# Maths and nature Comenius Why Maths

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The file was prepared as a part of the Comenius project Why Maths? by the polish studetns from Anna Vasa school in Golub-Dobrzy (Poland)

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• 1.Gimnazjum im. Anny Wazwny Golub-Dobrzy Poland

2. Probably most of us have never taken the time to examine very carefully the number or arrangement of petals on a flower. If we were to do so, we would find that the number of petals on a flower, that still has all of its petals intact and has not lost any, for many flowers is a Fibonacci number: 3. 3 petals: lily, iris 5 petals: buttercup, wild rose, larkspur, columbine (aquilegia) 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 4. There is also a link between Fibbonacci sequence and and a special number that ancient civilizations called the golden ratio. 5. Logarithmic Spiral of a common shell. The Fibonacci numbers increase at a ratio that is revealed in objects and spirals. The Chambered Nautilus (which was so special to my husband and I) if cut in half reveals a series of chambers. Each chamber increases in size as the mollusk grows. They also grow in a spiral shape. 6. This same spiral and ratio is present in a great many products of nature; the pinecone, the pineapple Look at the bottom of a pinecone. It has those same kinds of spirals. They dont go around and around in a circle they go out likefireworks. Look at the pictures above to see what that looks like. 7. Golden Spiral also appears in hurricanes, ram's horns, 8. sea-horse tails growing fern leaves 9. seed patterns of sunflowers All the sunflowers in the world show a number of spirals that are within the Fibonacci Sequence. 10. Look at the following images of a sunflower: By observing closely the seeds configuration you will see how appears a kind of spiral patterns. In the top left picture we have highlighted three of the spirals typologies that could be found on almost any sunflower. Well, if you look at one of the typologies, for example the one in green, and you go to the illustration above right you can check that there is a certain number of spirals like this, specifically 55 spirals. 11. We have more examples in the two upper panels, cyan and orange, they are also arranged following values that are within the sequence: 34 and 21 spirals. 12. A lot of people love honey made by tiny bees. These insects use so much mathematical strategy throughout their daily lives. Just their hives use angles, shape, tessellation and addition. Wasps and bees exhibit polygons in their nests. Hexagons create nests that require less material and work to build. It is an efficient way of partitioning that also saves energy. 13. Hexagonal cell requires minimum amount of wax for construction while it stores maximum amount of honey. Why hexagons? Not squares or triangles? Hexagons fit most closely together without any gaps, so they are an ideal shape to maximise the available space. 14. Fractals aren't just something we learn about in math class. They are also a gorgeous part of the natural world. Here are some of the most stunning examples of these repeating patterns. Romanesco broccoli is a particularly symmetrical fractal. 15. The fern is one of many flora that are fractal; its an especially good example. Each part is the roughly the same as the whole. When we break a leaf off of the original and it looks like the original break a leaf off of that leaf and that looks like the original also. 16. The delicate Queen Annes Lace, which is really just wild carrot, is a beautiful example of a floral fractal. Each blossom produces smaller iterative blooms. This particular image was shot from underneath to demonstrate the fractal nature of the plant. 17. The Giant's Causeway, located in Ireland, is an fascinating formation found in nature. It is a collection of hexagons tesselating the ground - even in 3D at some points. In nature we can see samples of tessellations. This phenomenon is really beautiful and incredible. Here you can see some examples : 18. Rock formation in "White Pocket", Vermillion Cliffs National Monument, 19. Veins in a leaf Dragonfly 20. Cracked dried mud 21. Links: http://www.scienzainrete.it/en/content/article/nature-numbers http://nutters.edublogs.org/maths-in-nature/ http://static.panoramio.com/photos/large/2776550.jpg