Bao l\u00e2u nay con ng\u01b0\u1eddi v\u1eabn \u0111ang lu\u00f4n t\u00ecm ki\u1ebfm ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed t\u1ef1 \u0111\u1ed9ng, hi v\u1ecdng c\u00f3 m\u1ed9t ng\u00e0y \u0111\u01b0a v\u00e0o m\u00e1y t\u00ednh m\u1ed9t \u0111\u1ecbnh l\u00ed to\u00e1n c\u1ea7n ch\u1ee9ng minh, v\u1eadn h\u00e0nh h\u1ec7 th\u1ed1ng ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed c\u1ee7a m\u00e1y, v\u00e0 r\u1ed3i r\u1ea5t nhanh \u0111\u00e3 nh\u1eadn \u0111\u01b0\u1ee3c l\u1eddi ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed.<\/p>\n\n\n\n
Ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed t\u1ef1 \u0111\u1ed9ng c\u0169ng g\u1ecdi l\u00e0 “ch\u1ee9ng minh b\u1eb1ng m\u00e1y t\u00ednh”.<\/p>\n\n\n\n
M\u00e1y t\u00ednh s\u1edf d\u0129 c\u00f3 ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed l\u00e0 v\u00ec c\u00e1c chuy\u00ean gia<\/a> tr\u01b0\u1edbc h\u1ebft \u0111\u00e3 k\u00ed hi\u1ec7u h\u00f3a m\u1ed9t s\u1ed1 c\u00f4ng th\u1ee9c v\u00e0 quy t\u1eafc, l\u01b0u tr\u1eef v\u00e0o m\u00e1y t\u00ednh. R\u1ed3i l\u1ea1i l\u1eadp tr\u00ecnh<\/a> cho n\u00f3. Nh\u1eefng ch\u01b0\u01a1ng tr\u00ecnh n\u00e0y c\u00f3 th\u1ec3 m\u00f4 ph\u1ecfng ph\u01b0\u01a1ng th\u1ee9c suy l\u00ed c\u1ee7a con ng\u01b0\u1eddi. Khi b\u1ea1n \u0111\u00e3 \u0111\u01b0a v\u00e0o m\u00e1y t\u00ednh c\u00e1c ti\u1ec1n \u0111\u1ec1 v\u00e0 k\u1ebft lu\u1eadn c\u1ee7a \u0111\u1ecbnh l\u00ed b\u1eb1ng h\u00ecnh th\u1ee9c k\u00ed hi\u1ec7u quy \u0111\u1ecbnh, ch\u01b0\u01a1ng tr\u00ecnh s\u1ebd kh\u00f4ng ng\u1eebng ti\u1ebfn h\u00e0nh c\u00f4ng vi\u1ec7c t\u00ecm ki\u1ebfm v\u00e0 k\u1ebft lu\u1eadn v\u1edbi vi\u1ec7c th\u1eed nghi\u1ec7m c\u00e1c c\u00f4ng th\u1ee9c, quy t\u1eafc v\u00e0 ti\u1ec1n \u0111\u1ec1, cho \u0111\u1ebfn khi \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 ph\u00f9 h\u1ee3p v\u1edbi k\u1ebft lu\u1eadn. Kh\u1ea3 n\u0103ng ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed c\u1ee7a m\u00e1y l\u00e0 m\u1ea1nh hay y\u1ebfu, ch\u1ee7 y\u1ebfu quy\u1ebft \u0111\u1ecbnh b\u1edfi ch\u1ea5t l\u01b0\u1ee3ng hay d\u1edf c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh v\u00e0 s\u1ed1 l\u01b0\u1ee3ng c\u00f4ng th\u1ee9c, quy t\u1eafc \u0111\u01b0\u1ee3c l\u01b0u tr\u1eef trong m\u00e1y. Ch\u01b0\u01a1ng tr\u00ecnh thi\u1ebft k\u1ebf<\/a> c\u00e0ng t\u1ed1t, c\u00f4ng th\u1ee9c v\u00e0 quy t\u1eafc l\u01b0u tr\u1eef c\u00e0ng nhi\u1ec1u th\u00ec kh\u1ea3 n\u0103ng ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed c\u1ee7a m\u00e1y c\u00e0ng m\u1ea1nh. \u0110\u01b0\u01a1ng nhi\u00ean khi \u0111\u00e3 l\u01b0u tr\u1eef nhi\u1ec1u c\u00f4ng th\u1ee9c v\u00e0 quy t\u1eafc th\u00ec hi\u1ec7u qu\u1ea3 c\u1ee7a ch\u01b0\u01a1ng tr\u00ecnh s\u1ebd b\u1ecb h\u1ea1n ch\u1ebf.