{"id":29907,"date":"2023-04-18T14:40:41","date_gmt":"2023-04-18T07:40:41","guid":{"rendered":"https:\/\/chanhkien.org\/?p=29907"},"modified":"2025-05-12T10:20:10","modified_gmt":"2025-05-12T03:20:10","slug":"toan-thuat-man-dam-quy-luat-cua-cac-chu-so-tren-lac-thu","status":"publish","type":"post","link":"https:\/\/chanhkien.org\/2023\/04\/toan-thuat-man-dam-quy-luat-cua-cac-chu-so-tren-lac-thu.html","title":{"rendered":"Thu\u1eadt s\u1ed1 m\u1ea1n \u0111\u00e0m: Quy lu\u1eadt c\u1ee7a c\u00e1c ch\u1eef s\u1ed1 tr\u00ean L\u1ea1c th\u01b0"},"content":{"rendered":"

[ChanhKien.org]<\/b><\/p>\n

S\u1ef1 s\u1eafp x\u1ebfp c\u1ee7a c\u00e1c ch\u1eef s\u1ed1 tr\u00ean L\u1ea1c th\u01b0, nh\u00ecn th\u00ec th\u1ea5y r\u1ea5t \u0111\u01a1n gi\u1ea3n, ch\u1ec9 c\u00f3 1, 2, 3, 4, 5, 6, 7, 8, 9, ch\u1ec9 c\u00f3 9 ch\u1eef s\u1ed1 \u0111\u00f3. Nh\u01b0ng c\u00e1c ch\u1eef s\u1ed1 \u0111\u01a1n gi\u1ea3n, chi\u1ec3u theo c\u00e1ch s\u1eafp x\u1ebfp \u0111\u1eb7c bi\u1ec7t c\u1ee7a n\u00f3, k\u1ebft qu\u1ea3 l\u1ea1i s\u1ea3n sinh ra c\u00e1c quy lu\u1eadt ch\u1eef s\u1ed1 kh\u00f4ng \u0111\u01a1n gi\u1ea3n.<\/p>\n\n\n\n\n\n
4<\/td>\n9<\/td>\n2<\/td>\n<\/tr>\n
3<\/td>\n5<\/td>\n7<\/td>\n<\/tr>\n
8<\/td>\n1<\/td>\n6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

L\u1ea1c th\u01b0 nh\u00ecn th\u00ec th\u1ea5y l\u00e0 m\u1ed9t \u0111\u1ed3 h\u00ecnh h\u00ecnh vu\u00f4ng, g\u1ecdi l\u00e0 \u201cph\u01b0\u01a1ng \u0111\u1ed3\u201d. C\u00f3 ba h\u00e0ng, g\u1ecdi l\u00e0 ho\u00e0nh, c\u00f3 ba c\u1ed9t, g\u1ecdi l\u00e0 tung. Ng\u01b0\u1eddi ta c\u0169ng g\u1ecdi L\u1ea1c th\u01b0 l\u00e0 Tung Ho\u00e0nh \u0110\u1ed3.<\/p>\n

<\/span>Quy lu\u1eadt th\u1ee9 nh\u1ea5t:<\/b><\/span><\/p>\n

H\u00e0ng tr\u00ean l\u00e0 4, 9, 2, c\u1ed9ng l\u1ea1i l\u00e0 15, h\u00e0ng gi\u1eefa l\u00e0 3, 5, 7, c\u1ed9ng l\u1ea1i l\u00e0 15, h\u00e0ng d\u01b0\u1edbi l\u00e0 8, 1, 6, c\u1ed9ng l\u1ea1i l\u00e0 15.<\/p>\n

4+9+2=15<\/p>\n

3+5+7=15<\/p>\n

8+1+6=15<\/p>\n

C\u1ed9t tr\u00e1i l\u00e0 4, 3, 8, c\u1ed9ng l\u1ea1i l\u00e0 15, c\u1ed9t gi\u1eefa l\u00e0 9, 5, 1, c\u1ed9ng l\u1ea1i l\u00e0 15, c\u1ed9t ph\u1ea3i l\u00e0 2, 7, 6, c\u1ed9ng l\u1ea1i l\u00e0 15.<\/p>\n

