File:An iterated direct similarity yields spirals.svg

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Captions

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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.

Summary[edit]

Description
English: Composed  with  itself  repeatedly,  similarity  F  of  center  S  enlarges the smallest regular pentagon 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  transformation  F  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.
Français : À suivre…
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Author Arthur Baelde
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Three  analogous  figures.
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