Some nice relations between right-angled triangles and the Golden Section

Golden right triangles and the golden quadrilateral

“…A golden right triangle of first type is a right triangle such that the shortest side is the golden section of the hypotenuse as defined in [1], [2]. If we consider a golden rectangle and one of its diagonals, we obtain a right triangle with the shortest side being the golden section of the other side; this right triangle will be named golden right triangle of second type.…”

103.40 Identifying golden and equilateral triangles that arise from the golden Arbelos

“…The archimedean Arbelos is one of the most fascinating geometric figures studied by many mathematicians who have explored its fine properties since ancient times. The so-called golden Arbelos was first studied by Bankoff [1] and then by other mathematicians ( [2,3,4,5,6,7,8]). The aim of this paper is to show some configurations of golden and equilateral triangles arising from the golden Arbelos.…”