4+3+8=15<\/p>\n

9+5+1=15<\/p>\n

2+7+6=15<\/p>\n

\u0110\u01b0\u1eddng ch\u00e9o ch\u00ednh l\u00e0 4, 5, 6, c\u1ed9ng l\u1ea1i l\u00e0 15, \u0111\u01b0\u1eddng ch\u00e9o ph\u1ee5 l\u00e0 2, 5, 8, c\u1ed9ng l\u1ea1i l\u00e0 15.<\/p>\n

4+5+6=15<\/p>\n

2+5+8=15<\/p>\n

Ngang d\u1ecdc v\u00e0 \u0111\u01b0\u1eddng ch\u00e9o, c\u00e1c ph\u01b0\u01a1ng h\u01b0\u1edbng kh\u00e1c nhau, ba s\u1ed1 c\u1ed9ng l\u1ea1i, \u0111\u1ec1u l\u00e0 15. Qu\u1ea3 th\u1ef1c r\u1ea5t th\u1ea7n k\u1ef3, do \u0111\u00f3 ng\u01b0\u1eddi ta c\u0169ng g\u1ecdi L\u1ea1c th\u01b0 l\u00e0 huy\u1ec1n ph\u01b0\u01a1ng (h\u00ecnh vu\u00f4ng huy\u1ec1n di\u1ec7u).<\/p>\n

<\/span>Quy lu\u1eadt th\u1ee9 hai:<\/b><\/span><\/p>\n

Ph\u01b0\u01a1ng, r\u1ea5t d\u1ec5 khi\u1ebfn ng\u01b0\u1eddi ta ngh\u0129 \u0111\u1ebfn b\u00ecnh ph\u01b0\u01a1ng. B\u00ecnh ph\u01b0\u01a1ng, c\u00e1ch d\u00f9ng s\u01a1 khai l\u00fac ban \u0111\u1ea7u l\u00e0 \u0111\u1ec3 t\u00ednh to\u00e1n di\u1ec7n t\u00edch, di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng b\u1eb1ng b\u00ecnh ph\u01b0\u01a1ng \u0111\u1ed9 d\u00e0i c\u1ea1nh. Khi ch\u00fang ta d\u00f9ng b\u00ecnh ph\u01b0\u01a1ng \u0111\u1ec3 t\u00ednh to\u00e1n L\u1ea1c th\u01b0, th\u00ec xu\u1ea5t hi\u1ec7n nhi\u1ec1u quy lu\u1eadt ch\u1eef s\u1ed1 h\u01a1n.<\/p>\n

H\u00e0ng tr\u00ean l\u00e0 4, 9, 2, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 101; h\u00e0ng d\u01b0\u1edbi l\u00e0 8, 1, 6, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 101.<\/p>\n

4^2+9^2+2^2=101<\/p>\n

8^2+1^2+6^2=101<\/p>\n

C\u1ed9t tr\u00e1i l\u00e0 4, 3, 8, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 89; c\u1ed9t ph\u1ea3i l\u00e0 2, 7, 6, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 89.<\/p>\n

4^2+3^2+8^2=89<\/p>\n

2^2+7^2+6^2=89<\/p>\n

<\/span>Quy lu\u1eadt th\u1ee9 ba:<\/b><\/span><\/p>\n

T\u1ed5ng h\u1ee3p v\u1eadn d\u1ee5ng hai quy lu\u1eadt \u1edf tr\u00ean, c\u00f2n c\u00f3 m\u1ed9t s\u1ed1 c\u00e1ch t\u00ednh th\u00fa v\u1ecb sau:<\/p>\n

