1.3 Fibonacci Sequence

Question 1

It was invented by the Italian
Leonardo Pisano Bigollo (1180-1250), who is known in mathematical history by several names: Leonardo
of Pisa (Pisano means “from Pisa”) and Fibonacci (which means “son of Bonacci”).

Answer 1

The Fibonacci Sequence

Question 2

It starts by defining some initial values and defines the next term as a function of
the previous terms.

Answer 2

Recursive Definition

Question 3

Formally define a Fibonacci Sequence.

Answer 3

We start by defining
F1 = 1 and F2 = 1.

For n > 2, we define
Fn := Fn−1 + Fn−2

The sequence F1, F2, F3, … is then a Fibonacci Sequence

Question 4

What is the symbol for golden Ratio?

Answer 4

Edi 6 na sosyal

Question 5

Golden Ratio Fomula:

Answer 5

Golden Ratio

:= lim n→∞ Fn/Fn−1

Question 6

Golden Ratio =
(1 + √5)/2

which is approximately?

Answer 6

≈ 1:6180339887

Question 7

What is Binet Formula?

Answer 7

Fn = Gr^n - (bar of) Gr^n over √5

Question 8

Fibonacci Sequence Exists in nature, the examples are:

Answer 8

• Pinecones, Speed Heads, Vegetables and Fruit
• Flowers and Branches
• Honeybees
• The Human Body
• Geography, Weather and Galaxies
• Architecture.
• Arts