DescriptionAn iterated direct similarity yields spirals.svg
English: Composed with itself repeatedly, similarityF of centerS enlarges the smallest regularpentagon into successive concentric pentagons, in manner that the outline of each one passes through all vertices of the previous pentagon, of which it is the image under F. If transformationF is iterated indefinitely, then A and K are the starting points of two infinite spirals. Similarity F is direct, its oriented angle equals + 18°, its ratio two times as written at the image bottom.
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A direct similarity F of center S, + 18° angle and ratio 2 × cos 54° transforms repeatedly a regular pentagon into successive concentric pentagons, and one of its vertices into those of a beginning of spiral, in red or in green.
Une similitude directe de centre S, d’angle + 18° et de rapport 2 × cos 54° transforme plusieurs fois de suite un pentagone régulier en une succession de pentagones concentriques, et l’un de ses sommets en ceux d’une spirale, en rouge ou en vert.