L\u1ea5y h\u00e0ng tr\u00ean v\u00e0 h\u00e0ng d\u01b0\u1edbi, chi\u1ec3u theo c\u00e1ch k\u1ebft h\u1ee3p v\u1ecb tr\u00ed t\u1eeb tr\u00e1i qua ph\u1ea3i m\u00e0 t\u1ed5ng h\u1ee3p ra s\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1. H\u00e0ng tr\u00ean \u0111\u01b0\u1ee3c 49, 92, 24, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a ch\u00fang l\u00e0 11441. H\u00e0ng d\u01b0\u1edbi \u0111\u01b0\u1ee3c ba s\u1ed1 l\u00e0 81, 16, 68, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng c\u0169ng l\u00e0 11441.<\/p>\n

49^2+92^2+24^2=11441<\/p>\n

81^2+16^2+68^2=11441<\/p>\n

L\u1ea5y c\u1ed9t tr\u00e1i v\u00e0 c\u1ed9t ph\u1ea3i, chi\u1ec3u theo c\u00e1ch t\u1ed5 h\u1ee3p t\u01b0\u01a1ng t\u1ef1 nh\u01b0 tr\u00ean. C\u1ed9t tr\u00e1i \u0111\u01b0\u1ee3c 43, 38, 84, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 10349, c\u1ed9t ph\u1ea3i \u0111\u01b0\u1ee3c 27, 76, 62, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 10349.<\/p>\n

43^2+38^2+84^2=10349<\/p>\n

27^2+76^2+62^2=10349<\/p>\n

L\u1ea5y h\u00e0ng tr\u00ean v\u00e0 h\u00e0ng d\u01b0\u1edbi, chi\u1ec3u theo c\u00e1ch t\u1ed5 h\u1ee3p t\u1eeb tr\u00e1i sang ph\u1ea3i m\u00e0 t\u1ed5 h\u1ee3p th\u00e0nh s\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1. H\u00e0ng tr\u00ean \u0111\u01b0\u1ee3c 492, 924, 249. T\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 1157841<\/span>. H\u00e0ng d\u01b0\u1edbi \u0111\u01b0\u1ee3c 816, 168, 681, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 1157841<\/span>.<\/p>\n

492^2+924^2+249^2=1157841<\/span><\/p>\n

816^2+168^2+681^2=1157841<\/span><\/p>\n

L\u1ea5y c\u1ed9t tr\u00e1i v\u00e0 c\u1ed9t ph\u1ea3i, chi\u1ec3u theo c\u00e1ch t\u1ed5 h\u1ee3p t\u1eeb tr\u00ean xu\u1ed1ng d\u01b0\u1edbi m\u00e0 t\u1ed5 h\u1ee3p th\u00e0nh s\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1, c\u1ed9t tr\u00e1i \u0111\u01b0\u1ee3c 438, 384, 843, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 1049949<\/span>. C\u1ed9t ph\u1ea3i \u0111\u01b0\u1ee3c 276, 762, 627, t\u1ed5ng b\u00ecnh ph\u01b0\u01a1ng l\u00e0 1049949<\/span>.<\/p>\n

438^2+384^2+843^2=1049949<\/span><\/p>\n

276^2+762^2+627^2=1049949<\/span><\/p>\n

N\u1ebfu l\u1ea5y s\u1ed1 c\u00f3 b\u1ed1n ch\u1eef s\u1ed1, th\u00ec c\u0169ng ra \u0111\u01b0\u1ee3c quy lu\u1eadt t\u01b0\u01a1ng t\u1ef1.<\/p>\n

<\/span>Quy lu\u1eadt th\u1ee9 t\u01b0:<\/b><\/span><\/p>\n

\u1ede tr\u00ean n\u00f3i v\u1ec1 c\u00e1c c\u00e1ch t\u00ednh b\u00ecnh ph\u01b0\u01a1ng, v\u00e0 kh\u00f4ng d\u00f9ng \u0111\u1ebfn h\u00e0ng gi\u1eefa v\u00e0 c\u1ed9t gi\u1eefa, n\u1ebfu d\u00f9ng \u0111\u1ec3 t\u00ednh th\u00ec c\u0169ng c\u00f3 nh\u1eefng quy lu\u1eadt r\u1ea5t th\u00fa v\u1ecb.<\/p>\n

