FIBONACCI SEQUENCE - CIAG FIBONACCIEGO

FIBONACCISEQUENCE

CIAG FIBONACCIEGO

Fiona Ciechalska 3ma

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INDEX

WHAT IS IT?CO TO JEST?

EXAMPLE - POPULATIONPRZYKLAD - POPULACJA

EXAMPLE - MUSICPRZYKLAD - MUZYKA

HOW IT WORKS?JAK TO DZIALA?

EXAMPLE OF THE COUNTING PROCESSPRZYKLAD PROCESU LICZENIA

FUN FACTSCIEKAWOSTKI

SUMMARYPODSUMOWANIE

EXAMPLES -PASCALS TRIANGLE AND FLOWERS PRZYKLADY - TROJKAT PASKALA I KWIATY

WHAT IS THE FIBONACCI SEQUENCE?

CZYM JEST CIAG FIBONACCIEGO?

The Fibonacci sequence is a set of numbers that starts with a one or a zero, followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the preceding two numbers.

Ciąg Fibonacciego to zbiór liczb, który zaczyna się od jedynki lub zera, po których następuje jedynka, i opiera się na zasadzie, że każda liczba (zwana liczbą Fibonacciego) jest równa sumie dwóch poprzednich liczb.

INFO

HOW DOES IT WORK?

JAK TO DZIALA?

The Fibonacci Sequence is the series of numbers:

THEN...

the 3 is found by adding the two numbers before it (1+2),

0,1,1,2,3,5,8,13,21,34...

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The next number is found by adding up the two numbers before it

AND THEN...

the 5 is (2+3) and so on

the 2 is found by adding the two numbers before it (1+1),

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EXAMPLE OF A COUNTING PROCESSPRZYKLAD PROCESU LICZENIA

5+3=8

8+5=13

13+5=21

21+13=34

PASCAL'S TRIANG

The sum of the numbers on the red lines gives us the next numbers in the Fibonacci sequence.

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FLOWERS

Since a petal is formed at the end of each spiral, this explains why the numbers of petals in different flowers are usually expressions of the Fibonacci sequence.

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POPULATION GRAPH

WYKRES - POPULACJA LUDZI NA SWIECIE Z UWZGLEDNIENIEM KOLEJNYCH LICZB CIAGU FIBONACCIEGO

MUSIC

From time to time in the music of all genres there is a characteristic, simple melodic line which comes from Pachelbel's D-Dur canon. The notation of a given piece is based on the Fibonacci sequence, which gives it a timeless harmony and rhythm.

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1.618

If we divide any, the next two terms of the Fibonacci sequence, eg 987: 610:89: 55, the ratio of these numbers will always be the same number, approximately 1.618. The larger the terms of the sequence we divide, the more precise the approximation of this number is obtained. This number is called the "golden number" and is denoted by the Greek letter φ (pronounced "fi").

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HUMAN BODY AND THE FIBONACCI SEQUENCE

The Fibonacci sequence numbers closest to the human body are 1.2 and 5. We have two arms and legs, five senses, three head protrusions (two ears and nose), three head openings (two eyes and a mouth), and single organs. The golden ratio and the number of phi can also be found in the proportions of our body. Proof? For example, consider the ratio of a person's height to the distance from the feet to the navel, which is fi (1.618).

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SUMMARY;PODSUMOWANIE

As we have seen, the Fibonacci sequence accompanies us in our everyday life, almost at every step. Whether in mathematics, nature, music, or even in our body, the Fibonacci sequence is visible. Jak moglismy zauwazyc, ciag Fibonacciego towarzyszy nam w zyciu codziennym, prawie ze na kazdym kroku. Czy to w matematyce, przyrodzie, muzyce, czy tez nawet w naszym ciele, ciag Fibonacciego jest widoczny.

THANK YOU!DZIEKUJE!