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File:An iterated direct similarity yields spirals.svg

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English: Composed  with  itself  repeatedly,  similarity  of  center  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  is  iterated  indefinitely,   then    and    are the starting points of two  infinite spirals.  Similarity  is direct,  its oriented angle equals + 18°,  its ratio  two times  as written at the image bottom.
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Author Arthur Baelde
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Three  analogous  figures.
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Attribution: Arthur Baelde
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Captions

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.

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25 May 2022

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current09:05, 25 May 2022Thumbnail for version as of 09:05, 25 May 2022660 × 684 (5 KB)Arthur BaeldeUploaded own work with UploadWizard
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