M\u1ecdi ng\u01b0\u1eddi \u0111\u1ec1u bi\u1ebft c\u00e2u chuy\u1ec7n ng\u01b0\u1eddi m\u00f9 s\u1edd voi. Theo truy\u1ec1n thuy\u1ebft, c\u00f3 ba ng\u01b0\u1eddi m\u00f9 ch\u01b0a t\u1eebng th\u1ea5y m\u1ed9t con voi l\u1edbn, th\u1ebf nh\u01b0ng h\u1ecd l\u1ea1i mu\u1ed1n bi\u1ebft con voi l\u1edbn nh\u1ecf ra sao, do \u0111\u00f3 h\u1ecd ngh\u0129 c\u00e1ch \u0111i s\u1edd voi.<\/p>\n\n\n\n
M\u1ed9t ng\u01b0\u1eddi s\u1edd tr\u00fang \u0111u\u00f4i voi, anh ta cho r\u1eb1ng con voi gi\u1ed1ng m\u1ed9t con r\u1eafn. Ng\u01b0\u1eddi th\u1ee9 hai s\u1edd \u0111\u00fang tai voi, anh ta cho r\u1eb1ng con voi gi\u1ed1ng nh\u01b0 chi\u1ebfc qu\u1ea1t l\u1edbn. Ng\u01b0\u1eddi th\u1ee9 ba s\u1edd \u0111\u00fang ch\u00e2n voi, anh ta ngh\u0129 ngay \u0111\u1ebfn vi\u1ec7c con voi gi\u1ed1ng nh\u01b0 m\u1ed9t c\u00e2y c\u1ed9t \u0111\u00ecnh.<\/p>\n\n\n\n
C\u00e2u chuy\u1ec7n v\u1ec1 ng\u01b0\u1eddi m\u00f9 s\u1edd voi c\u1ea3nh b\u00e1o cho ch\u00fang ta v\u1ec1 vi\u1ec7c nh\u1eadn th\u1ee9c s\u1ef1 v\u1eadt kh\u00f4ng \u0111\u01b0\u1ee3c \u0111\u1ea1i kh\u00e1i m\u00e0 ph\u1ea3i nh\u00ecn t\u1eeb nhi\u1ec1u ph\u00eda. N\u1ebfu ch\u00fang ta d\u00f9ng con m\u1eaft h\u00ecnh h\u1ecdc tr\u1eebu t\u01b0\u1ee3ng \u0111\u1ec3 xem x\u00e9t, ta c\u00f3 th\u1ec3 gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1 kh\u00e1i ni\u1ec7m s\u1ed1 chi\u1ec1u. \u0110u\u00f4i voi ch\u1ec9 c\u00f3 th\u1ec3 ph\u00e2n bi\u1ec7t \u0111\u01b0\u1ee3c tr\u00ean d\u01b0\u1edbi l\u00e0 c\u00f3 m\u1ed9t chi\u1ec1u. Tai voi nh\u01b0 c\u00e1i qu\u1ea1t c\u00f3 chi\u1ec1u tr\u00ean d\u01b0\u1edbi, c\u00f3 chi\u1ec1u tr\u01b0\u1edbc sau n\u00ean c\u00f3 hai chi\u1ec1u. Ch\u00e2n voi c\u00f3 th\u1ec3 ph\u00e2n bi\u1ec7t tr\u00ean d\u01b0\u1edbi, tr\u01b0\u1edbc sau, tr\u00e1i ph\u1ea3i n\u00ean c\u00f3 ba chi\u1ec1u. Trong h\u00ecnh h\u1ecdc c\u00e1c lo\u1ea1i \u0111\u01b0\u1eddng nh\u01b0 \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng chu vi, ch\u00fang ch\u1ec9 c\u00f3 m\u1ed9t ph\u01b0\u01a1ng h\u01b0\u1edbng \u0111\u1ed9c l\u1eadp \u0111\u1ec1u c\u00f3 m\u1ed9t chi\u1ec1u. Ch\u1ec9 c\u00f3 th\u1ec3 h\u01b0\u1edbng t\u1edbi tr\u01b0\u1edbc