Trong b\u1ed9 s\u00e1ch to\u00e1n c\u1ed5 n\u1ed5i ti\u1ebfng c\u1ee7a Trung Qu\u1ed1c \u201cChu B\u00ec to\u00e1n kinh\u201d \u1edf ch\u01b0\u01a1ng I c\u00f3 n\u00eau l\u00ean b\u1ed9 s\u1ed1 tam gi\u00e1c 3, 4, 5. S\u1edf d\u0129 g\u1ecdi l\u00e0 b\u1ed9 s\u1ed1 tam gi\u00e1c l\u00e0 ba ch\u1eef s\u1ed1 n\u00e0y bi\u1ec3u di\u1ec5n m\u1ed1i li\u00ean quan gi\u1eefa hai c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng v\u1edbi c\u1ea1nh huy\u1ec1n c\u00f3 \u0111\u1ed9 d\u00e0i t\u01b0\u01a1ng \u1ee9ng l\u00e0 3, 4, 5. Ba s\u1ed1 3, 4, 5 l\u00e0 b\u1ed9 s\u1ed1 tam gi\u00e1c v\u00ec \u0111\u00f3 l\u00e0 ba s\u1ed1 c\u1ee7a c\u00e1c c\u1ea1nh c\u1ee7a g\u00f3c vu\u00f4ng v\u1edbi c\u1ea1nh huy\u1ec1n theo \u0111\u00fang \u0111\u1ecbnh l\u00ed m\u00e0 ng\u01b0\u1eddi ta th\u01b0\u1eddng g\u1ecdi l\u00e0 \u0111\u1ecbnh l\u00ed Pitago (Pythagore).<\/p>\n\n\n\n
Ngo\u00e0i ba s\u1ed1 3, 4, 5 c\u00f2n c\u00f3 nhi\u1ec1u b\u1ed9 ba s\u1ed1 kh\u00e1c tu\u00e2n theo \u0111\u1ecbnh l\u00ed Pitago nh\u01b0: 5, 12, 13; 8, 15, 17 v.v\u2026 C\u00e1c b\u1ed9 ba s\u1ed1 n\u00e0y tho\u1ea3 m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh x2 + y2 = z2; c\u00e1c s\u1ed1 x, y, z tho\u1ea3 m\u00e3n ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y g\u1ecdi l\u00e0 b\u1ed9 s\u1ed1 tam gi\u00e1c. V\u00ec ph\u01b0\u01a1ng tr\u00ecnh tr\u00ean l\u00e0 ph\u01b0\u01a1ng tr\u00ecnh c\u00f3 ba \u1ea9n s\u1ed1, n\u00ean c\u00f3 v\u00f4 s\u1ed1 nghi\u1ec7m, ng\u01b0\u1eddi ta g\u1ecdi \u0111\u00e2y l\u00e0 lo\u1ea1i ph\u01b0\u01a1ng tr\u00ecnh v\u00f4 \u0111\u1ecbnh. R\u00f5 r\u00e0ng l\u00e0 n\u1ebfu 3 s\u1ed1 x, y, z l\u00e0 b\u1ed9 s\u1ed1 Pitago th\u00ec b\u1ed9 ba s\u1ed1 (kx, ky, kz) c\u0169ng l\u00e0 b\u1ed9 s\u1ed1 Pitago. V\u00e0 n\u1ebfu hai s\u1ed1 x, y c\u00f3 \u01b0\u1edbc s\u1ed1 chung l\u00e0 d, th\u00ec d c\u0169ng l\u00e0 \u01b0\u1edbc s\u1ed1 c\u1ee7a z. N\u00f3i c\u00e1ch kh\u00e1c b\u1ed9 s\u1ed1 Pitago n\u1ebfu c\u00f3 \u01b0\u1edbc s\u1ed1 chung th\u00ec c\u00e1c \u01b0\u1edbc s\u1ed1 ph\u1ea3i b\u1eb1ng nhau. V\u00ec v\u1eady khi xem x\u00e9t ta ch\u1ec9 ch\u00fa \u00fd \u0111\u1ebfn c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau.<\/p>\n\n\n\n
V\u1eady c\u00e1c s\u1ed1 trong b\u1ed9 s\u1ed1 Pitago c\u00f3 m\u1ed1i quan h\u1ec7 g\u00ec v\u1edbi nhau kh\u00f4ng, hay n\u00f3i c\u00e1ch kh\u00e1c, b\u1ed9 s\u1ed1 Pitago \u0111\u01b0\u1ee3c c\u1ea5u t\u1ea1o nh\u01b0 th\u1ebf n\u00e0o?<\/p>\n\n\n\n
