File:2 areas multiplied by 5 under similarities from golden tilings.svg

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Summary
[edit]Description2 areas multiplied by 5 under similarities from golden tilings.svg |
English:
A regular decagon with interlaced sides has its ten vertices on the sides of a convex regular pentagon:
Every tiling element of any shape is called golden triangle because of its length ratio of two sides, equal :
The triangular tilings of two or ten elements are constructed in the same way as the pentagonal tessellation. Any similar elements of tilings are congruent, and these tilings are contructed edge‑to‑edge: every boundary between two adjacent elements is a full edge of one and the other element. On the left, the two triangular tilings are similar to a smallest tiling element, because of their two 36° angles. So their largest length ratios of two sides equal On the right, 18 triangular elements labelled either from 1 to 11 or from 'a' to 'g', according to their shapes, fill one fifth ( Français : Un décagone régulier aux côtés entrelacés a ses dix sommets sur les côtés d’un pentagone régulier convexe :
Tout élément de pavage de n’importe quelle forme s’appelle un triangle d’or en raison d’un rapport des longueurs de deux côtés égal :
Les pavages triangulaires de deux ou dix éléments sont construits de la même façon que le pavage pentagonal. N’importe quels éléments de pavages qui sont semblables peuvent se superposer exactement : ils sont isométriques. Ces pavages sont construits bord à bord, chaque frontière entre deux éléments adjacents est un côté complet de l’un et l’autre élément. À gauche, les deux pavages triangulaires sont semblables aux plus petits éléments des pavages, à cause de leurs deux angles de 36°. Alors leurs plus grands rapports de longueurs de deux côtés valent |
Date | |
Source | Own work |
Author | Arthur Baelde |
SVG development InfoField | ![]() This /Baelde was created with a text editor. |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 15:29, 28 February 2023 | ![]() | 1,056 × 594 (11 KB) | Arthur Baelde (talk | contribs) | Some improvements, notably a split segment in yellow and pink |
16:05, 8 June 2022 | ![]() | 1,056 × 594 (11 KB) | Arthur Baelde (talk | contribs) | plus 17 names of points, useful for comments or geometric proofs, and other improvements | |
09:28, 6 January 2022 | ![]() | 1,280 × 720 (9 KB) | Arthur Baelde (talk | contribs) | in order to make darker the lines of tilings and more visible the star decagon | |
09:09, 10 October 2021 | ![]() | 1,280 × 720 (10 KB) | Arthur Baelde (talk | contribs) | Uploaded own work with UploadWizard |
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Height | 594 |