v\u00e0 h\u01b0\u1edbng v\u1ec1 sau. \u0110\u01b0\u1eddng cong c\u00f3 hai chi\u1ec1u ph\u1ea3i c\u00f3 hai ph\u01b0\u01a1ng h\u01b0\u1edbng \u0111\u1ed9c l\u1eadp: ph\u01b0\u01a1ng h\u01b0\u1edbng chuy\u1ec3n \u0111\u1ed9ng tr\u01b0\u1edbc sau, h\u01b0\u1edbng tr\u00e1i v\u00e0 h\u01b0\u1edbng ph\u1ea3i l\u00e0 hai h\u01b0\u1edbng \u0111\u1ed9c l\u1eadp. C\u00f2n kh\u00f4ng gian m\u00e0 ng\u01b0\u1eddi ta sinh s\u1ed1ng c\u00f3 ba ph\u01b0\u01a1ng h\u01b0\u1edbng \u0111\u1ed9c l\u1eadp: tr\u01b0\u1edbc sau, tr\u00ean d\u01b0\u1edbi v\u00e0 tr\u00e1i ph\u1ea3i t\u1ee9c c\u00f3 ba chi\u1ec1u. V\u1eady ti\u00eau ch\u00ed \u0111\u1ec3 \u0111\u1eb7c tr\u01b0ng cho s\u1ed1 chi\u1ec1u th\u1ef1c t\u1ebf l\u00e0 ti\u00eau ch\u00ed \u0111\u1eb7c tr\u01b0ng cho s\u1ef1 v\u1eadt.<\/p>\n\n\n\n
Th\u1ebf \u0111\u1ed1i v\u1edbi \u0111\u01b0\u1eddng v\u1ebd hoa tuy\u1ebft s\u1ebd ra sao? V\u1ea5n \u0111\u1ec1 n\u00e0y \u0111\u01b0\u1ee3c nh\u00e0 to\u00e1n h\u1ecdc Thu\u1ef5 \u0110i\u1ec3n l\u00e0 Ahe \u0111\u00e3 \u0111\u01b0a v\u00e0o m\u00f4 h\u00ecnh c\u1ee7a gi\u1edbi t\u1ef1 nhi\u00ean \u0111\u1ec3 \u0111\u01b0a ra s\u1ed1 chi\u1ec1u c\u1ee7a \u0111\u01b0\u1eddng v\u1ebd hoa tuy\u1ebft. Qu\u00e1 tr\u00ecnh th\u1ef1c hi\u1ec7n nh\u01b0 sau:<\/p>\n\n\n\n
Gi\u1ea3 s\u1eed E0 l\u00e0 tam gi\u00e1c \u0111\u1ec1u c\u00f3 c\u1ea1nh b\u1eb1ng 1. Ta chia c\u1ea1nh E0 c\u1ee7a tam gi\u00e1c th\u00e0nh ba ph\u1ea7n \u0111\u1ec1u nhau. M\u1ed7i \u0111\u1ed9 d\u00e0i b\u1eb1ng 1\/3 c\u1ea1nh tam gi\u00e1c c\u0169 s\u1ebd l\u00e0 c\u1ea1nh c\u1ee7a tam gi\u00e1c \u0111\u1ec1u. Ta g\u1ecdi h\u00ecnh tam gi\u00e1c trung gian c\u00f3 c\u1ea1nh b\u1eb1ng l\u00e0 E1. Ta l\u1ea1i l\u00e0m nh\u01b0 \u0111\u00e3 th\u1ef1c hi\u1ec7n v\u1edbi h\u00ecnh E, l\u1ea1i chia c\u1ea1nh c\u1ee7a<\/p>\n\n\n\n
E1 th\u00e0nh 3 ph\u1ea7n \u0111\u1ec1u nhau, ta \u0111\u01b0\u1ee3c tam gi\u00e1c E2\u2026 v\u00e0 c\u1ee9 th\u1ebf ti\u1ebfp t\u1ee5c.<\/p>\n\n\n\n
