A golden ratio is (1+sqrt5)/2. It is the positive
solution of of the equation x^2-x-1 = 0.
A golden triangle
is a special isosceles triangle whose isosceles side and the base are in the ratio
(1+sqrt5)/2 : 1. Or (1+sqrt5):2.
The angles of the golden
triangles are 72 degree , 72 degree and 36 degree. Or the angles of a golden triangle
are in the ratio 2:2:1.
In a regular 10 sided regular
polygon, the the lines joining the centre and the ends of a side make the required
golden triagle.
We can construct the golden triangle very
easily.
We can our own unit AB., drawn on a
paper.
Take 2 units and 3 units as the side of a right
angle and its hypotenuse. Then the other side gives us the value of sqrt(3^2-2^2) =
sqrt5. So with our own unit , sqrt 5 units we can construct a special golden triangle
of 2 units base and each of isosceles sides with (sqrt5+1)
units.
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