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WonderScience fact

In the Fibonacci sequence, 1, 1, 2, 3, 5, 8, 13, 21…, each number is the sum of the two before it. It really does appear in plants: the spirals on a sunflower head or a pine cone usually come in two neighbouring Fibonacci numbers. But many popular examples, such as the nautilus shell, do not fit.

Liber Abaci, 1202

Science

The story behind the card

The sequence is named after Leonardo of Pisa, known as Fibonacci, who used it in his 1202 book Liber Abaci to solve a puzzle about breeding rabbits. Indian scholars had described it centuries earlier, while counting the rhythms possible in Sanskrit poetry. In plants the pattern comes from the way they grow: each new seed or leaf forms at about 137.5 degrees from the last, the so-called golden angle, which packs them without gaps, and the spirals that result come in Fibonacci numbers. Not every species follows it, however. The nautilus shell is a spiral, but not the golden spiral it is often said to be, and many claims about the proportions of human faces and bodies are stretched to fit.

Türkçe oku
Fibonacci dizisinde (1, 1, 2, 3, 5, 8, 13, 21…) her sayı kendinden önceki iki sayının toplamıdır. Bu dizi bitkilerde gerçekten karşımıza çıkar: Ayçiçeği tablasındaki ya da çam kozalağındaki sarmalları sayınca çoğunlukla ardışık iki Fibonacci sayısı bulunur. Ama nautilus kabuğu gibi pek çok popüler örnek bu kalıba uymaz.
Liber Abaci, 1202

Dizi, adını Fibonacci olarak bilinen Pisalı Leonardo'dan alır. Leonardo 1202'de yazdığı Liber Abaci (Hesap Kitabı) adlı eserinde, tavşanların çoğalmasıyla ilgili bir bulmacayı bu diziyle çözdü. Hint bilginleri diziyi yüzyıllar önce, Sanskrit şiirinde kurulabilecek ritimleri sayarken bulmuştu. Bitkilerde bu düzen büyüme biçiminden kaynaklanır: Her yeni tohum ya da yaprak, bir öncekine göre “altın açı” denen yaklaşık 137,5 derecelik bir açıyla oluşur. Bu açı tohumları boşluk bırakmadan yerleştirir ve ortaya çıkan sarmalların sayısı Fibonacci sayıları olur. Ancak her bitki türü bu kurala uymaz. Nautilus kabuğu da bir sarmaldır, ama sıkça söylendiği gibi altın oranlı bir sarmal değildir. İnsan yüzü ve bedeninin oranlarıyla ilgili pek çok iddia da kalıba uydurmak için zorlanır.

Sources and further reading

Background reading: Fibonacci sequence
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