{"id":263,"date":"2018-08-05T16:08:54","date_gmt":"2018-08-05T14:08:54","guid":{"rendered":"https:\/\/blogs.futura-sciences.com\/lehning\/?p=263"},"modified":"2018-08-19T10:04:18","modified_gmt":"2018-08-19T08:04:18","slug":"des-plantes-et-des-maths","status":"publish","type":"post","link":"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/08\/05\/des-plantes-et-des-maths\/","title":{"rendered":"Des plantes et des maths"},"content":{"rendered":"

Les plantes ont un rapport \u00e9tonnant avec les math\u00e9matiques, hasard ou n\u00e9cessit\u00e9\u00a0? Je vous laisse juger.<\/span><\/span><\/p>\n

Suite de Fibonacci<\/h2>\n

L\u00e9onard de Pise, dit Fibonacci, a cr\u00e9\u00e9 sa suite comme un simple exercice d\u2019arithm\u00e9tique\u00a0:<\/span><\/span><\/p>\n

Un homme met un couple de lapins dans un lieu isol\u00e9 de tous les c\u00f4t\u00e9s par un mur. Combien de couples obtient-on en un an si chaque couple engendre tous les mois un nouveau couple \u00e0 compter du troisi\u00e8me mois de son existence\u00a0?<\/em>\u00a0<\/span><\/span><\/p>\n

Le calcul est simple, la suite donne\u00a0: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, etc. Chaque nombre est la somme des deux qui le pr\u00e9c\u00e8dent.<\/span><\/span>Cette r\u00e8gle a fascin\u00e9 au-del\u00e0 de l\u2019exercice. De plus, on la retrouve souvent dans la nature. En voici quelques exemples.<\/span><\/span><\/p>\n

\"\"
1, 2, 3, fleurs dans le d\u00e9sert du Namib (Namibie). \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a9 Herv\u00e9 Lehning<\/figcaption><\/figure>\n

Cette suite se retrouve plus souvent dans le d\u00e9compte des p\u00e9tales des fleurs. La seule fa\u00e7on de les compter est malheureusement de les effeuiller \u2026<\/span><\/span><\/p>\n

\"\"
Saurez-vous trouver le nombre de Fibonacci derri\u00e8re ces p\u00e9tales de griffes de sorci\u00e8re (littoral du sud de la France) ? \u00a9 Herv\u00e9 Lehning<\/figcaption><\/figure>\n

La g\u00e9om\u00e9trie, des rosaces \u00e0 la sph\u00e8re<\/h2>\n

Apr\u00e8s l\u2019arithm\u00e9tique, nous trouvons la g\u00e9om\u00e9trie avec des rotations surprenantes et des d\u00e9veloppements en sph\u00e8re.<\/span><\/span><\/p>\n

\"\"
Rotation naturelle dans une plante succulente. La r\u00e8gle de formation des feuilles implique que celles-ci se d\u00e9duisent l\u2019une de l\u2019autre par rotation. Littoral du sud de la France. \u00a0 \u00a0 \u00a9 Herv\u00e9 Lehning<\/figcaption><\/figure>\n
\"\"
Cette plante sauvage des Alpes se d\u00e9veloppe naturellement en sph\u00e8re. Parc des \u00c9crins \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a9 Herv\u00e9 Lehning<\/figcaption><\/figure>\n

Intersection d’un cercle et d’une droite dans la toundra<\/h2>\n
\"\"
Cercle et droite sur une plante de la toundra. Groenland \u00a0 \u00a0\u00a0 \u00a9 Herv\u00e9 Lehning<\/figcaption><\/figure>\n

Cette plante de la toundra groenlandaise pr\u00e9sente deux formes g\u00e9om\u00e9triques simples\u00a0: un cercle et une droite. Le cercle est naturel. Il correspond au d\u00e9veloppement de la plante dans toutes les directions \u00e0 partir d\u2019une graine, mais pourquoi a-t-elle d\u00e9p\u00e9ri d\u2019un seul c\u00f4t\u00e9 d\u2019une droite\u00a0?<\/span><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Les plantes ont un rapport \u00e9tonnant avec les math\u00e9matiques, hasard ou n\u00e9cessit\u00e9\u00a0? Je vous laisse juger. Suite de Fibonacci L\u00e9onard de Pise, dit Fibonacci, a cr\u00e9\u00e9 sa suite comme un simple exercice d\u2019arithm\u00e9tique\u00a0: Un homme met un couple de lapins dans un lieu isol\u00e9 de tous les c\u00f4t\u00e9s par un mur. Combien de couples obtient-on … Continuer la lecture de Des plantes et des maths<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":272,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"categories":[67,29,11,13,4,10],"tags":[31,130,131],"class_list":["post-263","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ecologie","category-maths-2","category-nature","category-photographies","category-regard-sur-le-monde","category-voyages","tag-fibonacci","tag-fleur","tag-plante"],"yoast_head":"\nDes plantes et des maths, par Herv\u00e9 Lehning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.futura-sciences.com\/lehning\/2018\/08\/05\/des-plantes-et-des-maths\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Des plantes et des maths, par Herv\u00e9 Lehning\" \/>\n<meta property=\"og:description\" content=\"Les plantes ont un rapport \u00e9tonnant avec les math\u00e9matiques, hasard ou n\u00e9cessit\u00e9\u00a0? Je vous laisse juger. Suite de Fibonacci L\u00e9onard de Pise, dit Fibonacci, a cr\u00e9\u00e9 sa suite comme un simple exercice d\u2019arithm\u00e9tique\u00a0: Un homme met un couple de lapins dans un lieu isol\u00e9 de tous les c\u00f4t\u00e9s par un mur. 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