<\/p>\n\n\n\n Sau \u0111\u00e2y s\u1ebd quan s\u00e1t m\u1ed9t v\u00ed d\u1ee5 \u0111\u01a1n gi\u1ea3n.<\/p>\n\n\n\n Xem x\u00e9t h\u00ecnh v\u1ebd 1 \u0111\u00e3 cho, gi\u1ea3 thi\u1ebft m\u00e1y t\u00ednh \u0111\u00e3 l\u01b0u tr\u1eef c\u00f4ng th\u1ee9c v\u1ec1 h\u00ecnh 1:<\/p>\n\n\n\n C\u00f4ng th\u1ee9c 1: V\u1edbi h\u00ecnh thang \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh b\u1edfi b\u1ed1n \u0111i\u1ec3m X; Y; U; V b\u1ea5t k\u00ec, trong \u0111\u00f3 X l\u00e0 \u0111i\u1ec3m \u0111\u1ec9nh tr\u00e1i b\u00ean tr\u00ean, Y l\u00e0 \u0111i\u1ec3m \u0111\u1ec9nh ph\u1ea3i b\u00ean tr\u00ean, U l\u00e0 \u0111i\u1ec3m \u0111\u1ec9nh ph\u1ea3i b\u00ean d\u01b0\u1edbi, VY l\u00e0 \u0111\u01b0\u1eddng ch\u00e9o n\u1ed1i hai \u0111\u1ec9nh \u0111\u1ed1i nhau. N\u1ebfu XYUV l\u00e0 m\u1ed9t h\u00ecnh thang th\u00ec \u0111o\u1ea1n th\u1eb3ng XY song song v\u1edbi \u0111o\u1ea1n UV.<\/p>\n\n\n\n C\u00f4ng th\u1ee9c 2: N\u1ebfu XY song song v\u1edbi \u0111o\u1ea1n UV th\u00ec \u2220 XYV v\u00e0 \u2220 UVY b\u1eb1ng nhau.<\/p>\n\n\n\n Cho m\u1ed9t h\u00ecnh thang ABCD nh\u01b0 h\u00ecnh 2. \u0110o\u1ea1n th\u1eb3ng DB l\u00e0 \u0111\u01b0\u1eddng n\u1ed1i hai \u0111\u1ec9nh \u0111\u1ed1i nhau. Ch\u1ee9ng minh 2 g\u00f3c so le trong \u2220 ABD v\u00e0 \u2220 BDC b\u1eb1ng nhau. T\u1ee9c l\u00e0 ph\u1ea3i ch\u1ee9ng minh: n\u1ebfu ABCD l\u00e0 h\u00ecnh thang th\u00ec \u2220 ABD v\u00e0 \u2220 BDC b\u1eb1ng nhau.<\/p>\n\n\n\n Ti\u1ec1n \u0111\u1ec1 \u0111\u01b0a v\u00e0o m\u00e1y t\u00ednh l\u00e0: m\u1ed9t h\u00ecnh thang t\u1ea1o th\u00e0nh b\u1edfi b\u1ed1n \u0111\u1ec9nh \u0111i\u1ec3m ABCD. Trong \u0111\u00f3 A l\u00e0 \u0111i\u1ec3m \u0111\u1ec9nh tr\u00e1i b\u00ean tr\u00ean, B l\u00e0 \u0111i\u1ec3m \u0111\u1ec9nh ph\u1ea3i b\u00ean tr\u00ean, C l\u00e0 \u0111i\u1ec3m \u0111\u1ec9nh ph\u1ea3i \u1edf d\u01b0\u1edbi, D l\u00e0 \u0111i\u1ec3m \u0111\u1ec9nh tr\u00e1i \u1edf d\u01b0\u1edbi, BD l\u00e0 \u0111\u01b0\u1eddng n\u1ed1i hai \u0111\u1ec9nh \u0111\u1ed1i nhau. ABCD l\u00e0 h\u00ecnh thang. K\u1ebft lu\u1eadn: \u2220 ABD v\u00e0 \u2220 BDC b\u1eb1ng nhau.