Kh\u00e1i qu\u00e1t l\u1ea1i v\u1edbi tam gi\u00e1c Ek+1 s\u1ebd c\u00f3 c\u1ea1nh b\u1eb1ng 1\/3K+1 c\u1ea1nh c\u1ee7a tam gi\u00e1c EK. N\u1ebfu K c\u00e0ng ng\u00e0y c\u00e0ng l\u1edbn th\u00ec EK s\u1ebd ng\u00e0y c\u00e0ng ph\u1ee9c t\u1ea1p v\u00e0 s\u1ed1 r\u0103ng c\u1ee7a hoa tuy\u1ebft s\u1ebd tr\u1edf n\u00ean ng\u00e0y c\u00e0ng d\u00e0y \u0111\u1eb7c. S\u1ef1 th\u1ef1c th\u00ec c\u1ea5u t\u1ea1o c\u1ee7a hoa tuy\u1ebft s\u1ebd tr\u1edf n\u00ean v\u00f4 h\u1ea1n. Ch\u1ec9 c\u00f3 \u0111i\u1ec1u v\u0129nh vi\u1ec5n ng\u01b0\u1eddi ta s\u1ebd kh\u00f4ng \u0111\u1ea1t \u0111\u1ebfn tr\u1ea1ng th\u00e1i l\u00ed t\u01b0\u1edfng.<\/p>\n\n\n\n
Hi\u1ec3n nhi\u00ean \u201cc\u00e1i \u0111i\u1ec1u v\u0129nh vi\u1ec5n kh\u00f4ng th\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng cong l\u00ed t\u01b0\u1edfng\u201d l\u00e0 kh\u00f4ng th\u1ec3 b\u00e0n c\u00e3i. Th\u1ebf v\u1edbi m\u1ed9t \u0111\u01b0\u1eddng cong n\u00f3i chung c\u00f2n c\u00f3 \u0111i\u1ec1u g\u00ec \u0111\u1eb7c bi\u1ec7t n\u1eefa? C\u00f3. Tr\u01b0\u1edbc h\u1ebft \u0111\u00f3 l\u00e0 \u0111\u01b0\u1eddng cong kh\u00e9p k\u00edn, gi\u1edbi h\u1ea1n m\u1ed9t khu v\u1ef1c m\u1eb7t ph\u1eb3ng, c\u00f3 di\u1ec7n t\u00edch x\u00e1c \u0111\u1ecbnh. Th\u1ebf cu\u1ed1i c\u00f9ng \u0111\u01b0\u1eddng \u1ea5y c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng bao nhi\u00eau? X\u00e9t theo qu\u00e1 tr\u00ecnh c\u1ea5u t\u1ea1o ta c\u00f3 th\u1ec3 th\u1ea5y m\u1ed7i b\u01b0\u1edbc thao t\u00e1c \u0111\u1ec1u l\u00e0m t\u0103ng \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u01b0\u1eddng cong th\u00eam 1\/3 t\u1ee9c c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng 4\/3 \u0111\u1ed9 d\u00e0i ban \u0111\u1ea7u. Tu\u1ef3 theo s\u1ed1 b\u01b0\u1edbc thao t\u00e1c ti\u1ebfp t\u1ee5c s\u1ebd l\u00e0m cho \u0111\u1ed9 d\u00e0i c\u1ee7a \u0111\u01b0\u1eddng v\u1ebd ng\u00f4i sao l\u1edbn \u0111\u1ebfn v\u00f4 h\u1ea1n. Cu\u1ed1i c\u00f9ng n\u1ebfu ta thu h\u1eb9p t\u1ea7m nh\u00ecn, t\u1eadp trung \u00e1nh m\u1eaft v\u00e0o m\u1ed9t b\u1ed9 ph\u1eadn c\u1ee7a \u0111\u01b0\u1eddng v\u1ebd hoa tuy\u1ebft ta s\u1ebd ph\u00e1t hi\u1ec7n m\u1ed9t \u0111i\u1ec1u k\u00ec l\u1ea1 l\u00e0 \u0111\u01b0\u1eddng v\u1ebd ban \u0111\u1ea7u v\u00e0 ph\u1ea7n c\u1ee5c b\u1ed9 gi\u1ed1ng nhau. \u0110\u01b0\u1eddng v\u1ebd hoa tuy\u1ebft c\u00f3 nh\u1eefng \u0111i\u1ec3m \u0111\u1eb7c bi\u1ec7t nh\u01b0 v\u1eady ch\u1ee9ng t\u1ecf n\u00f3 kh\u00f4ng ph\u1ea3i l\u00e0 \u0111\u01b0\u1eddng b\u00ecnh th\u01b0\u1eddng. Th\u1ef1c t\u1ebf n\u00f3 l\u00e0 m\u1ed9t \u0111\u01b0\u1eddng cong chia nh\u1ecf h\u00ecnh (hay \u0111\u01b0\u1eddng ph\u00e2n h\u00ecnh, hay fractan – btv).