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

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Construct a logarithmic spiral using golden ratio triangles with isosceles side of length 3 units

 

Solution

 

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}.ba​=21+5​​.

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

Please describe the construction steps in the solution of the question.

 

 

 

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