Th\u1ebf nh\u01b0ng b\u1ea1n c\u00f3 bi\u1ebft c\u00e1ch v\u1ebd ch\u00ednh x\u00e1c m\u1ed9t ng\u00f4i sao n\u0103m c\u00e1nh? D\u01b0\u1edbi \u0111\u00e2y ch\u00fang t\u00f4i xin gi\u1edbi thi\u1ec7u m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p v\u1ebd ng\u00f4i sao n\u0103m c\u00e1nh ch\u00ednh x\u00e1c.<\/p>\n\n\n\n
V\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n t\u00e2m O.<\/p>\n\n\n\n
V\u1ebd hai \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a v\u00f2ng tr\u00f2n AZ v\u00e0 XY vu\u00f4ng g\u00f3c v\u1edbi nhau.<\/p>\n\n\n\n
Ch\u1ecdn M l\u00e0 \u0111i\u1ec3m gi\u1eefa c\u1ee7a OY.<\/p>\n\n\n\n
L\u1ea5y M l\u00e0m t\u00e2m, MA l\u00e0m b\u00e1n k\u00ednh, v\u1ebd cung tr\u00f2n AN, cung tr\u00f2n c\u1eaft OX t\u1ea1i \u0111i\u1ec3m N.<\/p>\n\n\n\n
L\u1ea5y A l\u00e0m t\u00e2m, MA l\u00e0m b\u00e1n k\u00ednh c\u1eaft tr\u00ean v\u00f2ng tr\u00f2n c\u00e1c cung tr\u00f2n li\u00ean ti\u1ebfp b\u1eb1ng nhau: AB = BC = CD = DE = EA.<\/p>\n\n\n\n
N\u1ed1i li\u00ean ti\u1ebfp c\u00e1c \u0111\u1ec9nh AD, AC, EB, EC, BD, ta \u0111\u00e3 v\u1ebd xong ng\u00f4i sao n\u0103m c\u00e1nh.<\/p>\n\n\n\n
D\u01b0\u1edbi \u0111\u00e2y ta s\u1ebd ch\u1ee9ng minh t\u00ednh ch\u00ednh x\u00e1c c\u1ee7a c\u00e1ch v\u1ebd v\u1eeba tr\u00ecnh b\u00e0y. Cho v\u00f2ng tr\u00f2n c\u00f3 b\u00e1n k\u00ednh R. T\u1eeb c\u00e1ch v\u1ebd tr\u00ean \u0111\u00e2y ra th\u1ea5y:<\/p>\n\n\n\n
AN2 = AO2 + ON2 = AO2 + (AM – OM)2<\/p>\n\n\n\n
V\u00ec v\u1eady<\/p>\n\n\n\n
N\u1ebfu qu\u1ea3 h\u00ecnh ng\u00f4i sao v\u1eeba v\u1ebd l\u00e0 ch\u00ednh x\u00e1c th\u00ec n\u0103m \u0111\u1ec9nh c\u1ee7a ng\u00f4i sao ph\u1ea3i n\u1ed9i ti\u1ebfp trong v\u00f2ng tr\u00f2n b\u00e1n k\u00ednh R. N\u00f3i kh\u00e1c \u0111i, ta ph\u1ea3i ch\u1ee9ng minh AN ch\u00ednh b\u1eb1ng \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a ng\u0169 gi\u00e1c \u0111\u1ec1u n\u1ed9i ti\u1ebfp trong b\u00e1n k\u00ednh v\u00f2ng tr\u00f2n ngo\u1ea1i ti\u1ebfp c\u1ee7a ng\u00f4i sao n\u0103m c\u00e1nh.<\/p>\n\n\n\n
Theo c\u00e1c ki\u1ebfn th\u1ee9c \u0111\u00e3 h\u1ecdc \u1edf b\u1eadc trung h\u1ecdc, ta bi\u1ebft c\u1ea1nh c\u1ee7a h\u00ecnh th\u1eadp gi\u00e1c \u0111\u1ec1u n\u1ed9i ti\u1ebfp trong h\u00ecnh tr\u00f2n b\u00e1n k\u00ednh R s\u1ebd b\u1eb1ng a10 = 1\/2 (\u221a5 – 1)R a10 l\u00e0 \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a th\u1eadp gi\u00e1c \u0111\u1ec1u n\u1ed9i ti\u1ebfp trong v\u00f2ng tr\u00f2n b\u00e1n k\u00ednh R.<\/p>\n\n\n\n
D\u01b0\u1edbi \u0111\u00e2y ta s\u1ebd t\u00ednh c\u1ea1nh c\u1ee7a ng\u0169 gi\u00e1c \u0111\u1ec1u n\u1ed9i ti\u1ebfp trong v\u00f2ng tr\u00f2n b\u00e1n k\u00ednh R. Gi\u1ea3 s\u1eed DZ = ZC = a10 l\u00e0 c\u1ea1nh c\u1ee7a th\u1eadp gi\u00e1c \u0111\u1ec1u n\u1ed9i ti\u1ebfp c\u00f2n DC = a5 l\u00e0 c\u1ea1nh c\u1ee7a ng\u0169 gi\u00e1c \u0111\u1ec1u n\u1ed9i ti\u1ebfp.<\/p>\n\n\n\n
Tam gi\u00e1c c\u00e2n ODZ c\u00f3 di\u1ec7n t\u00edch<\/p>\n\n\n\n
