An equilateral triangle and several line segments. What fraction is purple?
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Solution
The purple fraction is 1/7.
Poem
The holy number
It could be 777
Straight across and right from heaven
Or maybe another one
But it could be a number
The golden ratio
That’s not even a 0
Known from Pythagoras and Euclide
The golden number in geometry
A number that’s holy
For thinkers, poets in each century
One reply on “The holy number”
ABC equilateral triangle with AB top horizontal side. D midpoint of AB. E midpoint of DC. F is point on AE and DF perpendicular to AE.
Triangle DFB = triangle ADF.
AD=1, DE=√3/2. Hence AE=√7/2
Triangle ADE = (1/2)*AD*DE = (1/2)*DF*AE giving DF=√3/√7
Hence AF=2/√7 from triangle ADF
Area of triangle ADF=(1/2)*AF*DF=√3/7
Area of triangle ABC=(1/2)*AD*DC=√3
Hence the proportion is (√3/7)/(√3)=1/7 or 0.142857