French
DeutschFile:A proportion to conceive square root of 5.svg
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Summary
| Description | English: An area ratio between similar figures equals the square of the ratio between corresponding lengths of such figures – length ratio called the ratio of this similarity –. The image shows a first right triangle, of which the perpendicular sides measure 1 and 2. All congruent to this small triangle, the elements of tessellation numbered from 1 to 4 form a triangular tessellation, similar to the largest tiling and the initial triangle, because of their equal angles. Two enlargements to scales of √4 = 2 or √5, because of their areas multiplied by 4 or 5. This result can be found again by writing the proportionality between side lengths. The Pythagorean theorem is another way to find this unique positive number of which the square is 1 2 + 2 2: square root of 5. Français : Le rapport des aires entre figures semblables est égal au carré du rapport entre les longueurs correspondantes de telles figures – rapport de longueurs appelé le rapport de la similitude –. L’image montre un premier triangle rectangle, dont les côtés perpendiculaires mesurent 1 et 2. Tous superposables à ce petit triangle, les éléments de pavage numérotés de 1 à 4 forment un pavage triangulaire, semblable au pavage le plus grand et au triangle initial, à cause de leurs angles égaux. Deux agrandissements à l’échelle √4 = 2 ou √5, à cause de leurs aires multipliées par 4 ou 5. On retrouve ce résultat en écrivant la proportionnalité entre les longueurs des côtés. Le théorème de Pythagore est un autre outil pour trouver le seul nombre positif dont le carré est 1 2 + 2 2 : racine carrée de 5. |
| Date | |
| Source | Own work |
| Author | Arthur Baelde |
| Other versions | Also with a Pythagorean tiling In history of science or in pedagogy, square root of 5 begins to exist in geometry |
| SVG development |  This /Baelde was created with a text editor. |
Licensing
Arthur Baelde, the copyright holder of this work, hereby publishes it under the following license:
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Attribution: Arthur Baelde
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:45, 15 March 2022 | | 608 × 576 (4 KB) | Arthur Baelde | In order to show similarities of ratios 2 and √5, now a dashed line divides the triangular tiling into similar parts, one of the two being 2 times as large as the other, and then some little things are improved |
| 15:59, 11 January 2022 |  | 600 × 600 (4 KB) | Arthur Baelde | Uploaded own work with UploadWizard |
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