Question

explain about the self generating golden triangle

Answer 1



A golden triangle. The ratio a:b is equivalent to the golden ratio φ.



Golden gnomon.

A golden triangle, also known as the sublime triangle,[1]is an isosceles triangle in which the duplicated side is in the golden ratio to the distinct side:

{\displaystyle {a \over b}=\varphi ={1+{\sqrt {5}} \over 2}.}

Golden triangles are found in the nets of several stellations of dodecahedrons and icosahedrons.

Also, it is the shape of the triangles found in the points of pentagrams. The vertex angle is equal to

{\displaystyle \theta =\cos ^{-1}\left({\varphi \over 2}\right)={\pi \over 5}=36^{\circ }.}

Since the angles of a triangle sum to 180°, base angles are therefore 72° each.[1] The golden triangle can also be found in a decagon, or a ten-sided polygon, by connecting any two adjacent vertices to the center. This will form a golden triangle. This is because: 180(10-2)/10=144 degrees is the interior angle and bisecting it through the vertex to the center, 144/2=72.[1]


The golden triangle is also uniquely identified as the only triangle to have its three angles in 2:2:1 proportions.

Answer 2

A golden triangle have their equal sides matching each other in length are called as a golden triangle.
This triangle also called isosceles triangle because their property are similar to each other.