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victoria1 victoria1
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5 years ago
20.  The numerical equation from Qin Jiushao’s Shushu jiuzhang analyzed in Section 7.4.2 came from the geometrical problem of finding the area of a pointed field. If the sides and one diagonal are labelled as in Figure 7.22 (shown below)

-- Show that the area of the lower triangle is given by: B = (c/2) sqrt(b2 - (c/2)2) and that of the upper triangle by: A = (c/2) sqrt(a2 - (c/2)2) then the area x of the entire field is given by x = A + B.
-- Show that x satisfies the fourth-degree polynomial equation x4 + 2(A2+ B2)x2 - (A2 - B2)2 = 0. If a = 39, b = 20, and c = 30, show that this equation becomes the one solved by Qin in the text.
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Educator
5 years ago
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A month ago
thank you
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