L\u1ea5y h\u00e0ng tr\u00ean v\u00e0 h\u00e0ng gi\u1eefa, t\u1ed5 h\u1ee3p l\u1ea7n l\u01b0\u1ee3t th\u00e0nh c\u00e1c s\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1, th\u00ec \u0111\u01b0\u1ee3c 43, 95, 27; l\u1ea5y h\u00e0ng d\u01b0\u1edbi v\u00e0 h\u00e0ng gi\u1eefa, t\u1ed5 h\u1ee3p l\u1ea7n l\u01b0\u1ee3t th\u00e0nh c\u00e1c s\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1, th\u00ec \u0111\u01b0\u1ee3c 83, 15, 67.<\/p>\n

43^2+95^2+27^2=11603<\/p>\n

83^2+15^2+67^2=11603<\/p>\n

L\u1ea5y c\u1ed9t tr\u00e1i v\u00e0 c\u1ed9t gi\u1eefa, chi\u1ec3u theo c\u00e1ch t\u1ed5 h\u1ee3p l\u1ea7n l\u01b0\u1ee3t \u0111\u1ec3 h\u00ecnh th\u00e0nh c\u00e1c s\u1ed1 c\u00f3 hai ch\u1eef s\u1ed1 th\u00ec \u0111\u01b0\u1ee3c 49, 35, 81. L\u1ea5y c\u1ed9t ph\u1ea3i, c\u1ed9t gi\u1eefa, t\u1ed5 h\u1ee3p \u0111\u01b0\u1ee3c c\u00e1c s\u1ed1 29, 75, 61.<\/p>\n

49^2+35^2+81^2=10187<\/p>\n

29^2+75^2+61^2=10181<\/p>\n

<\/span>Quy lu\u1eadt th\u1ee9 n\u0103m:<\/b><\/span><\/p>\n

N\u1ebfu d\u00f9ng h\u1ebft c\u00e1c s\u1ed1 c\u1ee7a c\u00e1c h\u00e0ng c\u00e1c c\u1ed9t, c\u0169ng \u0111\u01b0\u1ee3c m\u1ed9t quy lu\u1eadt k\u1ef3 di\u1ec7u:<\/p>\n

L\u1ea5y ba h\u00e0ng, theo th\u1ee9 t\u1ef1 xu\u00f4i v\u00e0 ng\u01b0\u1ee3c m\u00e0 t\u1ed5 h\u1ee3p th\u00e0nh c\u00e1c s\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1:<\/p>\n

492^2+357^2+816^2=1035369<\/span><\/p>\n

294^2+753^2+618^2=1035369<\/span><\/p>\n

L\u1ea5y ba c\u1ed9t, c\u0169ng theo th\u1ee9 t\u1ef1 xu\u00f4i ng\u01b0\u1ee3c m\u00e0 t\u1ed5ng h\u1ee3p th\u00e0nh c\u00e1c s\u1ed1 c\u00f3 ba ch\u1eef s\u1ed1:<\/p>\n

438^2+951^2+276^2=1172421<\/span><\/p>\n

834^2+159^2+672^2=1172421<\/span><\/p>\n

\u1ede \u0111\u00e2y ch\u00fang t\u00f4i ch\u1ec9 \u0111\u01b0a ra n\u0103m quy lu\u1eadt, ch\u1ec9 l\u00e0 ph\u1ea7n n\u00f4ng nh\u1ea5t c\u1ee7a L\u1ea1c th\u01b0, nh\u1eefng \u0111i\u1ec1u n\u00e0y ch\u1ec9 thu\u1ea7n t\u00fay l\u00e0 t\u00ednh to\u00e1n ch\u1eef s\u1ed1. Suy ngh\u0129 c\u1ea9n th\u1eadn m\u1ed9t ch\u00fat, ch\u00fang ta nh\u1ea5t \u0111\u1ecbnh s\u1ebd c\u1ea3m \u0111\u1ed9ng s\u00e2u s\u1eafc \u0111\u1ed1i v\u1edbi L\u1ea1c th\u01b0. Bi\u1ec3u \u0111\u1ed3 s\u1ed1 \u0111\u01a1n gi\u1ea3n nh\u01b0 v\u1eady m\u00e0 l\u1ea1i c\u00f3 th\u1ec3 \u1ea9n t\u00e0ng nhi\u1ec1u quy lu\u1eadt \u0111\u1ebfn th\u1ebf.<\/p>\n

