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현재 위치

The length of one side of a regular pentagon made by the diagonals of the regular pentagon

작성자 Uploader : narsha 작성일 Upload Date: 2019-09-30변경일 Update Date: 2022-06-17조회수 View : 87

As shown in the figure, the length x of one side of a regular pentagon composed of the diagonals of a regular pentagon with a side length a is calculated as follows.

The length of the diagonal AC is

AC = (1+5^(1/2))*a/2 = 1.618033989 = αa

If the length of AB is y, the following equation holds.

AC = 2y + x = αa

Since ΔABE and ΔACD are similar,

y : AC = x : CD

y : αa = x : a

y = αx and substituting this into the above equation,

2*αx + x = αa

x = αa / (2*α+1)

*** 참고문헌[References] ***

x = α*a / (2*α+1)

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변수명 Variable	변수값 Value	변 수 설 명 Description of the variable

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현재 위치

The length of one side of a regular pentagon made by the diagonals of the regular pentagon

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