V\u00e0o th\u1ebf k\u1ec9 th\u1ee9 VI tr\u01b0\u1edbc C\u00f4ng nguy\u00ean, nh\u00e0 to\u00e1n h\u1ecdc c\u1ed5 Hy L\u1ea1p Pitago \u0111\u00e3 \u0111\u01b0a ra ph\u01b0\u01a1ng ph\u00e1p: l\u1ea5y m\u1ed9t s\u1ed1 l\u1ebb tu\u1ef3 \u00fd n\u00e2ng l\u00ean lu\u1ef9 th\u1eeba b\u1eadc hai r\u1ed3i ph\u00e2n chia th\u00e0nh hai s\u1ed1 sai kh\u00e1c nhau 1 \u0111\u01a1n v\u1ecb th\u00ec s\u1ed1 thu \u0111\u01b0\u1ee3c l\u00e0 m\u1ed9t b\u1ed9 ba s\u1ed1 Pitago. V\u00ed d\u1ee5 l\u1ea5y s\u1ed1 2x + 1, n\u00e2ng l\u00ean lu\u1ef9 th\u1eeba hai ta c\u00f3 4×2 + 4x + 1, chia s\u1ed1 v\u1eeba thu \u0111\u01b0\u1ee3c th\u00e0nh hai s\u1ed1 sai kh\u00e1c nhau 1 \u0111\u01a1n v\u1ecb l\u00e0 2×2 + 2x v\u00e0 2×2 + 2x + 1.<\/p>\n\n\n\n
V\u1eady ba s\u1ed1 2x + 1, 2×2 + 2x v\u00e0 2×2 +2x + 1 l\u00e0 m\u1ed9t b\u1ed9 s\u1ed1 Pitago. V\u00ed nh\u01b0 b\u1ed9 s\u1ed1 67, 2244 v\u00e0 2245 l\u00e0 b\u1ed9 s\u1ed1 Pitago.<\/p>\n\n\n\n
V\u00e0o th\u1ebf k\u1ec9 th\u1ee9 nh\u1ea5t sau C\u00f4ng nguy\u00ean, trong \u201cS\u00e1ch to\u00e1n ch\u00edn ch\u01b0\u01a1ng\u201d c\u00f2n \u0111\u01b0a ra m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p kh\u00e9o l\u00e9o h\u01a1n; ta ch\u1ecdn c\u00e1c s\u1ed1 m, n th\u1ebf th\u00ec (m2 – n2), mn v\u00e0 1\/2(m2 + n2) s\u1ebd l\u00e0 m\u1ed9t b\u1ed9 s\u1ed1 Pitago. V\u00ed d\u1ee5 m = 7, n = 3, ta c\u00f3 th\u1ec3 t\u00ednh ra c\u00e1c s\u1ed1 20, 21, 29 l\u00e0 m\u1ed9t b\u1ed9 s\u1ed1 Pitago;<\/p>\n\n\n\n
Khi m = 5 v\u00e0 n = 3, ta t\u00ednh ra 8, 15, 17. V\u00e0o th\u1ebf k\u1ec9 th\u1ee9 ba sau C\u00f4ng nguy\u00ean, nh\u00e0 to\u00e1n h\u1ecdc Trung Qu\u1ed1c L\u01b0u Huy \u0111\u00e3 ch\u1ee9ng minh ph\u01b0\u01a1ng ph\u00e1p n\u00e0y b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p h\u00ecnh h\u1ecdc.<\/p>\n\n\n\n
C\u0169ng v\u00e0o th\u1ebf k\u1ec9 III, nh\u00e0 to\u00e1n h\u1ecdc c\u1ed5 Hy L\u1ea1p Diophan \u0111\u00e3 \u0111\u01b0a ra c\u00f4ng th\u1ee9c:<\/p>\n\n\n\n
N\u1ebfu ch\u1ecdn m = u\/v, z = u2 + v2, ta s\u1ebd nh\u1eadn \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 2uv, u2 – v2, u2 + v2. B\u1ea1n c\u00f3 th\u1ec3 t\u00ecm th\u1ea5y c\u00f4ng th\u1ee9c n\u00e0y ch\u1ec9 kh\u00e1c c\u00f4ng th\u1ee9c trong \u201cS\u00e1ch to\u00e1n ch\u00edn ch\u01b0\u01a1ng\u201d \u1edf h\u1ec7 s\u1ed1 2, c\u00f2n c\u00f4ng th\u1ee9c Pitago c\u0169ng ch\u00ednh l\u00e0 tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t c\u1ee7a c\u00f4ng th\u1ee9c n\u00e0y. u = z + 1, v = z.<\/p>\n\n\n\n
