Answer to Question #241961 in Geometry for lene

Question

Construct a logarithmic spiral using golden ratio triangles with isosceles side of length 3 units

Answer 1

An isosceles triangle is a triangle whose two sides are of equal length.

A golden ratio triangle is an isosceles triangle in which the two longer sides are of equal length and the ratio of this length to that of the length of smaller side of the triangle is the golden ratio.

i.e., If a is the length of two equal longer sides of the triangle and b is the length of the smaller side of the triangle, then $\frac{a}{b} =\frac{ 1 + \sqrt{5}}{2}.$

Thus, a logarithmic spiral using golden ratio triangles with isosceles side of length 3 units is given below:

Step 1 Construct golden triangles (the biggest with isosceles side of 3) using a ruler and drafting

Step 2 Сonnect the vertices of the triangles by spline by hand and get a logarithmic spiral: