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[개념 기사] 무한 초콜릿 페러독스
느티나무 Math 2021.02.08 22:27

무한 초콜릿 패러독스

이번엔 수학 실험도 겸할 수 있는 재미있는 초콜릿 패러독스를 살펴보자. 이는 한때 인터넷을 돌며 네티즌을 뜨겁게 달구고 진실 여부로 머리를 싸매게 했던 문제다. 제목부터가 흥미로운 ‘무한히 초콜릿 먹는 법’입니다. 아래 그림을 따라 방법을 확인해 봅시다.

 

출처: pinterest

 

 

가로 다섯 칸, 세로 다섯 칸 판 초콜릿에서 시작한다. 먼저 대각선으로 자르고 잘린 조각의 윗부분을 세로로 자른다(❶). 그다음 잘린 왼쪽 조각을 한 번 더 가로로 자르고(❷) 오른쪽 조각과 왼쪽 조각의 자리를 바꾼다(❸). 남는 공간에 ❷번 과정에서 생긴 작은 조각을 붙인다(❹). 직사각형 모양을 완성하면 초콜릿 한 칸이 넘친다. 이 부분을 잘라 낸다(❺). 잘라 낸 한 칸을 먹는다. 다시 초콜릿을 세어 본다. 초콜릿은 여전히 가로 다섯 칸 세로 다섯 칸이다. 따라서 ❶~❺번 과정을 무한히 반복하면 계속 초콜릿 한 칸씩을 먹으면서 초콜릿을 보존할 수 있다.

 

질량과 부피가 주어진 물질을 아무리 잘라 내도 같은 상태로 보존된다는 것은 상식적으로 말이 안 된다. 그러나 그림에서는 물론이고 실제 초콜릿을 가지고 실험해 봐도 정말 칸수가 동일하다는 것을 확인할 수 있다. 초콜릿으로 식량난을 해결할 수 있는 시대가 온 걸까? 비결은 다음과 같다.

 

무한 초콜릿 문제는 기하학적 오류를 이용한 ‘패러독스 퍼즐’이다. 패러독스 퍼즐은 ‘잃어버린 사각형 퍼즐’이라고도 불리며, 사람의 눈으로 쉽게 알아차리기 힘든 기하학적 눈속임을 이용해 모순을 일으킨다. 초콜릿을 칼로 자르면 아무리 정교해도 경계면이 아주 매끄러울 수는 없는데, 이 때문에 사람들은 조각을 옮기고 붙이면서 발생한 틈새의 변화를 쉽게 눈치채지 못한다고 한다.

 

전 초콜릿을 좋아하는데.. 너무 좋네요^^

 

 

 

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