<\/p>\n\n\n\n Ch\u01b0\u01a1ng tr\u00ecnh c\u0103n c\u1ee9 v\u00e0o ti\u1ec1n \u0111\u1ec1 v\u00e0 t\u00ecm c\u00f4ng th\u1ee9c \u0111\u1ed5i bi\u1ebfn l\u01b0\u1ee3ng X; Y; U; V trong c\u00f4ng th\u1ee9c 1 l\u1ea7n l\u01b0\u1ee3t l\u00e0 A; B; C; D. C\u00f3 \u0111\u01b0\u1ee3c m\u1ed9t v\u00ed d\u1ee5 th\u1ef1c t\u1ebf: n\u1ebfu ABCD l\u00e0 h\u00ecnh thang th\u00ec AB song song v\u1edbi CD. L\u1ea1i v\u00ec “ABCD l\u00e0 m\u1ed9t h\u00ecnh thang” l\u00e0 ti\u1ec1n \u0111\u1ec1, th\u1ebf l\u00e0 c\u00f3 \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 trung gian, t\u1ee9c k\u1ebft lu\u1eadn c\u1ee7a v\u00ed d\u1ee5 th\u1ef1c t\u1ebf thu\u1ed9c c\u00f4ng th\u1ee9c 1: AB song song v\u1edbi CD. L\u1ea1i t\u1eeb k\u1ebft qu\u1ea3 trung gian n\u00e0y m\u00e0 t\u00ecm ra c\u00f4ng th\u1ee9c 2, l\u1ea7n l\u01b0\u1ee3t thay th\u1ebf l\u01b0\u1ee3ng X, Y, U, V trong c\u00f4ng th\u1ee9c 2 th\u00e0nh A, B, C, D. S\u1ebd c\u00f3 m\u1ed9t v\u00ed d\u1ee5 th\u1ef1c t\u1ebf c\u1ee7a c\u00f4ng th\u1ee9c 2: n\u1ebfu AB song song v\u1edbi CD th\u00ec \u2220 ABD v\u00e0 \u2220 BDC b\u1eb1ng nhau. L\u00fac n\u00e0y k\u1ebft qu\u1ea3 trung gian “\u0111o\u1ea1n AB song song v\u1edbi \u0111o\u1ea1n CD”, nh\u1ea5t tr\u00ed v\u1edbi ti\u1ec1n \u0111\u1ec1 c\u1ee7a v\u00ed d\u1ee5 th\u1ef1c t\u1ebf trong c\u00f4ng th\u1ee9c 2. Th\u1ebf l\u00e0 c\u00f3 \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3, t\u1ee9c k\u1ebft lu\u1eadn c\u1ee7a v\u00ed d\u1ee5 th\u1ef1c t\u1ebf trong c\u00f4ng th\u1ee9c 2: \u2220 ABD v\u00e0 \u2220 BDC b\u1eb1ng nhau. \u0110\u00e2y ch\u00ednh l\u00e0 k\u1ebft lu\u1eadn c\u1ea7n c\u00f3. B\u1edfi v\u1eady \u0111\u1ecbnh l\u00ed \u0111\u00e3 \u0111\u01b0\u1ee3c ch\u1ee9ng minh.<\/p>\n\n\n\n \u1ede \u0111\u00e2y ch\u00fang ta ch\u1ec9 l\u00e0 mi\u00eau t\u1ea3 qu\u00e1 tr\u00ecnh ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed c\u1ee7a m\u00e1y t\u00ednh m\u1ed9t c\u00e1ch phi h\u00ecnh th\u1ee9c. Tr\u00ean th\u1ef1c t\u1ebf th\u00ec m\u00e1y ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed ho\u00e0n to\u00e0n l\u00e0 k\u00ed hi\u1ec7u h\u00f3a v\u00e0 h\u00ecnh th\u1ee9c h\u00f3a.