<\/p>\n\n\n\n
\u0110\u1ed1i v\u1edbi m\u1ed9t \u0111\u01b0\u1eddng cong ph\u00e2n chia h\u00ecnh, ta kh\u00f4ng xem l\u00e0 \u0111\u01b0\u1eddng cong c\u00f3 m\u1ed9t chi\u1ec1u. V\u00ec v\u1edbi \u0111\u01b0\u1eddng cong v\u1ebd hoa tuy\u1ebft c\u00f3 th\u1ec3 n\u00f3i \u0111\u00f3 l\u00e0 \u0111\u01b0\u1eddng cong kh\u00f4ng c\u00f3 ph\u01b0\u01a1ng h\u01b0\u1edbng. Ph\u01b0\u01a1ng h\u01b0\u1edbng c\u1ee7a \u0111\u01b0\u1eddng cong tu\u1ef3 thu\u1ed9c c\u00e1ch c\u1ea5u t\u1ea1o m\u00e0 thay \u0111\u1ed5i v\u00f4 s\u1ed1 l\u1ea7n. Th\u1ebf s\u1ebd \u0111\u1ecbnh ngh\u0129a s\u1ed1 chi\u1ec1u c\u1ee7a \u0111\u01b0\u1eddng n\u00e0y nh\u01b0 th\u1ebf n\u00e0o? Ch\u00fang ta b\u1eaft \u0111\u1ea7u b\u1eb1ng vi\u1ec7c nh\u00ecn c\u1ee5c b\u1ed9 k\u1ebft h\u1ee3p v\u1edbi to\u00e0n th\u1ec3.<\/p>\n\n\n\n
N\u1ebfu ta t\u0103ng \u0111\u1ed9 d\u00e0i c\u1ea1nh c\u1ee7a m\u1ed9t h\u00ecnh vu\u00f4ng c\u00f3 c\u1ea1nh b\u1eb1ng 1 l\u00ean g\u1ea5p \u0111\u00f4i th\u00ec s\u1ebd c\u00f3 32 = 9 h\u00ecnh vu\u00f4ng c\u1ea1nh b\u1eb1ng 1. S\u1ed1 chi\u1ec1u c\u1ee7a h\u00ecnh s\u1ebd l\u00e0 D(Q) = ln 9\/ln 3 = 2. N\u1ebfu t\u0103ng \u0111\u1ed9 d\u00e0i c\u1ee7a kh\u1ed1i l\u1eadp ph\u01b0\u01a1ng c\u1ea1nh b\u1eb1ng 1 l\u00ean g\u1ea5p \u0111\u00f4i th\u00ec s\u1ebd c\u00f3 33 h\u00ecnh l\u1eadp ph\u01b0\u01a1ng c\u1ea1nh b\u1eb1ng 1 v\u00e0 s\u1ed1 chi\u1ec1u D(C) = ln 27\/ln 3 = 3. \u0110i\u1ec1u n\u00e0y ho\u00e0n to\u00e0n ph\u00f9 h\u1ee3p v\u1edbi quan ni\u1ec7m v\u1ec1 s\u1ed1 chi\u1ec1u \u0111\u1ec1 ra t\u1eeb ban \u0111\u1ea7u. \u0110\u1ed1i v\u1edbi \u0111\u01b0\u1eddng cong v\u1ebd hoa tuy\u1ebft ta c\u00f3 th\u1ec3 xem x\u00e9t theo c\u00e1ch t\u01b0\u01a1ng t\u1ef1, \u00e1p d\u1ee5ng cho \u0111\u01b0\u1eddng cong v\u1ebd hoa tuy\u1ebft c\u1ea5p K. K l\u00e0 do h\u00ecnh tam gi\u00e1c \u0111\u1ec1u c\u1ea1nh 