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Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: model

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Function: get_footer

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

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[잡담] 피타고라스 정리를 증명하는 다른 한 가지 방법(지겨워 죽겠죠?)
Scubed 2021.09.02 06:11 조회 487
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

직각삼각형 ABC와 그 내접원을 그리면 다음과 같이 됩니다(각 C는 직각입니다)

여기서 피타고라스 정리를 증명하려면 (x+y)^{2}=(x+r)^{2}+(y+r)^{2}을 증명하면 됩니다.

전개하여 정리하면 2xy=2r(x+y)+2r^{2}, xy=r(x+y)+r^{2}임을 증명하면 됩니다.

함 해봅시다. 우선 직각삼각형의 넓이는 (밑변)*(높이)/2에서 

S=\frac{(x+r)(y+r)}{2}

그런데 내접원의 반지름을 이용하는 또 하나의 공식이 있지요. 바로 (둘레)*(내접원의 반지름)/2(이정도는 아시죠)입니다.

S=\frac{1}{2}r(x+r+y+r+x+y)=r(x+y+r)

위의 두 식을 같다 하고 정리하면

xy+r(x+y)+r^{2}=2r(x+y)+2r^{2}, r^{2}+r(x+y)=xy

증명되었네요...끝

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  •  
    Scubed Lv.7 2021.09.02 06:12

    직접 생각한 거긴 하나 누구나 생각할 수 있는 증명법입니다

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