Presentation 6

1. Fibonacci numbers

• Work performed by:
Artem Mekhonin
Students of the ISP –
105
Supervisor:
V.O. Pryanichnikova

2. Leonardo of Pisa (Fibonacci)

• Homeland: Italy, the city
of Pisa.
Merit: Replaced Roman
numerals with convenient
Arabic numerals (0-9) in
Europe.
Nickname: "Fibonacci"
means "son of Bonacci".The
discovery of the series:
Described the sequence in
1202 in the "Book of the
Abacus".
The first task: I deduced

3. What are Fibonacci numbers?

• The Fibonacci sequence is a numerical sequence in which
the first two terms are 0 and 1 (or 1 and 1), and each
subsequent number is the sum of the previous two. The
mathematical formula is \(F_n = F_{n-1} + F_{n-2}\). The
first elements of the row: 0, 1, 1, 2, 3, 5, 8, 13, 21,
34, 55, 89...

4. The proportion of harmony

• The magic limit: If you
divide each Fibonacci number
by the previous one (\(5/3\),
\(8/5\), the result will
tend to a constant value of
1.618.
The Golden Ratio: This
number is called the letter
\(\phi\) (Phi) — the
proportion of the Golden
Ratio, discovered in ancient
Greece.Human perception:
Objects with proportions
close to 1:1,618
subconsciously appear to be

5. The Fibonacci Spiral

Construction: Consists of
squares with sides in the
form of numbers in a row
(1, 1, 2, 3, 5...). Shape:
A smooth arc through the
corners of the squares
forms a golden
spiral.Property: As the
spiral grows, its shape and
proportions remain
unchanged.

6. Manifestation in wildlife

• Flowers: The number
of petals is most
often equal to the
numbers of the row
(3, 5, 8,
21).Seeds: The
spirals in
sunflowers and
cones go strictly
in a row (for
example, 34 and
55).Scale:
Hurricanes and
entire galaxies
spiral in the same

7. Where does it apply today?

• IT field: A basic algorithm
for studying recursion and
data optimization.
Design: The golden ratio rule
is used when creating logos
(Apple) and websites.
Trading: "Fibonacci Levels"
help analyze stock and crypto
price charts.

8. Conclusion

• Harmony: The Fibonacci series proves
that nature is designed according to
strict laws.Economy: Proportions help
plants survive and catch light
efficiently.Conclusion: Mathematics
is not boring formulas, but the
living code of our universe.