R\u00f5 r\u00e0ng l\u00e0 AN = a5. V\u00ec v\u1eady ph\u01b0\u01a1ng ph\u00e1p ta v\u1ebd ng\u00f4i sao n\u0103m c\u00e1nh tr\u00ecnh b\u00e0y \u1edf tr\u00ean l\u00e0 ch\u00ednh x\u00e1c.<\/p>\n\n\n\n
Kh\u00f4ng ph\u1ea3i b\u1ea5t k\u00ec \u0111a gi\u00e1c \u0111\u1ec1u n\u00e0o n\u1ed9i ti\u1ebfp trong v\u00f2ng tr\u00f2n \u0111\u1ec1u c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c b\u1eb1ng th\u01b0\u1edbc v\u00e0 compa. C\u00e1c h\u00ecnh tam gi\u00e1c \u0111\u1ec1u, ng\u0169 gi\u00e1c \u0111\u1ec1u, th\u1eadp gi\u00e1c \u0111\u1ec1u c\u0169ng nh\u01b0 c\u00e1c \u0111a gi\u00e1c \u0111\u1ec1u c\u00f3 ngu\u1ed3n g\u1ed1c tr\u1ef1c ti\u1ebfp t\u1eeb ch\u00fang nh\u01b0 c\u00e1c h\u00ecnh c\u00f3 s\u1ed1 c\u1ea1nh 2n, 2n x 3, 2n x 5, 2n x 15 (n l\u00e0 s\u1ed1 d\u01b0\u01a1ng) l\u00e0 nh\u1eefng \u0111a gi\u00e1c \u0111\u1ec1u m\u00e0 t\u1eeb h\u01a1n 2000 n\u0103m v\u1ec1 tr\u01b0\u1edbc v\u00e0o th\u1eddi \u0111\u1ea1i \u01a0clit ng\u01b0\u1eddi ta \u0111\u00e3 bi\u1ebft. T\u1eeb \u0111\u00f3 r\u1ea5t nhi\u1ec1u n\u0103m sau ch\u01b0a h\u1ec1 c\u00f3 b\u01b0\u1edbc \u0111\u1ed9t ph\u00e1 n\u00e0o, m\u00e3i \u0111\u1ebfn th\u1ebf k\u1ec9 XVIII Gauss m\u1edbi l\u1ea7n \u0111\u1ea7u ti\u00ean t\u00ecm ra c\u00e1ch v\u1ebd \u0111a gi\u00e1c 17 c\u1ea1nh. C\u00f3 th\u1ec3 ph\u00e1n \u0111o\u00e1n: m\u1ed9t \u0111a gi\u00e1c \u0111\u1ec1u n c\u1ea1nh th\u00ec n = 2m. P1. P2\u2026P m\u1edbi c\u00f3 th\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c b\u1eb1ng th\u01b0\u1edbc v\u00e0 compa. Trong \u0111\u00f3<\/p>\n\n\n\n
P1, P2\u2026P l\u00e0 c\u00e1c s\u1ed1 22k+1, m l\u00e0 s\u1ed1 d\u01b0\u01a1ng b\u1ea5t k\u00ec ho\u1eb7c b\u1eb1ng 0. L\u1eddi d\u1ef1 \u0111o\u00e1n tr\u00ean \u0111\u00e2y do Gauss \u0111\u01b0a ra v\u00e0 \u0111\u00e3 c\u00f9ng ch\u1ee9ng minh v\u1edbi m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc kh\u00e1c.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: H\u00ecnh nhi\u1ec1u c\u1ea1nh.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
Th\u1ebf nh\u01b0ng b\u1ea1n c\u00f3 bi\u1ebft c\u00e1ch v\u1ebd ch\u00ednh x\u00e1c m\u1ed9t ng\u00f4i sao n\u0103m c\u00e1nh? D\u01b0\u1edbi \u0111\u00e2y ch\u00fang t\u00f4i xin gi\u1edbi thi\u1ec7u m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p v\u1ebd ng\u00f4i sao n\u0103m c\u00e1nh ch\u00ednh x\u00e1c. V\u1ebd m\u1ed9t v\u00f2ng tr\u00f2n t\u00e2m O. V\u1ebd hai \u0111\u01b0\u1eddng k\u00ednh c\u1ee7a v\u00f2ng tr\u00f2n AZ v\u00e0 XY vu\u00f4ng g\u00f3c v\u1edbi nhau. Ch\u1ecdn M l\u00e0 \u0111i\u1ec3m […]<\/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-7549","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\/7549","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=7549"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7549\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7549"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7549"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7549"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}