<\/p>\n\n\n\n T\u1eeb nh\u1eefng n\u0103m 50 c\u1ee7a th\u1ebf k\u1ec9 XX, m\u00e1y t\u00ednh ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed t\u1eeb giai \u0111o\u1ea1n thi\u1ebft t\u01b0\u1edfng \u0111i t\u1edbi giai \u0111o\u1ea1n th\u1ef1c nghi\u1ec7m, v\u00e0 \u0111\u00e3 thu \u0111\u01b0\u1ee3c nhi\u1ec1u th\u00e0nh t\u00edch \u0111\u00e1ng m\u1eebng. N\u0103m 1956 nh\u00f3m Niu\u01a1 \u0111\u00e3 bi\u00ean so\u1ea1n ch\u01b0\u01a1ng tr\u00ecnh m\u00e1y t\u00ednh th\u1ec3 hi\u1ec7n qu\u00e1 tr\u00ecnh t\u01b0 duy suy l\u00ed di\u1ec5n d\u1ecbch c\u1ee7a b\u1ed9 n\u00e3o con ng\u01b0\u1eddi v\u1edbi c\u00e1c b\u01b0\u1edbc gi\u1ea3n h\u00f3a, k\u0129 x\u1ea3o, s\u00e1ch l\u01b0\u1ee3c, quy t\u1eafc. H\u1ecd \u0111\u00e3 ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed 38 trong 52 \u0111\u1ecbnh l\u00ed thu\u1ed9c ch\u01b0\u01a1ng 2 Nguy\u00ean l\u00ed to\u00e1n h\u1ecdc c\u1ee7a Bertrand Russell – Alfred North Whitehead. N\u0103m 1963, ch\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1ee3c c\u1ea3i ti\u1ebfn \u0111\u00e3 ch\u1ee9ng minh to\u00e0n b\u1ed9 52 \u0111\u1ecbnh l\u00ed. N\u0103m 1958 m\u1ed9t ng\u01b0\u1eddi M\u0129 g\u1ed1c Hoa l\u00e0 V\u01b0\u01a1ng<\/p>\n\n\n\n H\u1ea1o \u0111\u00e3 so\u1ea1n ba ch\u01b0\u01a1ng tr\u00ecnh so v\u1edbi ch\u01b0\u01a1ng tr\u00ecnh c\u1ee7a Niu\u01a1 c\u00f2n gi\u1ea3n \u0111\u01a1n v\u00e0 hi\u1ec7u qu\u1ea3 h\u01a1n, ch\u1ec9 n\u0103m ph\u00fat \u0111\u00e3 ch\u1ee9ng minh xong 52 \u0111\u1ecbnh l\u00ed. N\u0103m 1965 R\u00f4binx\u01a1n \u0111\u00e3 n\u00eau ra nguy\u00ean l\u00ed quy k\u1ebft, th\u00fac \u0111\u1ea9y s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a vi\u1ec7c ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed tr\u00ean m\u00e1y t\u00ednh v\u1edbi h\u00ecnh th\u1ee9c \u0111\u01a1n gi\u1ea3n cho c\u01a1 gi\u1edbi.<\/p>\n\n\n\n C\u00e1c nh\u00e0 khoa h\u1ecdc Trung Qu\u1ed1c trong c\u00f4ng cu\u1ed9c nghi\u00ean c\u1ee9u ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed tr\u00ean m\u00e1y t\u00ednh \u0111\u00e3 c\u00f3 \u0111\u01b0\u1ee3c b\u01b0\u1edbc ti\u1ebfn khi\u1ebfn m\u1ecdi ng\u01b0\u1eddi ph\u1ea3i ng\u1ea1c nhi\u00ean, \u0111\u01b0\u1ee3c gi\u1edbi khoa h\u1ecdc tr\u00ean th\u1ebf gi\u1edbi coi tr\u1ecdng v\u00e0 \u0111\u00e1nh gi\u00e1 cao. Trong \u0111\u00f3, th\u00e0nh qu\u1ea3 nghi\u00ean c\u1ee9u c\u1ee7a gi\u00e1o s\u01b0 Ng\u00f4 V\u0103n Tu\u1ea5n l\u00e0 n\u1ed5i b\u1eadt h\u01a1n c\u1ea3. Gi\u1eefa n\u0103m 1976 v\u00e0 1977 Ng\u00f4 V\u0103n Tu\u1ea5n \u0111\u00e3 t\u00ecm ra \u0111\u01b0\u1ee3c ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh b\u1eb1ng m\u00e1y t\u00ednh cho c\u00e1c \u0111\u1ecbnh l\u00ed h\u00ecnh h\u1ecdc, v\u00e0 \u0111\u00e3 ch\u1ee9ng minh \u0111\u01b0\u1ee3c h\u01a1n 100 \u0111\u1ecbnh l\u00ed b\u1eb1ng m\u00e1y t\u00ednh. V\u1ec1 sau \u00f4ng c\u00f2n m\u1edf r\u1ed9ng ph\u1ea1m vi ch\u1ee9ng minh b\u1eb1ng m\u00e1y t\u00ednh sang c\u00e1c l\u0129nh v\u1ef1c kh\u00e1c nh\u01b0 h\u00ecnh h\u1ecdc x\u1ea1 \u1ea3nh, h\u00ecnh h\u1ecdc phi \u01a0clit.