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As shown in the figure, there are two points on the line AB, m, N, am: MB = 4:11, n is the midpoint of am, and Mn = 1 to find the length of ab. a -- N -- m -- B Solve the equation, teach me. First the formula and the answer, then explain to me,
Because am: BM = 4:11 and N is the midpoint of am
So nm: BM = 2:11 and Mn = 1
So BM = 5.5 and am = 2nm = 2
So AB = am + MB = 5.5 + 2 = 7.5
Given that point m and point n are two golden section points of line AB, and ab = 1cm, then Mn ≈
(1×0.618×2)-1=0.236CM
If points m and N are the golden section points of line AB, then Mn is equal to
∵ the golden ratio is (√ 5-1) / 2
∴MB/AB=(√5-1)/2
AM/AB=(√5-1)/2
So NB = (1 - (√ 5-1) / 2) AB = (3 - √ 5) / 2Ab
MN=MB-NB=[(√5-1)/2-(3-√5)/2]AB=(√5-2)AB
The length of line AB is unknown, so the specific value can not be calculated, but the final result can be expressed by ab
It is known that m and N are the two golden section points of line ab. if AB = 2, then Mn is?
M. N is the two golden section points of line ab
AB=2
∴AM=﹙√5-1﹚／2×2=√5-1
BN=√5-1
∴MN=AM+BN-AB
=√5-1+√5-1-2
=2√5-4
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