수학동아 - 폴리매스

함께 풀고 싶은 문제

나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.

[문장제 문제&개념응용] 1+1=1?

백곰 2021.05.10 17:45 조회 455

문제 푼 사람 2명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

유튜버 로지컬의 1+1=1을 증명하는 영상을 보고이 영상이 틀렸음을 증명하여보자.

(힌트 : 수2에서 배운 극한을 사용하여 주어진 과정을 무한히 반복하였을 때의 길이를 계산하자.)

이전글 피타고라스 정리를 증명해보자

다음글 피타고라스 수

이 문제 어떠셨나요?

글쎄요

어려워요

문제 찜하기 목록보기

댓글 작성하기

해결

도전

시그마가싫어요 Lv.9 2021.05.10 23:43 비밀댓글

비밀 댓글이 등록 되었습니다.

댓글 작성하기 댓글수0
해결

도전

PF＿ Lv.8 2021.05.11 01:11 비밀댓글

비밀 댓글이 등록 되었습니다.

댓글 작성하기 댓글수0
수학싫은데좋아요 Lv.5 2021.05.12 01:23 비밀댓글

비밀 댓글이 등록 되었습니다.

댓글 작성하기 댓글수1
- 수학싫은데좋아요 Lv.5 2021.05.12 01:23
  
  유튜브에 반박글이 올라와있던데요?
  
  좋아요0
백곰 Lv.2 2021.05.12 18:03

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/f7a072d257ff6a0650968a4957c34809.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_get_contents(http://latex.codecogs.com/gif.latex?L%28x%29%20%3D%20%5Cfrac%7B2%5Ex%7D%7B2%5E%7Bx-1%7D%7D): Failed to open stream: No route to host

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_get_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/f7a072d257ff6a0650968a4957c34809.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/f7a072d257ff6a0650968a4957c34809.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: is_dir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 201

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 201
Function: is_dir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: mkdir(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 202

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 202
Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_exists(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/ffd5e890ead190e1c57bfdf752a63994.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 212

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 212
Function: file_exists

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_get_contents(http://latex.codecogs.com/gif.latex?%5Clim_%7Bx%5Crightarrow%20%5Cinfty%20%7D%5Cfrac%7B2%5E%7Bx%7D%7D%7B2%5E%7Bx-1%7D%7D%20%3D%202): Failed to open stream: No route to host

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_get_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(): open_basedir restriction in effect. File(/DATA/upload/polymath/latex/ffd5e890ead190e1c57bfdf752a63994.gif) is not within the allowed path(s): (/volume1/web/PhpstormProjects/www_polymath_co_kr:/volume1/web:/tmp:/var/tmp:/var/services/tmp:/var/services/web:/volume1/@tmp)

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: file_put_contents(/DATA/upload/polymath/latex/ffd5e890ead190e1c57bfdf752a63994.gif): Failed to open stream: Operation not permitted

Filename: libraries/Common.php

Line Number: 213

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 213
Function: file_put_contents

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 236
Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view_comment_list.php
Line: 90
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/view.php
Line: 343
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 558
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

많은 분들이 풀이를 적어주셨군요! (성은이 망극하옵니다(?) 저언하아)

일단 제가 푼 풀이를 알려드릴게여

처음 길이를 L(1), 두번째 길이를 L(2), ....라 하면 $L(x) = \frac{2^x}{2^{x-1}}$ ,

이때 이를 무한번 반복하였을 때의 길이는 $\lim_{x\rightarrow \infty }\frac{2^{x}}{2^{x-1}} = 2$ 이므로 1+1=2다.

다들 정말 잘 푸셨네여 ㄷㄷㄷ... 이게 너튜브에 있었다니;; ~~내가 먼저 올렸어야 했는데~~

댓글 작성하기 좋아요0 댓글수2
- PF＿ Lv.8 2021.05.15 00:41
  
  근데 왜 정답확인을 안해주시냐고요
  
  @백곰
  
  좋아요0
- 시그마가싫어요 Lv.9 2021.06.11 08:54
  
  전 그냥 나무위키...
  
  좋아요0
도전

루돈 Lv.5 2021.07.11 20:21 비밀댓글

확인요청중

비밀 댓글이 등록 되었습니다.

댓글 작성하기 댓글수0
역시나야 Lv.1 2022.01.29 08:43

무한반복해도 하나의 선이 안될걷같은ㄷ....

댓글 작성하기 좋아요0 댓글수0