건축 Architecture

The radius of a sphere inscribed in a square pyramid

작성자 Uploader : cannon 작성일 Upload Date: 2022-06-16변경일 Update Date: 2022-06-16조회수 View : 138

The radius r of a sphere inscribed inside a square pyramid can be calculated as follows.

h is the height of the square pyramid and a is the side length of a square base.

The length b of the perpendicular bisector of the side triangle to the base is:

b = ((a/2)^2 + h^2)^(1/2)

According to the similarity ratio of a right triangle,

b : a/2 = h-r : r


b*r = a*h/2 - a*r/2

r is as follows.

(a + 2*b)*r = a*h

r = a*h / (a + 2*b)

= a*h / (a + 2*((a/2)^2 + h^2)^(1/2))

*** 참고문헌[References] ***

r = a*h / (a + 2*((a/2)^2 + h^2)^(1/2))
변수명 Variable 변수값 Value 변 수 설 명 Description of the variable

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