<\/p>\n\n\n\n Do v\u1eady c\u00f3 th\u1ec3 th\u1ea5y r\u1eb1ng ng\u01b0\u1eddi ta c\u00f3 th\u1ec3 l\u00e0m cho m\u00e1y t\u00ednh c\u00f3 kh\u1ea3 n\u0103ng ch\u1ee9ng minh. M\u1ee5c \u0111\u00edch c\u1ee7a vi\u1ec7c nghi\u00ean c\u1ee9u ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed b\u1eb1ng m\u00e1y t\u00ednh l\u00e0 \u0111\u1ec3 m\u00e1y t\u00ednh tr\u1ef1c ti\u1ebfp can d\u1ef1 v\u00e0o qu\u00e1 tr\u00ecnh ho\u1ea1t \u0111\u1ed9ng t\u01b0 duy c\u1ee7a con ng\u01b0\u1eddi, n\u00e2ng cao kh\u1ea3 n\u0103ng v\u00e0 hi\u1ec7u qu\u1ea3 s\u00e1ng t\u1ea1o khoa h\u1ecdc c\u1ee7a lo\u00e0i ng\u01b0\u1eddi. \u00fd ngh\u0129a th\u1eadt l\u00e0 to l\u1edbn v\u00e0 s\u00e2u xa. V\u1ec1 m\u1eb7t n\u00e0y c\u00f2n c\u00f3 nhi\u1ec1u vi\u1ec7c ph\u1ea3i l\u00e0m n\u1eefa.<\/p>\n\n\n\n T\u1eeb kh\u00f3a: Suy lu\u1eadn l\u00f4gic; Ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed; Ch\u1ee9ng minh c\u01a1 gi\u1edbi.<\/p>\n","protected":false},"excerpt":{"rendered":" Bao l\u00e2u nay con ng\u01b0\u1eddi v\u1eabn \u0111ang lu\u00f4n t\u00ecm ki\u1ebfm ph\u01b0\u01a1ng ph\u00e1p ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed t\u1ef1 \u0111\u1ed9ng, hi v\u1ecdng c\u00f3 m\u1ed9t ng\u00e0y \u0111\u01b0a v\u00e0o m\u00e1y t\u00ednh m\u1ed9t \u0111\u1ecbnh l\u00ed to\u00e1n c\u1ea7n ch\u1ee9ng minh, v\u1eadn h\u00e0nh h\u1ec7 th\u1ed1ng ch\u1ee9ng minh \u0111\u1ecbnh l\u00ed c\u1ee7a m\u00e1y, v\u00e0 r\u1ed3i r\u1ea5t nhanh \u0111\u00e3 nh\u1eadn \u0111\u01b0\u1ee3c l\u1eddi ch\u1ee9ng minh \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":[15,13],"tags":[],"class_list":["post-10306","post","type-post","status-publish","format-standard","hentry","category-hoi-dap-khoa-hoc","category-tin-hoc"],"_links":{"self":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/10306","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=10306"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/10306\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=10306"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=10306"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=10306"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}