1 \u0111\u01a1n v\u1ecb t\u1ea1o n\u00ean (nh\u01b0 h\u00ecnh 1). N\u1ebfu t\u0103ng \u0111\u1ed9 d\u00e0i c\u1ee7a tam gi\u00e1c l\u00ean g\u1ea5p \u0111\u00f4i nh\u01b0 \u1edf h\u00ecnh 2 th\u00ec \u0111\u01b0\u1eddng v\u1ebd hoa tuy\u1ebft s\u1ebd t\u1ea1o n\u00ean b\u1ed1n h\u00ecnh c\u1ea5p K v\u00e0 D(K) = ln 4\/ln 3 = 1,26. N\u1ebfu t\u0103ng \u0111\u1ed9 d\u00e0i c\u1ea1nh \u0111\u1ebfn g\u1ea5p ba s\u1ebd \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng v\u1ebd ng\u00f4i sao nh\u01b0 \u1edf h\u00ecnh 3. Nh\u01b0 v\u1eady \u0111\u01b0\u1eddng v\u1ebd ng\u00f4i sao theo ki\u1ec3u ph\u00e2n h\u00ecnh \u0111\u00e3 \u0111\u01b0\u1ee3c t\u1ea1o ra b\u1eb1ng c\u00e1ch nh\u01b0 tr\u00ecnh b\u00e0y.<\/p>\n\n\n\n
C\u00e1ch v\u1ebd ra ph\u01b0\u01a1ng th\u1ee9c ph\u00e2n chia h\u00ecnh c\u1ee7a con \u0111\u01b0\u1eddng v\u1ebd hoa tuy\u1ebft v\u1ea1ch r\u00f5 t\u00ednh k\u00ec l\u1ea1 c\u1ee7a \u0111\u01b0\u1eddng hoa tuy\u1ebft.<\/p>\n\n\n\n
T\u1eeb kho\u00e1: H\u00ecnh hoa tuy\u1ebft.<\/p>\n\n\n\n
<\/p>\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"
M\u1ecdi ng\u01b0\u1eddi \u0111\u1ec1u bi\u1ebft c\u00e2u chuy\u1ec7n ng\u01b0\u1eddi m\u00f9 s\u1edd voi. Theo truy\u1ec1n thuy\u1ebft, c\u00f3 ba ng\u01b0\u1eddi m\u00f9 ch\u01b0a t\u1eebng th\u1ea5y m\u1ed9t con voi l\u1edbn, th\u1ebf nh\u01b0ng h\u1ecd l\u1ea1i mu\u1ed1n bi\u1ebft con voi l\u1edbn nh\u1ecf ra sao, do \u0111\u00f3 h\u1ecd ngh\u0129 c\u00e1ch \u0111i s\u1edd voi. M\u1ed9t ng\u01b0\u1eddi s\u1edd tr\u00fang \u0111u\u00f4i voi, anh ta cho r\u1eb1ng con […]<\/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-7714","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\/7714","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=7714"}],"version-history":[{"count":0,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/posts\/7714\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/media?parent=7714"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/categories?post=7714"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.vietlearn.org\/kien-thuc\/wp-json\/wp\/v2\/tags?post=7714"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}