Andrei Moldavanov, Classical
right-angled triangles and the golden ratio,
Forum Geometricorum, 17
(2017) 433--437.
Abstract. In this article, we consider the family of
classical right-angle triangles in 2-dimensional
Euclidean space. We consider triangle with an arbitrary leg ratio k and show that at 
, where p = ±1, the area of all built-in triangles is linked to
each other by the golden ratio φ. Keeping , we address changes in above
triangles occurring at the planar similarity transformation, prove an invariancy of the area ratio between predecessor and
successor triangle and show that evolution curve is a logarithmic spiral.
Reason of such geometrical features is associated with the unique nature of φ
providing parity between the linear and non-linear properties of geometry
objects.
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