# SECTION 1 AND 2 SOLUTIONS TO BIBLO - 99443

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## gurupatrick

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SECTION 1:

• Give several detailed examples of the appearances of Fibonacci numbers and the golden ratio in the plant world.

Fibonacci numbers and the golden ratio unlock a secret code that explains why so many plants appear as they do making the formation of plants and natural forms not as accidental as they may seem. From the number of rings and bumps on a tree trunk to the number of leaves and branches on a plant, the Fibonacci numbers try to explain.

It is important to note that Fibonacci numbers as they are expressed in plants take the form of spiral structures. The spiral structure within the plant construction is easily identified when photographs are embellished with superimposed lines.

Fibonacci numbers can often be found in the arrangement of leaves around a stem. This maximises for each leaf and can be found in closely packed leaves of succulent as well as cabbages, which have a similar ‘golden spiral’ formation to the rose- another Fibonacci preference.

Sunflowers form pretty patterns which are readily visible. In the sunflower case, the tell-tale sign is the number of different seed spiral on the sunflower surface. Sunflowers exhibit a near Fibonacci sequence and other mathematical pattern that compete and clash across the flower’s face. A study published by the Royal Society Open Science, reports that only one in five of the flowers had either a non-Fibonacci spiralling pattern or patterns were more complicated than has ever been reported. The sunflower head is constructed of 21 clockwise and 34 counter clockwise spirals.

The pinecone exhibits a similar construction relying on the consecutive Fibonacci Numbers, 8 and 13.

Some plants exhibit the Fibonacci sequence in their growth points, the places where tree branches form or split. One trunk grows until it produces a branch, resulting in two growth points. The main trunk then produces another branch, resulting in three growth points. Then the trunk and the first branch produce two more growth points, bringing the total to five. This pattern continues, following the Fibonacci numbers. Additionally, if you count t