V\u1eady n\u1ebfu tu\u1ef3 \u00fd ch\u1ecdn hai s\u1ed1 m, n ho\u1eb7c u, v li\u1ec7u c\u00f3 th\u1ec3 d\u00f9ng c\u00f4ng th\u1ee9c n\u00eau tr\u00ean \u0111\u1ec3 t\u00ednh c\u00e1c b\u1ed9 s\u1ed1 Pitago \u0111\u01b0\u1ee3c kh\u00f4ng? \u0110\u01b0\u01a1ng nhi\u00ean l\u00e0 kh\u00f4ng. V\u1eady th\u00eam \u0111i\u1ec1u ki\u1ec7n cho hai s\u1ed1 m v\u00e0 n l\u00e0 ch\u00fang ph\u1ea3i l\u00e0 c\u00e1c s\u1ed1 nguy\u00ean t\u1ed1 c\u00f9ng nhau. V\u1edbi \u0111i\u1ec1u ki\u1ec7n \u0111\u1eb7t ra th\u00ec d\u00f9ng c\u00f4ng th\u1ee9c n\u00eau trong \u201cS\u00e1ch to\u00e1n ch\u00edn ch\u01b0\u01a1ng\u201d ta c\u00f3 th\u1ec3 t\u00ecm ra b\u1ed9 s\u1ed1 Pitago, v\u00ec v\u1eady ng\u01b0\u1eddi ta g\u1ecdi ch\u00fang l\u00e0 c\u00f4ng th\u1ee9c chung \u0111\u1ec3 bi\u1ec3u di\u1ec5n nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh x2 + y2 = z2. \u0110\u01b0\u01a1ng nhi\u00ean c\u00f3 th\u1ec3 d\u00f9ng c\u00e1c c\u00f4ng th\u1ee9c kh\u00e1c nhau \u0111\u1ec3 t\u00ednh b\u1ed9 s\u1ed1 Pitago.<\/p>\n\n\n\n
Quan s\u00e1t k\u0129 b\u1ed9 s\u1ed1 tam gi\u00e1c ta th\u1ea5y ch\u00fang c\u00f3 m\u1ed1i t\u01b0\u01a1ng quan nh\u1ea5t \u0111\u1ecbnh v\u1ec1 t\u00ednh ch\u1eb5n l\u1ebb c\u1ee7a c\u00e1c s\u1ed1, v\u00ed d\u1ee5 c\u00f3 th\u1ec3 l\u00e0 hai l\u1ebb m\u1ed9t ch\u1eb5n. Nh\u01b0 x, y, z l\u00e0 b\u1ed9 s\u1ed1 Pitago th\u00ec hai s\u1ed1 x, y ph\u1ea3i l\u00e0 s\u1ed1 ch\u1eb5n, m\u1ed9t l\u1ebb, th\u00ec z ph\u1ea3i l\u00e0 s\u1ed1 l\u1ebb. T\u1ea1i sao nh\u01b0 v\u1eady c\u00e1c b\u1ea1n h\u00e3y t\u1ef1 suy ngh\u0129 v\u00e0 ch\u1ee9ng minh.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: \u0110\u1ecbnh l\u00ed tam gi\u00e1c; B\u1ed9 s\u1ed1 tam gi\u00e1c.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Trong b\u1ed9 s\u00e1ch to\u00e1n c\u1ed5 n\u1ed5i ti\u1ebfng c\u1ee7a Trung Qu\u1ed1c \u201cChu B\u00ec to\u00e1n kinh\u201d \u1edf ch\u01b0\u01a1ng I c\u00f3 n\u00eau l\u00ean b\u1ed9 s\u1ed1 tam gi\u00e1c 3, 4, 5. S\u1edf d\u0129 g\u1ecdi l\u00e0 b\u1ed9 s\u1ed1 tam gi\u00e1c l\u00e0 ba ch\u1eef s\u1ed1 n\u00e0y bi\u1ec3u di\u1ec5n m\u1ed1i li\u00ean quan gi\u1eefa hai c\u1ea1nh c\u1ee7a tam gi\u00e1c vu\u00f4ng v\u1edbi c\u1ea1nh huy\u1ec1n […]<\/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-7533","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\/7533","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=7533"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7533\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}