Trong con m\u1eaft c\u1ee7a ng\u01b0\u1eddi hi\u1ec7n \u0111\u1ea1i, L\u1ea1c th\u01b0 r\u1ea5t \u0111\u01a1n gi\u1ea3n, m\u1ed9t \u0111\u1ee9a tr\u1ebb con \u1ea5u tr\u0129 c\u0169ng c\u00f3 th\u1ec3 t\u00ednh to\u00e1n. \u0110a s\u1ed1 ng\u01b0\u1eddi tr\u01b0\u1edfng th\u00e0nh kh\u00f4ng c\u00f3 h\u1ee9ng th\u00fa g\u00ec v\u1edbi L\u1ea1c th\u01b0. Nh\u01b0ng v\u00e0o th\u1eddi c\u1ed5 \u0111\u1ea1i, n\u01a1i Trung Qu\u1ed1c \u1ea5y v\u1eabn lu\u00f4n l\u00e0 c\u00f3 nh\u1eefng ng\u01b0\u1eddi tr\u00ed hu\u1ec7 cao nh\u1ea5t \u0111i nghi\u00ean c\u1ee9u s\u1ef1 th\u00e2m s\u00e2u huy\u1ec1n b\u00ed c\u1ee7a L\u1ea1c th\u01b0.<\/p>\n

Trong m\u1eaft c\u1ee7a c\u1ed5 nh\u00e2n, L\u1ea1c th\u01b0 l\u00e0 \u0111\u1ed3 h\u00ecnh sao th\u1eddi th\u01b0\u1ee3ng c\u1ed5, c\u00f3 \u1ea3nh h\u01b0\u1edfng huy\u1ec1n di\u1ec7u th\u00e2m s\u00e2u \u0111\u1ed1i v\u1edbi thi\u00ean v\u0103n \u0111\u1ecba l\u00fd. L\u1ea1c th\u01b0 l\u00e0 v\u0103n h\u00f3a ti\u1ec1n s\u1eed, bi\u1ec3u \u0111\u1ea1t nh\u1eadn th\u1ee9c c\u1ee7a con ng\u01b0\u1eddi th\u1eddi v\u0103n minh ti\u1ec1n s\u1eed \u0111\u1ed1i v\u1edbi quy lu\u1eadt v\u1eadn h\u00e0nh c\u1ee7a h\u1ec7 Ng\u00e2n H\u00e0. V\u0103n h\u00f3a thu\u1eadt s\u1ed1 qua c\u00e1c th\u1eddi \u0111\u1ea1i, kh\u00f4ng c\u00e1i n\u00e0o l\u00e0 kh\u00f4ng v\u1eadn d\u1ee5ng s\u1ef1 th\u00e2m s\u00e2u huy\u1ec1n di\u1ec7u c\u1ee7a L\u1ea1c th\u01b0.<\/p>\n

D\u1ecbch t\u1eeb: https:\/\/www.zhengjian.org\/node\/55397<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

[ChanhKien.org] S\u1ef1 s\u1eafp x\u1ebfp c\u1ee7a c\u00e1c ch\u1eef s\u1ed1 tr\u00ean L\u1ea1c th\u01b0, nh\u00ecn th\u00ec th\u1ea5y r\u1ea5t \u0111\u01a1n gi\u1ea3n, ch\u1ec9 c\u00f3 1, 2, 3, 4, 5, 6, 7, 8, 9, ch\u1ec9 c\u00f3 9 ch\u1eef s\u1ed1 \u0111\u00f3. 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