7n t\u1eed n\u00e0o c\u1ee7a M khi th\u1ef1c hi\u1ec7n \u0111\u1ed9ng t\u00e1c I c\u0169ng l\u00e0 ch\u00ednh \u0111\u1ed9ng t\u00e1c \u0111\u00f3. 1, b\u1edfi v\u00ec khi nh\u00e2n b\u1ea5t k\u00ec s\u1ed1 n\u00e0o v\u1edbi s\u1ed1 1 c\u0169ng \u0111\u01b0\u1ee3c ch\u00ednh s\u1ed1 \u0111\u00f3. Do \u0111\u00f3 I g\u1ecdi l\u00e0 ph\u1ea7n t\u1eed \u0111\u01a1n v\u1ecb.<\/p>\n\n\n\n
M\u1eb7t kh\u00e1c c\u0169ng nh\u01b0 m\u1ed9t s\u1ed1 t\u1ef1 nhi\u00ean a, \u0111\u1ec1u c\u00f3 s\u1ed1 ngh\u1ecbch \u0111\u1ea3o 1\/a, v\u1edbi b\u1ea5t k\u1ef3 m\u1ed9t ph\u1ea7n t\u1eed n\u00e0o c\u1ee7a M ta c\u0169ng c\u00f3 th\u1ec3 t\u00ecm \u0111\u01b0\u1ee3c m\u1ed9t ph\u1ea7n t\u1eed \u0111\u1ed1i \u1ee9ng \u0111\u1ec3 khi th\u1ef1c hi\u1ec7n li\u00ean ti\u1ebfp hai \u0111\u1ed9ng t\u00e1c \u0111\u00f3 ta l\u1ea1i \u0111\u01b0\u1ee3c I. Hai \u0111\u1ed9ng t\u00e1c nh\u01b0 v\u1eady \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 hai \u0111\u1ed9ng t\u00e1c ngh\u1ecbch \u0111\u1ea3o t\u01b0\u01a1ng \u1ee9ng v\u1edbi nhau.<\/p>\n\n\n\n
Th\u00f4ng qua b\u1ea3ng s\u01a1 \u0111\u1ed3 quan h\u1ec7 tr\u00ean \u0111\u00e2y ta c\u00f3 th\u1ec3 th\u1ea5y L, R l\u00e0 ngh\u1ecbch \u0111\u1ea3o t\u01b0\u01a1ng \u1ee9ng v\u1edbi nhau, I v\u00e0 H l\u00e0 hai ph\u1ea7n t\u1eed t\u1ef1 ngh\u1ecbch \u0111\u1ea3o \u0111\u1ed1i v\u1edbi b\u1ea3n th\u00e2n m\u00ecnh. M\u1eb7t kh\u00e1c, c\u00e1c ph\u00e9p t\u00ednh c\u1ee7a c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a t\u1eadp h\u1ee3p M c\u0169ng c\u00f3 m\u1ed9t s\u1ed1 t\u00ednh ch\u1ea5t: v\u00ed d\u1ee5 v\u1edbi ph\u00e9p t\u00ednh tinh ta c\u0169ng c\u00f3 quy lu\u1eadt k\u1ebft h\u1ee3p. V\u00ed d\u1ee5 (LoR)o H = IoH = H, c\u00f2n Lo(RoH) = LoL = H, v\u00ec v\u1eady (LoR)oH = Lo(RoH).<\/p>\n\n\n\n
T\u00f3m l\u1ea1i v\u1edbi b\u1ed1n y\u1ebfu t\u1ed1 c\u1ee7a t\u1eadp h\u1ee3p M: I, R, L, H khi th\u1ef1c hi\u1ec7n ph\u00e9p t\u00ednh 0, c\u00f3 y\u1ebfu t\u1ed1 \u0111\u01a1n v\u1ecb I, m\u1ed7i y\u1ebfu t\u1ed1 \u0111\u1ec1u c\u00f3 y\u1ebfu t\u1ed1 ngh\u1ecbch \u0111\u1ea3o, khi th\u1ef1c hi\u1ec7n c\u00e1c ph\u00e9p t\u00ednh v\u1edbi c\u00e1c y\u1ebfu t\u1ed1 c\u1ee7a M c\u00e1c ph\u00e9p t\u00ednh c\u0169ng c\u00f3 quy lu\u1eadt k\u1ebft h\u1ee3p. T\u1ea5t c\u1ea3 c\u00e1c quan h\u1ec7 v\u00e0 c\u00e1c ph\u00e9p t\u00ednh x\u00e1c \u0111\u1ecbnh k\u1ebft c\u1ea5u c\u1ee7a t\u1eadp h\u1ee3p M. To\u00e1n h\u1ecdc th\u01b0\u1eddng \u0111\u01b0\u1ee3c tr\u1eebu t\u01b0\u1ee3ng ho\u00e1 do vi\u1ec7c nghi\u00ean c\u1ee9u c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng c\u1ee5 th\u1ec3 nh\u01b0 v\u1eady. V\u00ec v\u1eady ch\u00fang ta n\u00f3i