Similar Triangles, Another Trace of the Golden Ratio

Subject Areas : Statistics

A.A. Rezaei ¹ , M. Eshraghi-Naeini ²

1 - Department of Mathematics, Kashan University, Kashan, Iran
2 - Department of Mathematics, Kashan University, Kashan, Iran

Received: 2017-03-28 Accepted : 2017-05-26 Published : 2017-02-01

Keywords: مثلث‌های متشابه‏, نسبت تشابه‏, نسبت طلایی‏, هندسه‌ی اقلیدسی,

Abstract :

In this paper we investigate similar triangles which are not congruent but have two pair congruent sides. We show that greatest lower bound of values for similarity ratio of such triangles is golden ratio. For right triangles, we prove that the supremum of values for similarity ratio is the square root of the golden ratio.