On many plants, the number of petals is a Fibonacci number:
buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals.
The links here are to various flower and plant catalogues: the Dutch Flowerweb's searchable index called Flowerbase.
The Helsinki Internet Directory for Botany has a wealth of information of all aspects of Botany and includes a gigantic section on Images with links to sites about plants all over the world. Try searching it to see where you can spot the golden section occurring and the Fibonacci numbers. The US Department of Agriculture's Plants Database containing over 1000 images, plant information and searchable database.
3 petals: lily, iris
Often lilies have 6 petals formed from two sets of 3. 5 petals: buttercup, wild rose, larkspur, columbine (aquilegia)
The humble buttercup has been bred into a multi-petalled form. 8 petals: delphiniums
13 petals: ragwort, corn marigold, cineraria, 21 petals: aster, black-eyed susan, chicory 34 petals: plantain, pyrethrum
55, 89 petals: michaelmas daisies, the asteraceae family
Some species are very precise about the number of petals they have - eg buttercups, but others have petals that are very near those above, with the average being a Fibonacci number.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ..More.. E
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