c\u00e1c \u0111\u1ed9ng t\u00e1c \u201c\u0111\u1ee9ng nghi\u00eam, quay ph\u1ea3i, quay tr\u00e1i, quay \u0111\u1eb1ng sau\u201d t\u1ea1o th\u00e0nh \u0111\u1ed1i t\u01b0\u1ee3ng c\u1ee7a to\u00e1n h\u1ecdc. M\u00f4n to\u00e1n h\u1ecdc l\u1ea5y c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng th\u1ef1c t\u1ebf n\u00e0y \u0111\u01b0\u1ee3c tr\u1eebu t\u01b0\u1ee3ng ho\u00e1 th\u00e0nh \u0111\u1ea1i s\u1ed1 \u201cnh\u00f3m\u201d. M\u1eddi c\u00e1c b\u1ea1n xem x\u00e9t s\u1ebd th\u1ea5y nh\u01b0 c\u00e1c ph\u1ea7n t\u1eed c\u1ee7a M s\u1ed1 nguy\u00ean, s\u1ed1 h\u1eefu t\u1ec9 c\u0169ng t\u1ea1o n\u00ean c\u1ea5u tr\u00fac nh\u00f3m trong ph\u00e9p t\u00ednh nh\u00e2n.<\/p>\n\n\n\n
Kh\u00e1i ni\u1ec7m nh\u00f3m do nh\u00e0 to\u00e1n h\u1ecdc Ph\u00e1p Galois \u0111\u01b0a ra, ng\u00e0y nay \u0111\u00e3 th\u00e2m nh\u1eadp v\u00e0o m\u1ecdi l\u0129nh v\u1ef1c kh\u00e1c nh\u01b0 v\u1eadt l\u00ed, ho\u00e1 h\u1ecdc c\u0169ng nh\u01b0 nhi\u1ec1u ng\u00e0nh khoa h\u1ecdc kh\u00e1c. Ngay c\u1ea3 \u0111\u1ecbnh l\u00ed v\u1ec1 vi\u1ec7c kh\u00f4ng gi\u1ea3i \u0111\u01b0\u1ee3c c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 b\u1eadc t\u1eeb n\u0103m tr\u1edf l\u00ean b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p c\u1ea7u ph\u01b0\u01a1ng c\u0169ng ph\u1ea3i d\u00f9ng l\u00ed thuy\u1ebft nh\u00f3m m\u1edbi ch\u1ee9ng minh \u0111\u01b0\u1ee3c.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: \u0110\u1ed1i t\u01b0\u1ee3ng ho\u00e1 h\u1ecdc; Y\u1ebfu t\u1ed1 \u0111\u01a1n v\u1ecb; \u0110\u01a1n v\u1ecb ngh\u1ecbch \u0111\u1ea3o;<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
\u201c\u0110\u1ee9ng nghi\u00eam, quay tr\u00e1i, quay ph\u1ea3i, quay \u0111\u1eb1ng sau\u201d l\u00e0 b\u1ed1n \u0111\u1ed9ng t\u00e1c kh\u00f4ng ph\u1ea3i l\u00e0 con s\u1ed1, kh\u00f4ng ph\u1ea3i l\u00e0 h\u00ecnh v\u1ebd v\u00ec sao l\u1ea1i tr\u1edf th\u00e0nh \u0111\u1ed1i t\u01b0\u1ee3ng c\u1ee7a to\u00e1n h\u1ecdc? Nhi\u1ec1u ng\u01b0\u1eddi kh\u00f4ng r\u00f5 t\u1ea1i sao. Tr\u01b0\u1edbc h\u1ebft ta th\u1eed ph\u00e2n t\u00edch m\u1ed1i quan h\u1ec7 n\u1ed9i t\u1ea1i c\u1ee7a b\u1ed1n \u0111\u1ed9ng t\u00e1c! \u0110\u1ec3 […]<\/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-7688","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\/7688","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=7688"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7688\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7688"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7688"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7688"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}